d Ifta Journal 00

IFTAJOURNAL INTERNATIONAL FEDERATION OF TECHNICAL ANALYSTS, INC.

Journal for the Colleagues of the International Federation of Technical Analysts

A Not-For-Profit Professional Organization Incorporated in 1986

Editorial Michael Smyrk, MSTA

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Technical Analysis in Securitiy Investment Theory Hiroshi Okamoto

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Using Technical Analysis in Asset Allocation of Japanese and U.S. Stocks Hiroshi Okamoto

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Head-and-Shoulders Accuracies and How to Trade Them Serge Laedermann

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A Different Way To Forecast An Index’s Behavior Based On The Very Old Principles Of Support And Resistance Ulysse-Oliver Traub, CMT

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The Accuracy of Candlestick Analysis Using the German Stock Market Index (DAX) Corporate Address International Federation of Technical Analysts, Inc. Post Office Box 1347 New York, New York 10009 USA Website: www.ifta.org IFTA Journal Editor Michael Smyrk Town House, High Street Haslemere, Surrey GU27 2JY, England E-mail: [email protected] Tel: 44-1428-643310, Fax: 44-1428-641080 IFTA Chairperson Bruno Estier Lombard Odier & Cie 11, Rue de la Corraterie 1204 Geneva, Switzerland E-mail: [email protected] Tel: 41-22-709-2041, Fax 41-22-709-2911

Reza Darius Montassér, CMT

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Predicting the Exchange Rate: A Comparison of Econometric Models, Neural Networks and Trading Systems Giampaolo Gabbi, Ruggero Colombo, Riccardo Bramante, Maria Paola Viola, Paolo de Vito, Alberto Tumietto

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International Federation of Technical Analysts

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1999-2000 IFTA Board of Directors & Committee Chairs

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Editorial Michael Smyrk, MSTA Once again this edition of the IFTA Journal attempts to compress a wide field inside a narrow span. Technical Analysts operate in a number of disparate spheres, covering an enormous variety of financial markets; these may fluctuate wildly over the short term (Nasdaq stocks or Energy prices), move erratically over the longer term (“old economy” stocks or Government bonds), or trend gracefully for varying periods of time (the Euro and certain commodity markets come to mind). The methods of analysing these different markets may vary, the time-spans may differ, the purposes of the analysis may be diverse, but the rationale for using this particular approach remains constant – the belief that the present behaviour of prices reflects the current state of supply and demand for those goods in that market, and that the progress of price activity indicates the likely increase or decrease in future supply and demand – not, in this case, the physical supply and demand that will meet a need, but the urge to buy or sell at a particular price level that will produce future price movement. The range of markets and methods is, hopefully, reflected in the contents of this Journal. With fashions in particular stocks and sectors growing then fading at an ever-increasing rate, it seems sensible to present studies on Indices rather than on individual equities; we have articles covering the Swiss Market Index (SMI), the German market index (DAX), and Japanese and US market indices (the Nikkei and the Dow). There is work on Currencies and Exchange Rates, and a paper referring to the Stock, Bond, Currency and Commodity sectors. Methodology includes Support and Resistance, Chart Patterns (Head & Shoulders), Econometric Models, Neural Networks and Trading Systems, and a Japanese technique (Candlesticks), presented by a German analyst as well as an adaptation of a Western technique (Moving Averages) provided by a Japanese analyst. IFTA is fortunate in having access to a very wide spectrum of nationalities, as far as both markets and analysts is concerned. This should expand even further over time, as new countries join the International Federation – Egypt, Portugal and New Zealand are this year’s new entrants, and this typifies the global spread of interest both in the subject matter and in the creation of local societies to cater for its study and dissemination. Enquiry is evident from even more scattered corners of the earth, and the Editor of the next edition is likely to have an even wider choice of markets and methods. Another increasingly important feature will be the availability of Papers submitted for Stage III of the DITA (Diploma in International Technical Analysis) exam process. This 3-stage process, run by IFTA for the benefit of its international membership, culminates in a test of TA knowledge that must be fulfilled by the submission of a 3/5,000 word paper that a) must be original, b) must deal with at least two different international markets, c) must develop a reasoned and logical argument and lead to a sound conclusion supported by the tests, studies and analysis contained in the paper, d) should be of practical application, and e) should add to the body of knowledge in the discipline of international technical analysis. Only one paper is included in this edition of the Journal (by Mr Hiroshi Okamoto), but recent submissions demonstrate a stimulating variety of new work which deserves a wider audience. We open this edition with another offering from Japan, the NTAA “Analysis Tree.” Created originally to assist their students in studying for the DITA exams, the tree demonstrates the linkage between the various branches of Technical Analysis, and is being used by IFTA as a framework for the current work on a “Body of Knowl-

edge.” In this endeavour, local societies have been asked to provide information on a number of Technical Analysis fields (Northern Europe, for example, is working on “price,” Southern Europeans on “volume,” North America on “indicators”). Ultimately, templates will be developed, asking a series of questions (ie: What is the name of this indicator? Who developed it? What is the commonly accepted formula? What are its strengths? What are its weaknesses? Show examples of this indicator at work. List all known references in books, magazines and journals, etc, etc); some of these templates have already been published on the MTA web site (www.mta.org), and they will soon be available on the IFTA web site (www.ifta.org), access to which does not require a password. The Japanese Society will be providing input on their traditional forms of analysis; in this edition of the Journal, however, the NTAA is represented by a previous President of that Society, Hiroshi Okamoto, who puts forward an original approach to asset allocation using his own “net momentum” study. (It should be noted that charts and comments in all cases are not up to date, but the principles underlying each presentation should remain valid.) An increasing amount of academics are spending time on Technical Analysis these days, and a good deal of their work relates to traditional methods, including (frequently) the Head-and-Shoulders pattern on charts. Serge Laedermann’s article may give them – as well as active practitioners – some new ideas on what works and what does not, expressed for once in a non-empirical fashion. Ulysse-Oliver Traub also goes back to traditional theories, of Support and Resistance, in an approach that relates significantly to practical experience in the market-place. This is an important factor at present, as Universities and Colleges move into the teaching of Technical Analysis; the rules as laid down in text-books may sometimes not work, but very often there is a good reason for this which is clear to the experienced practitioner but perhaps is not evident to the academic researcher. Reza Montassér’s work on Candlesticks appears academic, but he too is a practitioner, technical analyst and market strategist. This type of study is not just useful to those analysing the DAX Index (as Montasser does), but can be transferred to other markets where similar studies might produce differing results. However, this last comment is based on a personal view – that different markets have their own particular characteristics – a view that is empirical but experience-based. The closing article is presented by a mixed team of academics and professionals, comparing modern and traditional methods; much research is being carried out along these lines, and it will not be surprising to see further reference to this type of work in future editions of the Journal. This edition owes much, once again, to the enthusiasm and expertise (not to mention the patience) of Ms Barbara Gomperts, who creates the look and feel of the package which is so important in getting people to actually open the page. Without her assistance, and of course that of the writers in the first place, we would all be the poorer. And as before, many thanks are due to the MTA (Market Technicians Association) for permission to reprint articles first produced in their own Journal. In future, other Societies’ journals may prove equally fertile hunting-grounds for the next IFTA Journal Editor. Michael Smyrk

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Technical Analysis in Securitiy Investment Theory

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I-A-α

Macro Analysis

I-A-β

Micro Analysis

I-A-γ

Arbitrage Trading

I-B-a-X

Market Psychology

I-B-a-(1)-①-α

Trend Analysis

I-B-a-(1)-①-β

Moving Average

Kondratieff Cycle Official Discount Rate Diffusion Index Dividend Dividend Discount Model Yield Spread Basis Historical Volatility Spread Blow-Off Selling Climax Oversold/Overbought Primary Trend Parallel Trend Channel Trend Reversal Moving Average Channel Cross-Over Golden Cross

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I-B-a-(1)-①-γ

MACD

I-B-a-(1)-①-δ

Momentum Analysis

I-B-a-(1)-①-ε

RSI

I-B-a-(1)-①-ζ

Elliott Wave

I-B-a-(1)-①-η

Dow Theory

I-B-a-(1)-≠ -α

Consolidation Pattern Analysis

I-B-a-(1)-≠ -β

Candlestick Analysis

I-B-a-(2)-α

Point & Figure

I-B-a-(2)-β

Kagi-Ashi Chart

I-B-a-(2)-γ

Neri-Ashi Chart

I-B-a-(2)-δ

Shin-Ne-Ashi Chart

I-B-b-α

Volume Analysis

I-B-b-β

Analysis of Margin Trading Balance

I-B-b-γ

Other Market Statistics Analysis

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Ramdom Walk Theory

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Portfolio Analysis

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Portfolio Performance Evaluation

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Money Management

ESMA MACD EWMA Momentum Indicator Momentum Oscillator Soner Momentum RSI Non Equilibrium Index Relative Momentum Grand Super Cycle Fibonacci Numbers Extension Dow Jones 30 Industrial Average Three-Wave Pattern Confirmation Theory of DJ Industrials by Transportation Index Head and Shoulders Ascending Triangle Double Bottom Bar Chart Candlestick Chart Quarterly Chart 3-Point Reversal Bullish Triangle Quarterly Chart 10% Kagi-Ashi Chart 10 Yen Kagi-Ashi Chart 5-Yen Method 10% Neri-Ashi Chart 10 Yen Neri-Ashi Chart 50 Yen Neri-Ashi Chart Shin-Ne 3-Bon Ashi Shin-Ne 10-Bon Ashi Trend Line Upside/Downside Volume OBV Arms’ Method Analysis of Buying Balance Analysis of Short Selling Analysis of Buy/Sell Ratio Advance/Decline Line Advance/Decline Ratio Analysis of New Highs and New Lows Semi-Strong Monte Carlo Method Chaos Analysis MPT CAPM Efficient Frontier Benchmark Relative Performance Indexation Pyramiding Martingale Method Maximum Draw Down

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Using Technical Analysis in Asset Allocation of Japanese and U.S. Stocks Hiroshi Okamoto HISTORICAL DEVELOPMENT OF JAPANESE AND U.S. STOCK MARKETS AND DEDUCING ORDER FROM THEIR MOVEMENTS

When I examined the Japanese and US stock markets since the end of the war through the Dow Jones Industrial Average and the Nikkei Stock Price Average, I found that clear cross cycles (inverted cycles) had been formed. Sometimes this didn’t happen, but such occasions were infrequent. However I could find only one example of both markets moving in the same direction where there was no cross cycle, in other words, the seven years from the beginning of 1983 to the end of 1989 within the 40-year period lasting from 1960 to 1999. This happened only once, and for seven years only. So perhaps the reason why the stock price trends of both markets mutually move in opposite directions is because the environment that surrounds both markets is itself becoming a cross cycle. This being the case, I am interested in why this has happened, as both have adopted capitalist-style market economies as national policy within the framework of a liberal social system. My paper will examine this area first of all. Graphs 1 and 2 show the DJIA and the Nikkei from 1960 to laate 1999. For analytical purposes, I have grouped the two international markets into four periods, as follows. ■

Phase 1 (Graph 1-I, Graph 2-I), 6-year period from early 1960-end 1965

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Phase 2 (Graph 1-II, Graph 2-II), 17-year period from early 1966-end 1982

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Phase 3 (Graph 1-III, Graph 2-III), 7-year period from early 1983-end 1989

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Phase 4 (Graph 1-IV, Graph 2-IV), 10-year period from early 1990-1999 (as at October 1999)

Phase 1: DJIA Up, Nikkei Down Phase 1 (Graphs 1-I and 2-I) is a typical cross-cycle phase. In this period, the DJIA rises and the Nikkei falls. The DJIA’s rise has been dubbed the “Golden Sixties,” reflecting the booming US economy which is highly important in the country’s postwar period. In contrast, the fall of the Nikkei was due to medium-term stagnation of the Japanese economy, referred to as the Securities Recession. At that time, I think the very fundamentals of the Japanese and US economies as seen over the medium-term had formed a cross-cycle. In Phase 1, the DJIA had reached $1,000 (in February 1966) while the Nikkei had penetrated ¥1,020 (in July 1965), as each trend had almost reached its end. I shall go into this again later, but the $1,000 and ¥1,000 comparison creates an immediate impression. Phase 2: DJIA level over long-term, Nikkei on long-term uptrend I shall now move on to Phase 2 (Graphs 1-II and 2-II). Although the DJIA briefly hit $1,000 at the beginning of 1966, after that it remained level overall for 17 years. Although I say remaining level, please look at this based on the intent of Graph 1, which is a logarithmic graph. If we look at the course of this level movement in detail, we can see mini-cycles occurring every four years. Behind these mini-cycles are inventory investment cycles and what may be described as election cycles (economic cycles based on the presidential elections). The decline of the mini cycles is at times steep, and in 1974 the DJIA dropped to $500 (a level half its $1,000 high). That was when US President Nixon and Japanese Prime Minister Tanaka were forced to resign almost simultaneously, leaving the stain of corruption on the pages of the political history of both countries. As I remember it, it was around this time that The Wall

Street Journal ran a rather shocking advertisement describing it as “The day Wall Street died.” The advertiser was a major US securities company. In the 17 years that the DJIA remained sluggish, the Nikkei followed an upward trend. When the DJIA fell to 500 in 1974, the Nikkei also fell at one stage because of the oil shock. However, such a decline is occasionally seen with an uptrend, and is a type of correction of an abnormal deviation from a long-term trend. It was not enough to cause concern about a turnaround to a downtrend. The long-term uptrend in the Nikkei was attributable to Japan’s high economic growth, growth that continued at what can be described as an “extremely” high level. In fact during this period, Japan’s GDP had several years of double-digit growth in real terms. Putting this in microeconomic terms demonstrates the continued strong earnings performance of Japanese companies. This led to a number of books by renowned American writers such as The Sun Also Rises and Japan as Number One, and this truly was a time when such topics were popular in the world’s financial markets. Phase 3: DJIA Up, Nikkei Also Up, the Only Period Since the End of the War when Japan and the US were in Harmony Phase 3 (Graphs 1-III, 2-III), when the Japanese and US stock markets were in harmony, is referred to as a boom, a quite rare period and the first since the end of the war. In this period, the DJIA at long last was able to break away from the 1,000 level, and pushed on upwards for the first time in many years. The return of the uptrend was due to the US economy surviving two oil shocks unscathed and then getting safely through the difficult situation brought on by the savings and loan financial crisis. The tempo of the uptrend was powerful enough to rival the “Golden Sixties,” with its length also coinciding with this period. The Black Monday decline in October 1987 was sharper than expected, but its scars had healed completely within two years when the DJIA posted a new record high in 1989. Looking back now, it can be seen that the real reason for the bullish trend on the Japanese and US stock markets in Phase 3 was the victory of the West in the Cold War, verified a little while later. In other words, this trend seems to have preceded the triumph of the free market economy. Phase 3 is also regarded as a boom for the Tokyo stock exchange. Yet the Tokyo market was strongly speculative, later being termed the “bubble market.” The bubble itself was also huge, ranking with the Dutch Tulip Mania of the 17th Century and the South Sea Bubble of the 18th Century British company of the same name, and also with the New York stock market which by 1929 had become hugely speculative. This bubble in the Tokyo market did not confine itself to stocks, but spread over a vast area covering every avenue of capital stock including real estate, paintings, jewelry, and even golf club memberships. It’s funny to think about it now but at the time, the total market value of land in the Kanto area comprising metropolitan Tokyo and its four surrounding prefectures was equivalent to that of the whole of the US. This was the extent of the fever that gripped the Japanese economy then. The Nikkei had finally reached the ¥10,000 level in 1984, but five years later was on the retreat from almost ¥40,000. Such speed could be seen in the New York market recently.

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IFTAJOURNAL Phase 4: DJIA Up, Nikkei Down In Phase 4 (Graphs 1-IV and 2-IV), the performance of Japanese and US stocks again returned to a cross cycle. Reflecting the firmness of the US economy, the DJIA has maintained an uptrend since 1990, and even picked up speed after 1996. In technical terms, it seems to be currently following an upcurving trend line (note the logarithmic scale in Graphs 1 and 2). Assuming an upcurving trend line, the New York market is likely to rise even further for a little while. US industry is improving its earnings structure by promoting restructuring among its older corporations while new venture capital organizations stream onto the market. The US economy in general is buoyant like never before, and I believe the thriving stock market is the cause of this. One minor area deserving attention is the fact that the country’s savings rate is extremely low overall (recently estimated at zero, or slightly negative), and the rise in stocks is encouraging consumption activity. In such circumstances, the immediate concern is that any kind of sharp decline in stocks will quickly cool down personal consumption, and the worsening economy will then lead to a fall in stock prices. Such a result could give rise to the spiral phenomenon of a further stock price decline causing even more damage to the economy. Compared to the 24-year continuation period of the Nikkei’s uptrend (Graphs 1-II+III and 2-II+III), the continuation period of the DJIA’s uptrend is only 17 years (Graphs 1-III+IV and 2-III+IV). This should allow scope for further improvement in the US economic situation and the DJIA. Fortunately, the situation at present is moving in the right direction. However, there is such a thing as anticipation of stock prices. The footsteps of inflation can slowly be heard, and from a long-term perspective, there are concerns over the New York market. In contrast, the Nikkei has been following a downtrend since 1990. Seen in detail, the downward pattern is a bilateral symmetry pattern of the letter N, with the first stage of the decline continuing through to August 1992 (¥14,309) and a recovery to June 1996 (¥22,666), which was then followed by the second stage of the decline to October 1998 (¥12,879). The market later rebounded as expected and had recovered 50% from its bottom as at July 1999, yet it dipped through to October, fluctuating erratically at a high level. The situation needs to be watched a little longer to determine if this recovery marks the end of the bubble’s collapse and will lead to a genuine rally. My interpretation here is an interim report for reference purposes. The post-bubble market has seen the correction of the Nikkei continue for 10 years now, with the correction itself being ¥26,036 (down 66.9% from its high). In actuality, however, the benefits of a number of economic stimulus packages amounting to more than ¥100 trillion are finally starting to become apparent. Japan’s real economic growth in the January-March quarter of 1999 was up 1.9% on the previous term, a sharp increase which brings the annual rate to 7.9%. The AprilJune quarter also produced positive growth, although at a reduced rate. The 0.5% rate projected for the year by EPA chief Sakaiya has been revised up, and there are growing indications that this is achievable. OECD figures announced in early November project Japan’s growth rate (real GDP) for this and next (calendar) year at a high 1.4% for both years. On the other hand, Japanese interest rates remain low, and the monetary authorities continue to push interest rates to zero in the short-term money market. The 50% rise in the Nikkei since early autumn last year seems to reflect a favorable response to this. Moreover, a second supplementary budget is being debated as an economic stimulation measure for the second half of the fiscal year, and if it proves beneficial, it seems quite likely to lead to genuine economic recovery. In stock terms as well, just like thirty years ago when the trends of the Japanese and US stock markets turned as they stood at $1,000 and ¥1,000, the stock price trend point of change at present may perhaps be $12,000 and ¥12,000.

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The Nikkei’s low to date is ¥12,879 (October 1998) and the DJIA’s high is 11,107 (May 1999), bringing a touch of reality to this numerical combination. No Change in Phases of Dollar-Denominated Nikkei Graph 3 shows a revised dollar-denominated Nikkei Stock Price Average. It has been calculated based on a fixed exchange rate of $1/ ¥360 up until the day of the “Nixon Shock” (suspension of dollar convertibility into gold) in August 1971, and prevailing rates based on the floating exchange rate system since then. Graph 3 has been compiled by dividing the yen-based data of Graph 2 by these exchange rates. I have also used the same logarithmic scale used in Graph 2. I shall now compare both graphs and note the differences. There are three points worth mentioning. The first is that in the correction market from 1981 through to 1983 (the final stage of Graphs 2-II and 3-II), the range of the correction appears much larger in the dollar-denominated Nikkei. This is when the rapid weakening of the yen coincided with low stock prices, which to US investors appears as growing losses. The next is the rise of the Nikkei in Phase 3 (Graphs 2-III and 3-III). The pace of the rise is faster in the dollar-denominated Nikkei. Seen from the US, the sharp appreciation of the yen from around $1/¥250 to less than $1/¥150 gives a considerable boost to the upspeed of the Nikkei. US investors who bought Japanese stocks in 1983 boosted their profits in theory by combining stock gains with exchange rate gains. My final point is that the collapsing market since 1990 according to the dollar-denominated Nikkei (Graphs 2-IV and 3-IV) looks fairly mild compared to the yen-based Nikkei. Generally speaking, the strong yen trend continued until 1995, but then following the extreme phase of $1/¥80, the Japanese stock market’s decline suddenly got discounted in dollar terms, to a certain extent. In general however, there are no major differences in the market trends seen in Graphs 2 and 3. Both declined in Phase 1, rose in Phase 2 and again in Phase 3, and declined in Phase 4. The central issue of my paper relates to the cross cycles of US and Japanese stocks, so substituting Graph 3 for Graph 2 is not a problem. Therefore I would like to proceed with my analysis by comparing the dollar-denominated Nikkei with the DJIA. Application of Japanese and US Stock Price Cross Cycle If the existence of a cross cycle can be recognized with the DJIA and the Nikkei, then it has many applications in asset management. In other words, it could find practical application in investment activities, for example if there is a slowdown in the Japanese market, assets can be moved to the US market, or if there is a slowdown in the US market, then assets can be moved to the Japanese market. Of course, exchange rates have to be taken into account when shifting assets between countries, however this problem can be solved if the investors are foreign investors, particularly US investors, and analysis is conducted with the dollar-denominated Nikkei. The problem is rather whether reliable investment techniques can be established in order to correctly detect good stock investment opportunities in each of the US and Japanese stock markets respectively. I would like to develop my theme while introducing a trend analysis technique, which has been important to me for many years. READING MARKET PHASES AND SETTING PORTFOLIO HOLDING RATIOS FOR STOCKS WITH TREND ANALYSIS

Firstly, I wondered about how to express market trends. I must admit that the trend image I prepared (divided into four phases) to give an overview of the Japanese and US stock markets I outlined in general in Graphs 1, 2, and 3 is rather lacking in detail as a technique, but it is a type of method to recognize trends. In statistical analysis, this type of recognition method is called the Free Hand Method. The Nippon Techncial Analysts Assocition (NTAA) tree pattern model classifies trend recognition methods into regular

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time series and irregular time series types. Regular time series types include the Trend Line Method, the Moving Average Method, and the Indicator Smoothing Method. If I limit myself to Japanese techniques, there are many trend lines covered by, for example, Ichimoku Equilibrium. There are also various irregular time-series type expression methods such as P&F, the Kagi line (KAGI-ASHI), the Block Line (NERI-ASHI) and the New Price Line (SHINNEASHI). I could use some of these in my chosen topic of trend analysis of the Japanese and US stock markets. However, we have been asked by the examiner (IFTA’s Qualification System Committee) to use original or unpublished techniques in our papers, so I would like my report to reflect this requirement. In other words, I shall use my own “Okamoto Trend Analysis Method” which has been very important to me since my younger days. This is a new trend image hypothesis based on moving regression analysis. I would like to firstly explain this concept. The difference between this technique and conventional methods is that both actual and estimated stock prices are used in trend line assumptions. The hint for this came from moving average lines in statistics. With the moving average lines used in the stock market, the calculated average values usually have to correspond to the end of the average period. As a result, the cycle of a moving average line tends to lag compared to the cycle of actual stock prices and this lag, more or less, leads to delays in investment decisions. Of course, this lag can also be useful in its own way. In the upward phase of actual stock prices, the moving average line cycle will lag, so the moving average line acts like an uptrend line linking the lows of rising actual stock prices. In the same way, it plays the role of a downtrend line linking the highs in the downward phase of actual stock prices. From the effects of this lag, a classic investment technique has been born which sees trading opportunities when actual stock prices straddle the moving average line. However, delay certainly causes real confusion in the investment world. With minor cycles in particular, a turn may have just been confirmed when the next cycle begins. If smoothing curves with no lag exist, they would be a great asset to technical analysis. Actually, the calculated average value with primary moving average lines used in statistics corresponds to about the center of the average period, with no delay in the initial series, and the initial series trend being expressed as a gentle slope. The Okamoto Trend Line begins with the concept of the primary moving average line as used in statistics. In other words, it tries to calculate smoothing curves by targeting trend lines with no lag. However, if we try to make market timing decisions for the most recent period, having no calculations for this latest period is unadvisable. If you use the moving average line unchanged as used in statistics, it will show nothing for the latest period. So a certain operation must be conducted here using estimated stock prices to supplement the blank part. So how do you go about finding these estimated stock prices, and how do you conduct this operation? This is where regression analysis comes in. Graph 4 shows a 48-month moving average trend line of the DJIA, and Graph 5 shows a similar smoothing curve of the dollar-denominated Nikkei. But both of these are Okamoto Trend Lines and are different to 48-month moving average lines normally used in the stock market. At first glance, there seem to be only occasional lags compared to conventional 48month moving average lines. This applies particularly to the dollardenominated Nikkei, which has a large number of uneven movements. As an experiment, I prepared a 48-month moving average line as used in the stock market for the dollar-denominated Nikkei, which is shown in Graph 6. There is a clear difference between Graphs 5 and 6. The special feature of the Okamoto Trend Line technique is its ability to smooth stock price movements through fairly small lags. Double calculation is used to compile the Okamoto Trend Line. Firstly, I conduct regression analysis (primary regression) on the

IFTAJOURNAL first 24 items of a 48-month data series, and project 24 items of stock price data on the regression line. Then I try to find the 48-month average by linking the 24 items of hypothetical data estimated with the 24 items of real data based on regression analysis. I then plot (on a chart) the 48-month average value found which corresponds to the middle (the 24th month) of the average (48-month) period. This double calculation (regression calculation followed by calculation of the average) moves forward in monthly increments, and results in the Okamoto Trend Line. In the final stage of the data series (the latest period) the actual data for the last 24 months is regressed to give 24 items of projected data on the regression line. Then by averaging the total of the 24 items of actual data and 24 items of projected data over 48 months, a smoothed value for the latest period is obtained. These calculations are fairly difficult without a computer. The lower sections of Graphs 4 and 5 show the momentum (rate of change over previous month of smoothed curve) of the Okamoto Trend Line shown above. The plus region of the momentum indicates an upward phase of the market cycle (smoothed curve), and the minus region indicates a downward phase of the market cycle. You can follow the direction of the market by looking at the momentum in Graphs 4 and 5. Let’s firstly look at the DJIA in Graph 4. The characteristics of each of the phases in Graph 4 are already apparent. As Phase 1 (section I of the Graph), Phase 3 (section III), and Phase 4 (section IV) are upward phases of the DJIA, the momentum frequently appears in the plus zone. It occasionally falls into the minus zone, but without even pausing, immediately returns back to the plus zone. Its temporary penetration into the minus zone is regarded as a type of accent that forms a mini-cycle (a 4-year cycle). If the momentum falls into the minus zone and remains there for a long time with no signs of returning to the plus zone, it means that you should consider the likelihood of a trend reversal. On the other hand, in Phase 2 (section II), the momentum repeatedly swings erratically, straddling zero. Generally speaking, the momentum over this period stayed virtually the same amount of time in the plus and minus zones. This is the result of a continuously flat pattern, where the trend line neither rises nor falls over a long period of time. Going a step forward from this stage, the momentum gradually moves into the plus zone, and we can recognize an upward break in the trend, in other words, a move to Phase 3 (section III of the Graph). Based on this, what is the outlook for the DJIA (at the end of Phase 4)? I believe it is valid to say that the uptrend will continue for the time being (my view as at October 1999), and I see little likelihood of a downturn soon. However, the purpose of my paper is to look at New York in terms of a comparison with Tokyo. As this involves moving assets between two countries in accordance with the momentum of each market, a comparison of momentum is important. Even if New York is strong, the Tokyo market may be stronger, so it would only be natural for funds to be switched to the Tokyo market. What about the Tokyo market as shown in Graph 5? Let’s look at the Tokyo market’s momentum. Phase 2 (section II) and Phase 3 (section III) of the Tokyo market are upward phases, so generally speaking, the momentum at these times should be in the plus zone. So when we look at Graph 5, the momentum certainly appears frequently in the plus zone at these times. However there are exceptions. In particular, the momentum declined sharply in 1967, 1974 and 1982, so special consideration of such times is necessary. Actually, when we look at sections II and III, in other words, in the 25 years from 1967 to 1990, the theory holds (momentum in the plus zone) throughout the period, apart from these three times. Why do these three times deviate from the theory? We Japanese soon notice that the issue common to the environment surrounding these three times is “economic shocks from foreign pressure.” I have an example showing how weak Japan is against foreign pressure, which I will explain.

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IFTAJOURNAL Firstly in 1967 there was the so-called Nixon shock. The fixed exchange rate system ($1/¥360) which had lasted since the end of the war had collapsed by then, so a shock was inevitable. Many feared at the time that the trading nations would no longer be able to keep going without switching to a floating exchange rate system (meaning a sharp appreciation of the yen). This type of panic can easily lead to “technical chart-breaking.” As a result, momentum lingered in the minus zone for a year. Next came 1974. This was the year of the first oil shock, and when foreign pressure was at its strongest. The price of a barrel of crude oil had been stable at $2-3, but suddenly shot up to double-digit figures. Countries with processing trade as their national policy were greatly threatened. Moreover, political turmoil made matters worse. In October 1974, Prime Minister Tanaka was forced to resign because of the Lockheed bribery scandal. In 1983, inflationary pressures built up as a result of the second oil shock, and Japan’s official discount rate jumped to 9%. The added impact of such seismic shocks (much of them from foreign pressure) on the economy stunned investor sentiment. So even though the long-term cycle of stocks (the economy) is following an uptrend, the momentum is temporarily affected. Phases 1 and 4 (Graph 5-I and IV) of the Tokyo stock market are downtrends, and so the momentum of the Nikkei in general remains in the minus zone. Two areas deserve attention, firstly when it temporarily slipped into the plus zone in 1963, and then the rise in 1993-94. The rise in 1963 was from the temporary effects of the Tokyo Olympic Games, which were soon followed by the Securities Recession. In 1993-94 there was a mini recovery during the collapse of the bubble economy. The recovery of 1993-94 is not unconnected to the benefits of government policy, or perhaps a market (economic) trend reversal. The reason for momentum remaining only temporarily in the plus zone is the inadequate policies of the responsible authorities at the time. As a result, financial uncertainty increased, which laid the groundwork for the insolvency of a number of large Japanese financial institutions. Beginning with The Hokkaido Takushoku Bank Ltd., a succession of bankruptcies followed a few years later, including Sanyo Securities Co., Ltd., The Long Term Credit Bank of Japan, Yamaichi Securities Co., Ltd., and Nippon Credit Bank Ltd. After going through this process, the momentum of the dollar-denominated Nikkei again entered the plus zone in 1999. I would now like to have a closer look at around the end of the momentum section of Graph 5. The momentum of the dollar-denominated Nikkei in Graph 5 has now been in the plus zone for a year, and the rise (the momentum value) is sharp, more than 5%. A technical rally is less than 5%, so a rise of more than 5% ranks alongside those of 1972 and 1986. The latter is right in the middle of the bubble market, so such a large rise is to be expected. However the liquidity market of 1972 remains one of the most excessive in the history of the Japanese stock market, with the Nikkei doubling that year over the previous 12 months. It is not normal for the Tokyo market of late to be demonstrating momentum of that scale This may possibly mean that a major reversal of the correction trend which has continued for such a long time is close at hand, and certainly gives us something to think about. To quote one market saying: “A hibernating market will stand tall when awakened.” If this is the case, a comparison of momentum with New York should be made. Funds withdrawn from New York may have to be switched to Tokyo. How should this be decided? This is where the concept of net momentum comes in. Graphs 7 and 8 show the net momentum for the New York and Tokyo stock markets. The top section of Graph 7 is the DJIA and of Graph 8 is the dollar-denominated Nikkei, with the lower sections of both being the common indicator. In other words, net momentum. The net momentum is the result of subtracting the

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dollar-denominated Nikkei momentum from the DJIA momentum. (However, the momentum I have used here for both Japan and the US is not in comparison with the previous month, but with the previous six months.) In general, the DJIA and the Nikkei are moving in a cross cycle, so the momentum is also frequently divided between the plus and minus zones. For example, if New York is plus 1 and Tokyo is minus 1, the net momentum is plus 2 (minus 1 subtracted from 1 is 2). Based on this, investors would have to invest in New York. If we look at movements of net momentum, the indicator (net momentum) in Phases 1 and 4 (sections I and IV) is generally in the plus zone, which tells us that the New York market has the advantage. It is only natural that funds should be invested on the New York market in this period. What should be watched is Phase 3 (section III). In Phase 3, the DJIA finally returned to its uptrend, and after breaking $1,000, began to follow a powerful rising trend. In this period, however, the net momentum indicator was consistently in the minus zone, which tells us that funds should have been invested in the Tokyo market. At that time gains could only be made if funds were only invested on the New York market, so it could not be described as a mistake to invest contrary to the net momentum indicator. However global investment must be conducted in line with the indicators, which meant investing in the Tokyo market. The rate of advance of stocks also tells that ultimately there were greater profit opportunities in Tokyo. Let’s now look at Phase 4 (section IV). In Phase 4, the Japanese economic bubble had burst while the US economy continued to be buoyant, and the net momentum indicator was generally in the plus zone. So did this turn out to be correct? At that time, the DJIA was surging further ahead, surpassing $10,000, yet the Tokyo market remained sluggish. However I must point out that the situation has changed since the summer of 1999. The net momentum indicator has fallen sharply into the minus zone. As seen a little earlier, the New York market itself is firm, and the DJIA momentum (Graph 4 section IV) is in the plus zone. What we should note, however, is that the net momentum indicator (Graph 7-IV) has fallen into the minus zone. At present, the Tokyo market is firmer than New York, and is attracting funds from around the world. I would now like to study how Japanese and US stock holding ratios of fund management portfolios should be operated by using the net momentum indicator. From the characteristics of the indicator, the conclusion is already obvious. In other words, it would be correct to invest all funds in the DJIA when the net momentum indicator is in the plus zone, and all funds in the dollar-denominated Nikkei when the net momentum indicator is in the minus zone. Of course, the point of change in portfolio operations is when the net momentum indicator straddles the zero line. That is to say, when the net momentum indicator changes from minus to plus, conduct asset allocation by immediately selling Japanese stocks and buying US stocks, and turn to Japanese stocks when the net momentum indicator moves from plus to minus by immediately selling US stocks and investing the total amount in Japanese stocks. How reliable would such portfolio holding ratio operations be in actual fund management? I have explained this below based on verification of previous examples. ASSET ALLOCATION OPERATIONS AND PORTFOLIO PERFORMANCE EVALUATION OF JAPANESE AND US STOCKS

In the 40-year period from 1960 to 1999, the net momentum indicator straddled the zero line a total of 22 times. Please refer to Table 1. The change from minus to plus (shifting portfolios to New York stocks) occurred 11 times, and from plus to minus (shifting portfolios to Japanese stocks) occurred 11 times. To state my conclusion here, of these 22 portfolio operations, 16 were successful transactions and 6 were failures, which is a success rate of 72.7% on a transaction frequency basis (16/22 = 0.727). Reliability is also

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fairly high overall. For both the DJIA and the dollar-denominated Nikkei, the success or failure of the transactions was conditional on 1) the transaction being regarded as taking place at the price when the indicator reverses, and 2) the transaction cost not being included in the calculations. Now these are rough calculations, but I believe there is no doubt that they are sufficient to give a general indication of the effectiveness of this technique. The time required to the next reversal once the indicator had reversed was on average 20.6 months for the 22 transactions, in other words, a little over a year and a half. This can be considered the continuation period for the trend around the time of one transaction. This means that once a final decision on whether to choose New York or Tokyo as the investment market is made, investment funds should be left untouched for a year and a half. I think a year and a half is an appropriate investment period. However, we should note that twice there were extremely short-term false movementtype reversals. These were the New York market’s reversal in October 1985 and the Tokyo market’s reversal in March 1992. Both were short-term technical changes amid long-term uptrends that were again reversed the following month. Note also the last reversal, in other words, the reversal of July 1999 (a reversal from the New York market to the Tokyo market), and although the current trend is continuing, I had to finish it off in October 1999 in order to make my provisional calculations. This resulted in a period of only three months. From the market environment we can infer that this trend can reasonably be expected to continue for a long time. So if we exclude these three instances and have a denominator of 19 instead of 22, the average becomes a little longer, at 23.7 months. In addition, the average trend continuation periods for Japan and the US are about the same, so apart from the three extremely short-term examples mentioned above, the period for Japan is 24.5 months compared to 22.8 months for the US. This difference is not great enough to be a problem. Further analysis of the trend continuation periods reveals that of the 19 significant cases, a total of 8 had trends that continued for two years (24 months) or longer, 4 for New York and 4 for Tokyo. Moreover, a total of 17 cases had trends continuing for one year (12 months) or longer, 9 for New York and 8 for Tokyo. A trend continuing for one year or longer for 17 out of 19 cases indicates a fairly high degree of reliability for this technique. I believe this proves that it is quite suitable for use in international diversified investment. Investment in the Tokyo market in the longest investment period from November 1985 to July 1989 provided an annual margin ratio of 80.45% over that period. I would like to discuss these profit margins (rates of return relative to funds invested). The average profit ratio (annualized) of the 22 transactions was 13.94%, with the highest being on the Tokyo market in the second half of the 1980s (80.45% as mentioned above) and the lowest being -30.48% on the Tokyo market between May and October 1963. It should be noted in passing that a total of six transactions produced negative returns, far fewer than the 16 transactions that gave positive returns. The transactions with negative returns of course include the extremely short-term false movementrelated transactions. A breakdown of the transactions with negative returns shows that the US had two and Japan had four. Japan had more because two were post-bubble transactions. I looked a little further at these two transactions which occurred after the collapse of Japan’s economic bubble. One was a transaction in the extremely short period between March and April 1992 that produced the particularly large negative return of 127.2% (annualized, and should be regarded as an irregular transaction), while the other was a transaction during the 21-month period from May 1993 to February 1995 that gave -3.88% (annualized). Outstanding investment results were achieved from the previously-mentioned transactions in the 1980s when funds were boldly switched to the Tokyo market despite the New York market indi-

IFTAJOURNAL cator being plus, although there was a false movement-related transaction of funds being switched to New York in one month from October to November 1985. These were from a transaction in the 22-month period from December 1983 to October 1985 which provided an annual return of 23.29%, and a transaction in the 44month period from November 1985 to July 1989 that gave an annual return of 80.45%. However after the collapse of the Tokyo market bubble, asset allocation according to this technique generally meant investing in the New York market. As the main theme of my paper is the cross cycles of the Japanese and US stock markets, it should be noted that market movements divided into four separate phases in a free-hand style may not necessarily be the same with the Okamoto method. Both methods match exactly for Phase 1 until the end of 1965, but there is a slight lag in each from Phase 2 onwards. If we look at the connection between Phases 2 and 3, the trend reversal point is not at the end of 1989 but around July of that year. Phase 4 then follows. A bigger problem is the fact that with the Okamoto method, there are 22 divisions (in actuality, 19), not 4. More phases mean extra transactions, which leads to a decline in investment efficiency. Nevertheless, high marks should be given to the fact that average returns of above 13% per annum are achieved at a reliability level of more than 72%. This method can also be applicable to individual issues that generate cross cycles such as Sony Corp. and Mitsui Fudosan Co., Ltd., or Microsoft Corporation and USX Corporation. Of course it can also be used to analyze Mitsui Fudosan and Microsoft. Graph 1 DJIA

Graph 2 Nikkei Stock Price Average

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Graph 3 Dollar-Denominated Nikkei Stock Price Average

Graph 6 Dollar-Denominated Nikkei Stock Price Average

Graph 4 DJIA

Graph 7 DJIA and Momentum Differential (NY-225)

Graph 5 Dollar-denominated Nikkei Stock Price Average

Graph 8 Dollar-Denominated Nikkei Stock Price Average and Momentum Differential (NY-225)

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IFTAJOURNAL Table 1

Notes: N1-N11 refer to DJIA trading T1-T11 refer to dollar-denominated Nikkei Stock Price Average trading Price units for both N and T are dollars Time held refers to number of months Profit/Loss (annual) shown is percentage Stock price data is original data from stock price Graphs 1-8. BIOGRAPHY

Hiroshi Okamoto was graduated from Kohnan University in March of 1960. In April of 1960 he joined Nomura Securities Co. where he worked until his retirement in June of 1996 (becoming a Director of Nomura Investment Trust Co. in 1991). In 1990 Mr. Okamoto became Chair of the Nippon Technical Analysts Association and in 1994 he became a Vice Chair of IFTA covering the Pacific area.

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Head-and-Shoulders Accuracies and How to Trade Them Serge Laedermann INTRODUCTION

The Head-and-Shoulders pattern is probably one of the bestknown and venerable of chart formations. It is considered as one of the most reliable “by all odds” according to Edwards and Magee’s own words in their reference work. Martin J. Pring quotes the Head-and-Shoulders as “probably the most reliable of all chart patterns,” while John J. Murphy’s analysis is almost identical when considering “probably the best known and most reliable of all major reversal patterns.” Some official legitimacy was gained in August 1995, when the New York Federal Reserve astonished both economists and technicians in publishing a computer study on the validity of the case: “Head-and-Shoulders: Not just a flaky pattern.” The old formation undoubtedly stands the test of time and represents a powerful tool in today’s trading and analysis. The suggestion is to invite you on a journey inside the Head-and-Shoulders. Some discoveries are still to be made. Rounding Bottoms and Complex Head-and-Shoulders consisting of multiple left and right shoulders, and should be traded on a level of confidence that any technician should gain before acting. Traders have always been faced with some weakness when trying to profit from the pattern. It is not being irreverent to state that technical literature does not provide enough clear statistical accuracies on the subject. Most observations are pertinent or judicious, but they hardly help when dealing with a trade to do or to avoid. This paper will first specify what can be considered as a valid or adequate Head-and-Shoulders. Harmony limits and rules to follow will be shown according to classical practice. Secondly, the study will analyze ‘known facts’ about Head-and-Shoulders. Probabilities and numbers will be put forward on the major topics such as Volume, Measuring Objective, Pullback and Pattern Length, among others. In the third place, the paper will suggest trading techniques to profit from the pattern and how to estimate the Objective. The entry level, Stop and three different ways of measuring the Objective will be discussed. A complete track record will be established, showing the pattern degree of efficiency and the level of risk to take in order to make a living of it. Precise net valuations will be displayed.

room for various methods of assessment in that field; the margin is in fact pretty narrow. Despite the lack of statistics, many examples of Head-and-Shoulders are to be found in technical books, therefore diminishing misinterpretation. This work represents a full coverage of nearly eight years on four major liquid markets. All patterns discussed have been carefully selected in respect of the classical methodology as well as strict rules. The information and opinions contained have been compiled in good faith. The author asserts that ethical standards of professional conduct have been highly respected. He is at disposal, upon request, to defend any position or decision taken. This study is based on daily charts and deals solely with Headand-Shoulders which are tradable by everybody, in contrast with patterns which are only caught by floor traders. The patterns selected in this study meet two criteria. They are followed by a Close beyond the Neckline, and a Pullback either to the Breakout level or the Neckline, on a daily chart. In practice, you will have the time to analyze many markets and detect which one has just experienced a Breakout of a Head-and-Shoulders. Your next-day limit order will be easily calculated as well as your exit levels (Stop and Objective). RECOGNITION

According to Robert D. Edwards and John Magee, the only qualification on an up-sloping Neckline is that the Bottom of the recession between the Head and Right Shoulder must form appreciably below the general level of the top of the Left Shoulder. The logic applies for a down-sloping Neckline as well. In modern trading, the adverb ‘appreciably’ tends to disappear as commodities charts look more stretched than stock’s charts in the 1950s. Multiple or Complex Head-and-Shoulders consisting of some Left and Right Shoulders, or even Two-Headed, are common. However, the Neckline is not always easy to draw as two or even several possibilities often exist. Traders should take a position on any Pullback following an obvious Breakout, even in the case of multiple formations.

METHOD

Daily data from January 1990 till October 1997 have been selected on the S&P 500, US Treasury Bonds, Swiss Franc and Gold in an attempt to cover the major market sectors. Data are on a cash or spot basis in order to avoid roll-over gaps implied by the future market’s positive or negative carry. The idea is to detect possible divergences between stocks, interest rates, currencies and commodities. Do Head-and-Shoulders develop the same way on various markets? Are all markets profitable? Is the Risk-Reward indisputable? These questions need ‘tentative’ precise answers. Subjectivity is clearly the main difficulty when dealing with a pattern formation. ‘After the fact’ recognitions make trades more attractive than they are in the real world. Furthermore, patterns found on a chart may vary from one technician to another. Also, the picture may sometimes even prove to be rather different the following day for oneself! However, well-trained individuals know very well that there is no

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Head-and-Shoulders Tops or Bottoms are to be found at the end of a trend. One should not expect to consider as a true Head-andShoulders a pattern whose size is more than half the amplitude of the prior trend. John J. Murphy states that Reversal patterns can only be expected to reverse or retrace what has gone before them. In other words, the maximum objective is the size of the prior move.

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Therefore, too-big patterns may not reach their measuring objective, and imply a doubtful Risk-Reward ratio. Traders may avoid such trades which usually oblige them to place a Stop too far for fear of premature exit.

IFTAJOURNAL possible? This is a good example of an ‘After the fact’ trade. Whenever the first Breakout occurred, the Symmetry or Harmony of the Pattern was rather poor. The downward-sloping Neckline was steep, but not eliminatory. However, the Head and Left Shoulder distance as compared to the Head and Right Shoulder distance was a matter of worry. The lack of Harmony did not encourage the desire to trade when the Pullback eventually occurred. Later on, the pattern looked more balanced and the decision to trade was logically taken. This time, the market did not give another chance to get in. We must learn to live with it. FREQUENCY

Symmetry is the key word for a Head-and-Shoulders pattern, even more so in a group of related formations which carry the same technical implications. Rounding Tops and Bottoms are Multiple formations as well and should be traded on a Pullback as soon as an obvious Breakout is detected.

The pattern has to be in Harmony with the environment. The word is somewhat romantic, but describes the kind of level of confidence any trader should gain before acting. Some technicians may consider this Gold-Comex development as a valid Head-and-Shoulders Top, but the assumed Right Shoulder represents, in fact, the move which negated the formation. The objective completion, a few days later, does not alter the picture. Some situations are surprisingly not tradable. The Swiss Franc IMM picture looked promising in May 1997. Why was this trade not

One hundred and twenty one Head-and-Shoulders patterns have been found using daily charts on the S&P 500, Swiss Franc, US TBonds and Gold from January 1990 till October 1997 (94 months). Sixty percent of all formations were Head-and-Shoulders Bottoms, Gold recording an anomalous 76% of Bottoming patterns. Excluding Gold, Bottoming formations accounted for 53% of all patterns. PULLBACK

Sixty five of the 121 Head-and-Shoulders found experienced a Pullback powerful enough to initiate a trade. The entry or limit order has been placed at the Breakout point or the Neckline level, whichever was the less ‘ambitious.’ Whenever a Breakaway Gap occurred, the limit was placed at the less ambitious side of it (market should try to fill the Gap but may not succeed in true Breakaway situations). Pullbacks have been seen 59% of the time in the case of Top formations, but 69% of the time in Bottoming ones. This is a probable confirmation of the ‘gravity’ factor, showing that a market advance takes usually more time to develop than a market decline. Eighty percent of S&P 500 and US T-Bonds Bottom patterns experienced a Pullback after the Breakout. This analysis is not significant for currencies (either bullish or bearish, depending on the

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IFTAJOURNAL country). Gold had too few Top patterns to rely on the Pullback ratio observed in Top cases.

PULLBACK LIMIT ORDER

OBJECTIVE

The classical method to determine the minimum Objective is based on the height of the pattern. The vertical distance from the Head to the Neckline is projected from the point where the Neckline is broken (purists use a logarithmic scale). Our sample of 79 Head-and-Shoulders demonstrates that another method should be considered when trading patterns which are experiencing a Pullback (in other words, patterns which are tradable). The minimum Objective should be estimated by measuring the vertical distance from the Bottom of the hollow between the Head and the Right Shoulder, up to the trendline joining up the Head’s crest and the Right Shoulder’s crest.

That distance is then projected as in the classical style. An even more conservative method has been tested, using the vertical distance from the Right Shoulder’s crest to the Neckline, then projected as in the classical style. Cumulative total profits, on all trades, for the third method is 71.9%, clearly behind the classical measurement (77.8%) and the recommended one (79%).

Nearly 60% of minimum objectives have been reached using the recommended style, outperforming clearly the classical one (only 46% of objectives met). The conservative method managed to record an impressive, but misleading, 70% of success. This is where the Profit & Loss per trade comes into play, or the other side of the picture.

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IFTAJOURNAL numbers barely change. Future patterns failures are therefore not to be found using that statistic alone.

The performance per trade is unsurprisingly favorable to the classical method, almost compensating for the poor rate of success. However, method two is the best combination taking into account all the parameters.

The ‘Quality’ difference between method one and two is not so clear in terms of cumulative performances, but the picture is much better if we analyze the length of each transaction. On average, a trade (from the entry to the exit day) lasts 8 trading days with the recommended method, while it takes more than 10 days for the classical one. Considering that 2/3 of the trades in method 1 and 2 are identical, we have to understand what happens with 1/3 of them. Analysis shows that the classical measuring objective is often too ambitious and is therefore missed. Then, the short-term trend reverses, and either the Stop limit is activated or the position liquidated at the Objective when the initial trend resumes, much later on. A position lasts 6 trading days with the conservative method. The potential move is, however, chronically underestimated. Objective Not Tradable Thirty five percent of patterns did not experience a sufficient Pullback and have been considered as ‘not tradable.’ In almost 100% of the cases, the market reached the target quickly, sometimes the same day as the Breakout occurred. Two thirds of the ‘not tradable’ patterns lasted less than 10 days. It is highly probable that Pullbacks occurred on intra-day charts for the majority of these formations. VOLUME

Volume characteristics are considered of critical importance in assessing the validity of the pattern. Activity is normally high during the formation of the Left Shoulder and tends to be quite significant, but lighter, when the price is at the peak. Right Shoulder is usually accompanied by lower Volume, a typical warning of diminishing buying activity during a Head-and-Shoulder’s Top, or the end of the selling pressure in the case of a Head-and-Shoulder’s Bottom. Confirmation is provided in ranking the Volume: 55% of Left Shoulders recorded the highest Volume as compared to 32% for Heads and 13% for Right Shoulders. Objectives reached or not, the

The lowest Volume was recorded on 61% of Right Shoulders, 30% of Heads and 9% of Left Shoulders. Numbers were almost identical for Objectives completed and Objectives missed, which is again not helpful in detecting which Head-and-Shoulder is going to fail.

Thirty eight percent of the mid (or Nr 2) Volume has been recorded on Heads, 32% on Left Shoulders and 30% on Right Shoulders. Thirty four percent of patterns represented the ideal Volume sequence: Left Shoulder and the highest Volume, Head and the mid Volume, Right Shoulder and the lowest Volume. A small 4% developed in the most unusual way, with an inversed Volume sequence. Volume at Bottom Theory indicates that the most important difference between Head-and-Shoulders Tops and Bottoms is the Volume. At Bottoms, the market requires a significant increase in Buying pressure, reflected in higher Volume on up moves. The rally from the Head should show an increase of activity, often exceeding the Volume generated during the up move following the Left Shoulder. Thirteen percent of Right Shoulders recorded the highest Volume, 5% at Tops and 8% at Bottoms. In this particular situation, 75% of Head-and-Shoulders Tops missed the recommended Objective, while 80% of Bottom patterns succeeded. This is an indication that a high Right Shoulder Volume is not comforting at Tops, but not really detrimental at Bottoms. The Left Shoulder recorded the lowest Volume in 9% of all cases, 1% in Top and 8% in Bottom formations. Objectives have been met in slightly more than 50% of the formations. Volume Amplitude The specific Volume number is not of major importance to the Technician. However, it is often necessary to classify the Volume into one of three categories: High, Low, Average. Giving a mark to each category (1 point for High, 2 points for Average and 3 points

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IFTAJOURNAL for Low), the sample shows an extreme similarity to the ‘grading’ study described before.

gravity effect. It does require a much greater effort for the market to launch a new Bull trend. This characteristic is clearly confirmed by the current study. Top patterns lasted 23 days on average, while Bottom ones had a duration of 34 days, a 50% differential. Trades were completed after 8.3 days for Bottom formations, slightly above Top ones (7.6 days), showing that velocity was quite similar after the Breakout. Accordingly, Bottom trades tended to be shorter (in % of patterns’ sizes). However, the major outcome was that 86% of trades lasted, at the most, half the size of all the patterns found for both Head-andShoulders Tops and Bottoms. Symmetry is perfect knowing that 44% of trades lasted, at the most, 1/4 of the size of all patterns for both Top and Bottom formations. Lateral and vertical movements are proportional to each other as suggested by some theories, a statement of the obvious.

Forty one percent of patterns recorded the highest Volume (as compared to the Head and the Right Shoulder) and also a high Volume in amplitude, the typical case. Despite this ideal situation, the recommended objective has been met in only 63% of the cases, not a significant edge over ‘non typical’ situations. Twenty five percent of patterns recorded the lowest Volume on the Right Shoulder and a low Volume amplitude as well. This scenario produced an impressive 80% of accomplished Objectives, a remarkable performance.

A Head-and-Shoulders is not complete until the Neckline is decisively broken on a closing basis: The Breakout Day. A close beyond the Neckline not only completes the pattern, but also activates the minimum measuring Objective. A sharp increase in Volume is usual during the Break out, a factor not always dominant in a Head-and-Shoulders Top. Following a Breakout, the market runs and quickly peaks. In 85% of cases, the Breakout’s peak was reached the day of the Breakout (Day 1) or the following day (Day 2).

BREAKOUT

DURATION

Measuring Objectives is discussed in terms of height, but too few studies deal with classical Objectives durations. In our sample, Head-and-Shoulders lasted 30 trading days, on average, from the start of the pattern until completion. A pattern started whenever the move which was at the very beginning of the Left Shoulder, crossed the future Neckline. The end of the pattern was materialized by the Breakout. Trades, initiated on the Pullback day, lasted 8 days, or 27% of the pattern’s size, on average. This is a good indication of the time required when trading a Head-and-Shoulders. Trades’ duration were identical for both reached and missed recommended Objectives, which means that the Stop order method was efficient (see Trading).

One third of trades lasted less than 20% of Patterns’ sizes (for example, less than 6 days on a 30 days Pattern). One half were shorter than 30% and 2/3 less than 40%. However, the most significant observation lies in the 50% or less category where 86% of trades lasted, at the maximum. This is a nice probability to put forward whenever a measuring Objective is activated. Bottoms are generally flatter and generally take more time to develop, as the market falls to the floor more quickly due to the

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The average Breakout’s peak, or incursion level, reached 3/8 of the expected measured move. In other words, 3/8 of the Objectives were accomplished before the Pullbacks.

BREAKAWAY GAP

Start of 24 hour trading as well as a high liquidity explained the absence of Gaps (only 5%), still numerous on stock charts. RISK VS REWARD

The average gross profit at the recommended Objective was 1.497 higher than the potential loss at the Stop (Exit) level.

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TREND

Head-and-Shoulders are reversal patterns. Thus, 78% of trades were initiated against the Mid term Secondary trend. TRADING

As mentioned before, this study deals solely with Head-and-Shoulders which are tradable by everybody. One hundred and twenty one Head-and-Shoulders patterns have been detected using daily charts from 1990 until 1997. Pullbacks occurred 79 times, allowing in practice anyone to enter all 79 trades (see Frequency, Pullback & Method). The trades are first analyzed on a very straightforward basis showing yearly gross gains and losses on each market. 1990

S&P 500

SW FR

US TB

5.3%

-2.1%

2.6%

Gold 7.4%

1991

11.3

-4.3

3.2

8.3

1992

1.1

4.9

3.8

1.9

1993

0.5

5.1

-0.4

3.3

1994

-0.3

0.9

-1.3

1.7

1995

0.0

0.0

2.6

3.9

1996

-0.1

0.7

4.7

0.2

1997

9.2 26.9% 18 Trades

1.3 6.5% 19 Trades

3.5

2.2

18.8%

26.8%

21 Trades

In order to value the net return of our 79 trades in the real world, the following rules have been established: $100,000 was the initial cash put in the account. A contract position in any market never exceeded 2.5 times the account’s value, a reasonable leverage which boosted the performance. Margins never rose above 15% of the net equity and could have been multiplied by 3, with positions in all 4 markets, without causing any disturbance for the trading. Round turn Commission and Slippage were $80 per contract. At an average pace of 10 trades per year and knowing that each trade lasted 8 days on average, the interesting feature was the consistent high level of cash in the account.

21 Trades

Eighty nine percent of traded Pullbacks reached both the Neckline and the Breakout level. However, a limit placed at the most ambitious level (see Pullback) would have proved to be costly despite an estimated 10% ‘entry level’ savings. The total profit would have been cut by as much as 20%. Sixty three percent of trades generated a profit. The average profit per trade was 2.29%, much higher than the average loss of 0.90%. No loss above 2.50% had been recorded and a small 3% of trades lost more than 2%. Half of the winning trades exceeded 2% gain and 1 out of 10 exceeded 3% gain. SYSTEM

Winning Trades

50

Losing Trades

Average Gain

$10,312

Average Loss

-$5,798

Largest Gain

$29,200

Largest Loss

-$15,750

Largest % Gain Consec. Gain

17.7% 7

29

Largest % Loss Consec. Loss

Profitable Trades

63%

Total Gross Profit

$371,211

(63/37) * (10,312/5,798) =

Ratio Gain/Loss

Total Net Profit

$347,491

Profit Factor

-5.9% 2 1.78 3.03

19

2000 Edition

IFTAJOURNAL Therefore, nothing could be more justified than trading other technical patterns like Double Tops & Bottoms or Triangles using the same account equity and the same system. Short term traders may use 10 days of intra-day tick by tick charts and trade roughly 100 times per year.

94/11/28 94/12/06

B 6 US 98.51 S 6 US 100.30

10,260

253,906

REFERENCES

95/01/30 95/03/01

B 6 US 101.60 S 6 US 104.28

15,600

269,506

Edwards, Robert D. and Magee, John; Technical Analysis of Stock Trends, 6th Edition, 1992

95/02/06 95/02/17

B 16 GC 375.7 S 16 GC 378.1

2,560

272,066

Pring, Martin J.; Technical Analysis Explained, 3rd Edition, 1991

95/03/16 95/03/31

B 17 GC 385.6 S 17 GC 398.3

20,230

292,296

96/02/15 96/02/28

B 7 SF 83.40 S 7 SF 84.28

7,140

299,436

■

■

TRADES RECAP $243,646

■

Murphy, John J.; Technical Analysis of the Futures Markets, 1986

■

Murphy, John J.; Intermarket Technical Analysis, 1991

96/02/16 96/02/21

S 6 US 119.30 B 6 US 115.85

20,220

319,656

■

Shaleen, Kenneth H.; Volume and Open Interest, 1991

96/02/21 96/03/21

S 18 GC 399.8 B 18 GC 398.3

1,260

320,916

■

Shaleen, Kenneth H.; Technical Analysis & Options Strategies, 1992

96/03/22 96/04/02

B 20 GC 398.5 S 20 GC 393.8

-11,000

309,916

96/05/01 96/05/02

S 7 US 109.66 B 7 US 108.33

8,750

318,666

96/06/17 96/06/19

B 20 GC 384.4 S 20 GC 386.7

3,000

321,666

96/06/19 96/06/21

B 7 SF 79.92 S 7 SF 79.00

-8,610

313,056

96/06/26 96/06/28

B 7 US 108.13 S 7 US 109.51

9,100

322,156

96/08/01 96/08/05

B 20 GC 386.3 S 20 GC 389.9

5,600

327,756

96/08/23 96/08/30

B 7 US 110.17 S 7 US 108.00

-15.750

312.006

96/09/13 96/09/13

B 7 US 107.81 S 7 US 109.12

8,610

320,616

96/09/24 96/09/24

B 7 SF 80.80 S 7 SF 81.46

5,215

325,831

96/10/24 96/10/29

B 20 GC 383.3 S 20 GC 381.2

-5,800

320,031

96/10/28 96/11/01

S 4 SP 701.62 B 4 SP 708.25

-7,190

312,841

96/11/01 96/11/05

S 4 SP 701.62 B 4 SP 708.28

5,260

318,101

97/02/20 97/02/21

B 22 GC 346.1 S 22 GC 353.6

14,740

332,841

97/03/14 97/03/31

S 4 SP 791.42 B 4 SP 761.90

29,200

362,641

97/04/25 97/04/29

B 4 SP 768.06 S 4 SP 789.96

21,580

383,621

97/04/30 97/05/02

B 8 US 108.83 S 8 US 110.39

11,840

395,461

97/05/19 97/05/02

S 8 US 109.41 B 8 US 110.03

-5,600

389,861

97/06/10 97/07/03

B 8 US 110.83 S 8 US 113.69

22,240

412,101

97/08/14 97/08/18

S 4 SP 923.00 B 4 SP 899.83

22,850

434,951

97/10/21 97/10/21

S 12 SF 68.06 B 12 SF 67.16

12,540

447,491

Chang, Kevin P.H. and Osler, Carol; Federal Reserve of New York, August 1995 Report, Head & Shoulders: Not Just a Flaky Pattern

■

Etzkorn, Mark; Futures Magazine, January 1996 article, Fed & Shoulders

■

BIOGRAPHY

Since 1998, Serge Laedermann has been a partner at GF Geneva Finance (located in Geneva, Switzerland) focussing on Private Banking. Fundamental analysis is used for investment decisions as well as technical analysis, which represents his major and core tool. He is mainly a specialist on pattern recognition. In the 80s Mr. Laedermann was a floor trader and a technical analyst at Credit Suisse and, later on, Chief Economist and Analyst at Bank of New York - IMB, Geneva. Serge co-founded in 1987 the Swiss Association of Market Technicians (SAMT).

20

2000 Edition

IFTAJOURNAL

TRADES RECAP $100,000 90/02/08 90/02/13

B 3 SP 332.11 S 3 SP 329.91

-1,890

98,110

92/02/14 92/04/03

S 4 SF 68.75 B 4 SF 67.21

7,380

173,718

90/03/13 90/03/30

S 2 SF 65.92 B 2 SF 67.00

-2,860

95,250

92/04/07 92/04/13

B 5 SF 66.92 S 5 SF 66.06

-5,775

167,943

90/05/18 90/05/21

S 2 SF 71.26 B 2 SF 70.57

1,885

97,135

92/05/02 92/05/08

B 4 US 99.16 S 4 US 100.10

3,440

171,383

90/06/20 90/07/03

B 2 SF 70.54 S 2 SF 71.72

99,925

92/06/12 92/06/18

S 4 SP 411.24 B 4 SP 401.83

9,090

180,473

90/06/21 90/07/12

S 2 SP 359.92 B 2 SP 361.24

99,105

92/07/07 92/07/17

B 13 GC 346.0 S 13 GC 355.0

10,660

191,133

90/07/24 90/08/10

B 6 GC 367.5 S 6 GC 387.8

110,805

92/10/08 92/11/06

S 4 US 105.29 B 4 US 102.26

11,800

202,933

90/09/10 90/09/18

B 3 US 89.62 S 3 US 88.54

-3,480

107,325

92/10/23 92/11/02

S 5 SF 74.55 B 5 SF 71.78

16,913

219,846

90/09/12 90/09/14

S 2 SF 75.43 B 2 SF 76.92

-3,885

103,440

92/12/07 92/12/21

B 16 GC 335.0 S 16 GC 332.5

-5,280

214,566

90/10/22 90/11/27

B 2 US 91.29 S 2 US 94.78

6,660

110,100

92/12/09 93/01/08

B 5 US 105.06 S 5 US 104.99

-750

213,816

90/10/30 90/11/02

S 2 SF 77.98 B 2 SF 78.96

-2,610

107,490

93/01/21 93/01/25

B 6 SF 67.71 S 6 SF 68.95

8,820

222,636

90/11/06 90/12/06

B 3 SP 313.07 S 3 SP 332.77

14,535

122,025

93/02/23 93/02/24

B 5 SP 434.55 S 5 SP 438.74

4,837

227,473

90/12/14 90/12/19

B 8 GC 372.0 S 8 GC 378.8

126,825

93/03/19 93/04/01

B 6 SF 66.14 S 6 SF 67.64

10,770

238,243

90/12/28 90/12/31

S 3 SF 77.27 B 2 SF 79.10

119,723

93/03/23 93/03/25

S 5 SP 449.11 B 5 SP 451.03

-2,800

235,443

91/01/25 91/02/27

B 3 SP 334.50 S 3 SP 363.05

140,896

93/05/28 93/06/01

B 5 US 111.10 S 5 US 112.19

5,050

240,493

91/02/21 91/02/26

S 3 US 97.99 B 3 US 97.09

2,940

143,836

93/06/15 93/06/23

S 16 GC 365.4 B 16 GC 373.5

-14,240

226,253

91/03/19 91/03/26

S 9 GC 363.5 B 9 GC 357.6

4,590

148,426

93/06/17 93/07/09

S 7 SF 67.46 B 7 SF 65.56

16,065

242,318

91/05/13 91/06/12

S 3 US 95.58 B 3 US 93.41

6,270

154,696

93/08/03 93/08/10

B 7 SF 66.88 S 7 SF 65.63

-11,497

230,821

91/05/21 91/05/28

S 3 SP 374.30 B 3 SP 379.15

-3,878

150,818

93/09/22 93/09/27

S 4 US 119.37 B 4 US 120.95

-6,640

224,181

91/05/29 91/06/10

B 10 GC 361.7 S 10 GC 370.6

8,100

158,918

93/11/08 94/01/05

B 14 GC 375.7 S 14 GC 396.3

27,720

251,901

91/07/24 91/07/31

B 4 SP 393.1 S 4 SP 387.09

167,368

94/03/15 94/03/24

B 5 SP 466.98 S 5 SP 465.44

-2,425

249,476

91/09/20 91/09/27

B 4 SP 386.72 S 4 SP 384.28

164,608

94/06/10 94/06/16

B 5 US 105.49 S 5 US 104.06

-7,550

241,926

91/10/04 91/10/21

B 11 GC 356.1 S 11 GC 364.2

172,638

94/06/15 94/06/17

B 16 GC 383.9 S 16 GC 387.9

5,120

247,046

91/10/29 91/10/29

S 5 SF 66.56 B 5 SF 67.88

-8,650

163,988

94/08/05 94/08/11

B 5 US 104.15 S 5 US 102.37

-9,300

237,746

91/11/04 91/11/13

S 11 GC 356.8 B 11 GC 357.0

-1,100

162,888

94/08/25 94/08/26

S 6 SF 76.79 B 6 SF 76.11

4,620

242,366

91/12/17 91/12/23

B 4 SP 382.95 S 4 SP 392.10

8,830

171,718

94/10/05 94/10/07

S 15 GC 393.1 B 15 GC 389.1

4,800

247,166

92/01/30 92/02/12

S 4 SP 411.45 B 4 SP 416.51

-5,380

166,338

94/11/01 94/11/15

S 16 GC 384.1 B 16 GC 385.5

-3,520

243,646

2,790 -820 11,700

4,800 -7,102 21,173

8,450 -2,760 8,030

21

2000 Edition

IFTAJOURNAL

A Different Way To Forecast An Index’s Behavior Based On The Very Old Principles Of Support And Resistance Ulysse-Oliver Traub, CMT INTRODUCTION

“It’s the right moment to sell your index future position, because the index trades near its resistance,” and looking at index Chart 1, the market participant will agree with that proposition from his investment advisor and probably sell his position. At first sight the investment advisor is certainly right. The index is trading near its resistance and could sell off soon, but the index chart might tell us only half of the story. The main idea of this research paper is that the resistance and support levels on index charts could give misleading trading signals, because the index chart does not tell much about the index structure. Therefore, finding resistance and support levels for each stock in an index could probably enhance the assumption that a certain resistance or support level in an index had been reached. The result of the calculated support and resistance levels (e.g. capitalization weighted) may differ from the obvious resistance and support levels suggested by the index chart. It’s also a purpose of this paper to analyze whether this calculation can enhance trading performance by preventing wrong decisions and whipsaws. BACKGROUND: THE TRADITIONAL APPROACH TO OBTAIN AN INDEX FORECAST

To be able to get an idea what could happen in the near future (next few weeks) to a stock index, a technical analyst first looks for a confirmed trend (up- or down-trendline, at least three times tested). With this basic tool, the trend analysis, he gets the feeling in which direction the market is about to move (Chart 1). The volume should confirm the trend in the index, but in this paper, volume is not taken into consideration. As soon as a valid trend up or down is found, the technical analyst searches for support levels. These levels can be defined as points where the index comes to a temporary stop in a downtrend before it starts again to move in either direction. The main reason for this phenomenon is the fact that supply is superseded by demand. For resistance levels, the same principle is valid but inversely. At these levels, demand is superseded by supply and stops the rise of an index temporarily. These levels can also be called psychological levels, because whenever they are reached investors may be willing to buy or sell because they missed that price level the last time (Chart 1). Chart 1 SMI - Chart Market Index, January 3, 1990 - December 31, 1996

The following three attributes determine how important support and resistance levels are: the longer prices trade around a certain level the more significant the level gets; the trading volume and how recently the trading took place at these levels are also two significant indicators to properly define a support and resistance level. Putting all these factors together, a technical analyst makes a forecast of the future index behavior. POSSIBLE REASONS FOR THE INACCURACY OF THE DESCRIBED METHOD

The above described approach is certainly an applicable one for individual stocks and broad market indices (e.g. S&P 500). For an index with heavily weighted companies such as the Swiss Market Index (SMI), this forecast method could lead to an inaccurate picture of support and resistance levels and could trigger unnecessary trades with potential losses. The same applies to individual stock groups in the S&P 500 where the weightings among its index members show considerable variations (e.g. S&P Auto Parts & Equipment, Table 1). Table 1

19 Index WGT US

1) 2) 3) 4)

DGL1 Index W GT

S P A U T P Member Weightings S&P Auto Parts & Equip 4 Members GT GPC ECH CTB

UN UN UN UN

GOODYEAR TIRE GENUINE PARTS CO. ECHLIN INC COOPER TIRE & RU

49.033 % 30.604 % 10.664 % 9.693 %

Source: Bloomberg INDEX CALCULATION

In this paper, the Swiss Market Index (SMI) will be used as the relevant stock index. The SMI is a market-capitalized index and is a widely used Swiss stock index for performance comparisons. It has been calculated since June 30, 1988 and had a market capitalization of SFr. 402,490.3 Mil (US $300,365.9 millions) at the end of 1996. The main reason for the development of the SMI was to create an index which represented a diversified portfolio of Swiss blue chips on which derivative products could be applied. The SMI is the only stock index in Switzerland where hedging with futures is available. From its inception in June 1988 until 1996, there have been at least 18 shares from 16 different companies in the index (in Switzerland there are different classes of shares; e.g. bearer (B), registered (R) and non-voting shares (PS or GS). Capitalization-Weighted Index The SMI is a capitalization-weighted index and is calculated as follows (dividends are not included in the SMI): Current Market Capitalization* Current Index Value = ————————————— x Index Base Value Market Capitalization Base Period

(ut = uptrend, s = support, r = resistance)

22

Source: Bloomberg

* Market capitalization = Number of tradable shares x share price

2000 Edition

IFTAJOURNAL

Weighting stocks on the basis of their market capitalizations assigns a greater significance to the major companies than to smaller ones. But even in a blue-chip index like the SMI, there are still big differences in the weightings among the index members. A closer look at the individual weightings of the stocks in the SMI shows that 6 companies, each of them having larger weighting than 5 %, together make up 73.81 % of the entire index (Table 2). Table 2 Weightings of the Member of the Swiss Market Index (June 94)

SMI - Securities Securities SMI ABB B N100 CIBA-GY B CIBA-GY R CS HOLDING B CS HOLDING R ELEKTROWATT B HOLDERBK B NESTLE B ROCHE GS RUECKV R SAND OZ R SBG R SBV B SBV R SGS SURVEILL B SMH R N10 SULZER R W,THUR R N20 ZUERICH VERS B ZUERICH VERS R

June 1994 Securities Number

Closing Market Value Price # of Securities

21 62602 159152 159151 146249 146248 201676 188058 213768 224181 124558 217194 136101 135799 42204 249748 80044 237645 84434 82878 82876

1174.0 814.0 787.0 553.0 108.5 341.0 880.0 1,121.0 6,360.0 560.0 893.0 1,158.0 391.0 194.5 1,995.0 164.0 885.0 645.0 1,316.0 1,318.0

7,739,560 3,745,170 25,369,870 23,490,730 48,710,270 8,209,850 3,767,000 38,499,026 6,819,120 11,261,710 34,239,260 20,601,020 23,516,892 27,159,836 1,156,747 15,030,000 2,202,318 7,227,722 3,769,594 5,319,856

Market Cap. (Mil CHF) Weighting 237’317.8

100%

9,086.11 3,048.57 19,966.09 12,009.37 5,285.06 2799.49 3314.98 43,157.41 43,369.60 6,306.56 23,727.81 23,855.98 9,195.03 5,282.59 2,305.72 2,484.92 1,949.05 4,661.88 4,957.02 7,011.57

3.83% 1.29% 8.41% 5.47% 2.23% 1.18% 1.40% 18.19% 18.28% 2.66% 10.00% 10.05% 3.88% 2.23% 0.97% 1.04% 0.82% 1.96% 2,09% 2.96%

B=bearer, R=registered, PC & GS= non-voting shares Source: SWX Swiss Exchange Price-Weighted Average Unlike an index, which has a base value to which current values are compared, an average is simply the sum of each component’s prices, divided by a divisor (the divisor is changed to adjust the average for splits and changes in the component stocks). Formula price stock 1 + price stock 2 ....+ price stock N price weighted average = ——-––––––––––––––––——-–––––––––––– N*

* N is called the divisor. It is adjusted as splits and component changes occur. The Dow Jones Industrial Average is probably the best-known example of a price-weighted average. Because all point changes in prices affect the average equally, the higher-priced shares have more influence on the average than the lower-priced shares (a high-priced share will change more, in point terms, than a low-priced share, hence the name price-weighted average). This is the major disadvantage of this kind of average: price per share, not total market value determines each component’s influence on the average. Table 3 shows the weightings of the Dow Jones Industrial Average based on their prices per share.

Table 3 The Weightings of the Dow Jones Components (February 97)

INDU Index WGT US 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30)

DGL8 Index W GT

I N D U Component Weightings Dow Jones Industrial Average - 30 Components IBM MO PG DD BA GE TX XON JPM MRK EK MMM CAT DIS ALD UTX AA CHV AXP KO GM GT S MCD UK IP T Z WX BS

UN UN UN UN UN UN UN UN UN UN UN UN UN UN UN UN UN UN UN UN UN UN UN UN UN UN UN UN UN UN

INTL BUS MACHINE PHILIP MORRIS CO PROCTOR & GAMBLE DU PONT (EI) BOEING CO GEN ELECTRIC TEXACO INC EXXON CORP MORGAN (JP) MERCK & CO EASTMAN KODAK MINNESOTA MINING CATERPILLAR INC DISNEY (WALT) CO ALLIEDSIGNAL INC UNITED TECH CORP ALUM CORP OF AMER CHEVRON CORP AMER EXPRESS COCA-COLA CO GEN MOTORS GOODYEAR TIRE SEARS ROEBUCK MCDONALDS CORP UNION CARBIDE INTL PAPER CO AT&T CORP WOOLWORTH CORP WESTINGHOUSE ELE BETHLEHEM STEEL

6.997 % 5.534 % 5.279 % 4.888 % 4.876 % 4.729 % 4.729 % 4.650 % 4.621 % 4.134 % 3.929 % 3.839 % 3.476 % 3.311 % 3.238 % 3.124 % 3.107 % 2.994 % 2.790 % 2.693 % 2.614 % 2.523 % 2.183 % 2.058 % 2.053 % 1.888 % 1.780 % .907 % .822 % .386 %

Source: Bloomberg INTRODUCTION TO THE CAPITALIZATION-WEIGHTED INDEX BEHAVIOR FORECAST

Since the mid nineties, the trend to invest in large capital issues has continued to accelerate worldwide. The main reason for that may lie in the steady flow of capital into mutual and pension funds, which are professionally managed portfolios. Most of these funds are under performance pressure. Almost every portfolio manager of such a fund is measured against a capitalization-weighted index (e.g. S&P, SMI) on a quarterly and yearly basis as his benchmark. Because of that pressure he avoids investing a large proportion of the portfolio into small- and mid-cap stocks as well as the risk of buying a lagging stock which would produce an underperformance. Under such circumstances small- and midcap issues have lost performance in relation to the blue-chips not only in Switzerland (Chart 2) but in most developed markets worldwide. As examples, the Russell 2000 index and Wilshire 5000 index are severely lagging behind large cap stock indices in the US.

23

2000 Edition

IFTAJOURNAL Chart 2 A comparison between the Swiss Large Companies Index, bold line and Swiss Small Companies Index, thin line, 12/94-12/96 (both are total return indices) – December 31, 1994 = 100

Table 4 SMI 1 Jan. 93 1 Feb. 93 1 Mär. 93 1 Apr. 93 1 Mai. 93 1 Jun. 93 1 Jul. 93 1 Aug. 93 1 Sep. 93 1 Okt. 93 1 Nov. 93 1 Dez. 93 30 Dez. 93

Source: Datastream To enhance performance or for hedging purposes, portfolio managers use index futures on the SMI (the SMI is the only stock index in Switzerland which has futures). For this future trading to find the right entry and exit points, the portfolio manager needs to recognize resistance and support levels in the index. As stated earlier, the thesis of this paper is that the trading could be enhanced by calculating capitalization-weighted support and resistance levels and it is assumed that such levels are different from the obvious support and resistance levels in the index chart.

2,118 2,121 2,121 2,188 2,153 2,253 2,376 2,400 2,470 2,482 2,727 2,774 2,958

obvious capitalization-weighted support resistance support resistance 2,005 2,050 2,050 2,127 2,127 2,183 2,274 2,315 2,385 2,362 2,473 2,654 -

2,107 2,128 2,145 2,183 2,196 2,271 2,335 2,419 2,502 2,502 2,723 2,742 -

1,957 1,994 2,022 2,099 2,083 2,117 2,224 2,246 2,315 2,306 2,439 2,587 -

2,105 2,159 2,153 2,203 2,220 2,264 2,374 2,432 2,469 2,482 2,662 2,731 -

Chart 3 A graphical comparison between obvious (dotted lines) and capital weighted (bold straight lines) support and resistance levels with the SMI (straight line)

ANALYSIS METHOD

Short-Term Forecast (one calendar month, month-to-month data) The calculation of the capitalization-weighted support and resistance levels in January 1993. To define support and resistance, December 1992 data are used. February 1993 is based on January 1993 data, etc. Calculation Rules In each SMI member support is taken from a proven support level in previous month’s price chart. If a stock is in a downtrend with no data in the previous month’s price range the most recent support level is taken. The same procedure is applied to define resistance levels, only with an inverse approach. A proven support level is defined as a price level where demand stops the stock from further coming down and overcomes the supply at least temporarily. When all support and resistance levels in each member of the SMI are found, they are multiplied by their capital weight, then divided by the data of the previous month. The result shows the performance from one month to the next in support and resistance levels separately. The performance is then compounded with the previous support and resistance level. The results for 1993 are shown in Table 4 and Chart 3.

24

Interpretation The results from capitalization-weighted support and resistance levels vary slightly from the obvious support and resistance levels, but neither method would have constantly produced better results. To forecast the index on monthly basis, the obvious index chart provides quite good results and serves as well as capitalizationweighted support and resistance levels as a monthly forecast tool. A BEHAVIOR FORECAST OF THE SMI IN A ONE YEAR TRAILING PERIOD (1993 AND 1994)

For this type of analysis, two years are taken into account: 1993, a bull market, and 1994, a bear market and a consolidation period. These two years will provide almost every condition we witnessed in recent years and can stand as proxies for other years. This analysis method differs slightly from the short-term forecast (Method A) above. Here we are looking for individual support and resistance levels in each security of the SMI. The following rules are applied: ■ The psychology of alternation is applied (when a resistance level is broken it becomes a support level, and vice versa). ■ If there is only one trading day under support or over resistance, the level will not change immediately; two trading days are necessary to alter a support or resistance level (daily closing prices are used).

2000 Edition

If a stock trades in new high territory, the price is equal to its resistance until the stock consolidates and a resistance is established. Chart 4 shows individual support and resistance level data as applied to ABB bearer shares, a member of the SMI.

■

IFTAJOURNAL Chart 6 The SMI (price line) with its capitalization-weighted support and resistance levels for 1994 (bold straight lines)

Chart 4 A graphical comparison between obvious (dotted straight lines) and capital weighted (bold straight lines) support and resistance levels with the SMI (price line)

To calculate the capitalization-weighted support and resistance levels, the same formula is used as to calculate the SMI index, shown under D 1. Formula current market capitalization weighted support level** Current cws* value = ———————————— x support base value market capitalization weighted support level base period

Generally speaking, a capitalization-weighted support and resistance level forms a nice trading “band” around the SMI. The index rarely falls below support and rarely breaks resistance. Taking it one step farther, the comparison between the capitalization-weighted support and resistance levels with the obvious support and resistance levels would be reached (Chart 7 for 1993 and Chart 8 for 1994). Chart 7 A graphical comparison between obvious (dotted straight lines) and and capitalization-weighted (bold lines) support and resistance levels with the SMI (price line) for 1993

* cws = capitalization-weighted support ** Market cws level = Number of tradable shares x support level value of each index security For the capitalization-weighted resistance level the same formula has been used, but instead of support levels, the resistance levels have been taken into account. The most important thing is the first setting of support and resistance levels. For December 31, 1992, the starting point, the initial support and resistance levels are set equal to the obvious support and resistance levels. Chart 5 shows the outcome of a capitalizationweighted support and resistance levels for 1993 and Chart 6 for 1994. Chart 5 The SMI (price line) with its capitalization-weighted support and resistance levels for 1993 (bold straight lines)

Interpretation The capitalization-weighted support and resistance levels seem much more dynamic. Some trades could be made where an obvious support and resistance line is far away from the price index (May 1993). On the other hand, the capitalization-weighted support and resistance levels seem much more reliable (July 1993). An example of a classic whipsaw could have been avoided by using “ongoing” capitalization-weighted support and resistance levels instead of obvious ones. Because of a certain time lag, due to the construction of the capitalization-weighted support level, it was not possible to prevent investors from being whipsawed in early September 1993. In the period between October 1993 and December 1993 neither the capitalization-weighted nor the obvious support and resistance levels gave reliable trading signals, mainly because of an extremely good performance to new highs.

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IFTAJOURNAL Chart 8 A graphical comparison between obvious (dotted) and capitalization-weighted (bold straight lines) support and resistance levels with the SMI (price line) for 1994

BIBLIOGRAPHY ■

■ ■ ■ ■ ■ ■

Edwards, R., Magee, J., Technical Analysis of Stock Trends, New York Institute of Finance, New York, sixth edition, 1992, pp 253-281, 428-434. Murphy, John J., Technical Analysis of the Futures Market, New York Institute of Finance, New York, 1986, pp. 58-68 Schuppli, Peter, Swiss Stock Guide, Verlag Finanz und Wirtschaft AG, Zurich, August 1996. Swiss Exchange, SWISSINDEX , The Index Family of Swiss Stock Exchanges, Zurich, December 1994. SWX Swiss Exchange, Monthly report, Zurich, December 1992 until December 1994 Philipp, Beat, Union Bank of Switzerland, Stock and Bond Indices, Zurich, July 1996 Data sources for charts and tables are Datastream, Bloomberg and Reuters. BIOGRAPHY

Interpretation Due to the fact that major stocks turn before averages, losses could have been avoided by looking at the capitalization-weighted support level (in early February as well as in late April, early June and September 1994). Looking at resistance levels, it was obvious that the capitalization-weighted ones gave much more reliable trading signals. In the early 1994 correction phase, previous index resistance levels during reaction rallies were higher most of the time than the capitalization-weighted resistance level, and were therefore too high to give reliable trading signals (e.g. in early and late February and early April 1994). As a simple rule, going long (b = buy on chart 8) in the SMI futures when the index was trading near its capitalization-weighted support level and closing the position (s = sell in chart 8) when it was trading near its capitalization-weighted resistance level could have produced a profitable trading year in 1994, by utilizing its support and resistance “bands”. CONCLUSION AND RECOMMENDATION

Calculating a capitalization-weighted support and resistance level in a capitalization-weighted stock market index seems to make sense, especially when the performance of a few stocks could have considerable influence on the performance of the whole index, due to their weightings (compare Table 2). The results from Charts 7 and 8 look very promising and it is certainly worth the effort to take a second look at the calculated capitalization-weighted support and resistance level before making an investment decision based only on seemingly obvious index support and resistance levels. To better forecast an index’s behavior, investors and traders should take into consideration capitalization-weighted support and resistance “bands” which might be more sensitive to a trend change in the index (Chart 8). Therefore, it can be a helpful tool to prevent anyone from being whipsawed. Another step farther ahead would be to move these capitalization-weighted support and resistance levels up, down, to the left or to the right to produce an optimized trading system. But it was not the goal of this paper to produce the one and only solution. The main result, in respect to capitalization-weighted support and resistance levels, shows that trading performances could be improved by using these levels as opposed to obvious support and resistance levels which seem to be less accurate.

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Ulysse-Oliver Traub, CMT, is currently employed by J. Henry Schroder Bank AG in Zurich, Switzerland as Senior Portfolio Manager, and is part of the asset allocation committee and a member of the Senior Management of the bank. His principal responsibility is the discretionary management of fixed income and balanced portfolios for international private clients. Before joining Schroders he worked at Pictet & Cie and Bank Leu Ltd. in institutional portfolio management. Since 1996 he has been a member of the Market Technicians Association, and his technical analysis focus is on fixed income, index futures, equities and foreign exchange rates.

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The Accuracy of Candlestick Analysis Using the German Stock Market Index (DAX) Reza Darius Montassér, CMT I. INTRODUCTION

This paper is an historical, empirical and statistical examination of the forecasting accuracy of candlestick analysis shown by taking the example of the German Stock Market Index (DAX) on a daily, weekly and monthly basis. The candlestick chart technique is one of the four best-known methods to show the course of prices. Open, high, low and close prices for the time period under study are required. Contrary to the bar chart, another important piece of information is added. The analyst not only sees the movements in prices, but, thanks to the color of the single bar, can quickly recognize whether the prices have risen or fallen within the measured period. If prices rise within the trading period, as is the case when the day’s closing price is higher than the opening, the body of the bar is white. The upper and the lower limit of the body is the open and the close. If the close is lower than the opening price, the bar’s body is black. The color of the body is very important, as one can draw the conclusion as to whether optimists or pessimists had the upper hand during a given period of time. A future trend can be forecast by combining different candles. Chart 1 Candlestick Chart

mark. This is also one of the reasons why it is the most quoted German stock market index. The examinations made go back to early 1988 (on the weekly basis from 1959). The necessary data, such as the open, high and low of the DAX, were not available before that time. The examination ends on August 31, 1996. It is important, and worth mentioning, that the DAX was in a primary uptrend during the period under study. Thus the results apply to a bull market. The examination will be presented in a diagrammatic way as follows. Each individual candlestick formation is accompanied by an analysis of its accuracy. Of course, only the important cutoffs, which provide a significant statistical message, will be given here. 1. Statistical Analysis of Single White or Black Candles 1.1. A Single White Candle After a Black Candle After the appearance of a white candle in the period under study from January 1, 1988, to August 31, 1996, the DAX closed higher the next day, or remained unchanged, in 68% of the cases. On average, the DAX gained 3.8 points each time. However, in 32% of all these cases, the DAX lost the next day. It was also noticeable during these examinations that both the height of the candle body and the upper shadow are of statistical importance. It can be seen, all in all, that the length of the upper shadow has a high correlation to the price movement on the following day, i.e. the smaller the upper shadow, the higher the probability that the next day will be positive. The statistical result was as follows: if the upper shadow was smaller than five points, a rise by an average of eight points was seen the next day. A negative trend was to be expected the following day when the upper shadow became larger than 7 points. Table 1 Dependence of the Daily Performance on the Length of the Upper Shadow in Points (White Candles) Length of Upper Shadow 2

3

4

5

6

7

8

9

15

11

10

8

4

-2

-5

-7 -10

Daily Performance

10

II. MAIN SECTION

Contrary to the bar or line chart analysis, the forecast quality of the candlestick analysis can be derived from statistics very well. There is only limited scope for subjective interpretations, thanks to the precise rules. For this kind of analysis, it is, of course, also necessary to consider single candlestick formations in the context of price movements as a whole. That means that here, too, any situation has to be evaluated individually in order to relativize the message of the candle signals. However, the signals per se are set off by the basic rules of the candlestick method and are unambiguous. The following thesis is to make use of this advantage so that the significance of several fundamental candlestick formations for the German stock market is to be tested. Because an examination of individual shares or sectors is beyond the scope of this thesis, the author concentrates on an analysis of the German stock market index (DAX). The DAX comprises the 30 German corporations with the highest outside share capital. The index is capitalization-weighted and is statistically adjusted should there be dividend payments or other corrections (such as capital increases, capitalization issues). The DAX is a performance index, which means it can be used as a bench-

Chart 2 Dependence of the Daily Performance on the Length of the Upper Shadow in Points (White Candles)

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IFTAJOURNAL Table 1 shows that there is a statistical connection between the length of the upper shadow and the daily performance of the following day. The coefficient of determination R2 of 0.98 shows a very strong statistical relation between the upper shadow’s length and the daily performance for the given period of time. But the size of the white candle body also plays a crucial role. In general, it can be assumed that the projection for the next day is directly dependent on the size of the candle body. The following two factors became apparent during the course of the study: 1. The larger a white body, the higher the probability that the following day will close in the positive zone, 2. the larger a white body, the higher the median price gain the next day. The cutoff for the significance of the above-mentioned factors is around 5 DAX points. Only from this body height or greater can a high statistical probability be assumed.

limit for black bodies amounted to 5 points. The examinations led to the following result: Table 3 Dependence of the Daily Performance on the Height of the Body in Points (Black Candles) height of the body

5

6

daily performance

-15

-16

7 -16

8 -17

9 -18

10 -19

11 -20

Chart 4 Dependence of the Daily Performance on the Height of the Body in Points (Black Candles)

Table 2 Dependence of the Daily Performance on the Height of the Body in Points (White Candles) Height of the Body

5

6

7

8

9

10

11

Daily Performance

4

5

7

7

8

9

10

Chart 3 Dependence of the Daily Performance on the Height of the Body in Points (White Candles)

The graph shows what importance the body length of a black candle has on a Friday. The larger the black candle’s body on this day, the larger the daily loss on the following Monday. Within the period under observation, this applied with a statistical probability of 71%. The upper shadows length of black bodies did not have any significant statistical advantage. 1.3 Hammer and Hanging Man In candlestick analysis, single candles with certain lines have a certain meaning and thus special names. A small candle with a long lower shadow and a very small upper shadow (or none at all) is called Hammer or Hanging Man depending on whether it occurs after a downtrend or an uptrend. The statistical probability of the above-mentioned cases (height of the body, length of the upper shadow) is about 75% each. 1.2. A Single Black Candle after a White Candle After a black candle the DAX loses on average 1.8 points the following day. However, the statistical probability that the prices will fall the day after a black candle is about 50% and is thus rather coincidental. This “bad” statistical probability is connected with the fact that the DAX was in a primary uptrend during the period under observation so that single black candles did not have a high forecasting ability. This becomes evident if we look at secondary phases of consolidation, such as from September 1992 to February 1993. During these times the probability increased to more than 60%. In this regard, the height of the candle body, combined with the week day, played a statistically more important role. It was obvious that the black body’s heights themselves did not imply any significant statistical information on the further course, so that we have to assume a random result here. The height of the black bodies becomes interesting and statistically significant if it is combined with individual week days. Thus, filtering out on which week days the height of the black bodies showed significant correlations with future price movements. In this respect, Friday was the conspicuous and only statistically significant day. The significant minimum

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1.3.1 The Hammer Ideally, the Hammer appears at the end of a downtrend. Here prices fall sharply once again, but recover at the end of the day and finally close in the upper third of the movement as a whole. This movement provides evidence that sentiment has changed considerably during the course and that bulls are now gaining the upper hand. Chart 5 Hammer

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1.3.2 Hanging Man The Hanging Man is the equivalent to the Hammer and appears after an uptrend. At the outset, the market is bullish and prices continue to rise, but then they go down continuously and finally fall below the previous day’s close. At the end of the session, they start rising again and close in the upper third of the movement as a whole, near the open. The open is ideally the highest price or very close to it (chart 6). The psychograph of a Hanging Man is plausible. When the session opens and during its beginning phase, optimists have the upper hand. During the course of the session, however, they increasingly lose control and the pessimists gain ground. Although they succeed in making prices rise again at the end of the session, there is no change for the better, and prices close near the opening price. This shows clearly that the mood has noticeably deteriorated and the (buying) power is coming to an end. The next day’s opening will then confirm this. If the market opens below prior day’s close, it is almost certain that the bears have won the position. Chart 6 Hanging Man

1.3.3 Statistical Evaluation of Hanging Man and Hammer The statistical examination analyzed both formations at first. A Hammer and a Hanging Man appeared 68 times in the course of the DAX during the period under observation. On average, the DAX lost 9.5 points. Looking at each individually, the Hanging Man appeared 32 times. In around 66% of these cases, the DAX fell in the following days so that this formation is of high statistical significance. On average, it lost around 8 points three days later. The Hammer appeared 37 times. This formation proved to be of very high statistical significance with a hit ratio of 72% (in 72% the DAX rose in the following period) and an average 20-point increase in prices during the next three days. Both formations showed a very good forecast quality, although they consisted of “only” one candle. It was also conspicuous that the black Hammers’ accuracy was three times as high as that of the white ones. The same applies to the Hanging Man whose hit ratio, when black, is twice as high as when white. The white candles (Hanging Man and Hammer) appeared in the majority of cases as one- to three-day corrections and were good points of entry for a continuation of the trend. After a white Hammer, which had incidentally occurred 17 times, prices dropped by 7.5 points on average. However, the black candles often indicated a trend reversal and led to a sustained rise in prices. 1.3.4 The Inverted Hammer and the Shooting Star The Inverted Hammer and the Shooting Star are the close relations of the above-mentioned formations. As the name already implies, it is an Inverted Hammer formation: a small, white or black candle body without or almost without a lower shadow and with a very long upper shadow. Whether this formation appears at the end of an uptrend or downtrend has an influence on its name. At the end of a downtrend it is called Inverted Hammer and at the end of an uptrend a Shooting Star. Both indicate a trend reversal and are thus reversal patterns.

Chart 7 Inverted Hammer

1.3.5 Statistical Evaluation of Inverted Hammer and Shooting Star The examinations made clear that neither the Inverted Hammer nor the Shooting Star indicated a significant trend reversal; on average the result was even negative, i.e. prices continued their previous trend. Therefore, the formations were carried out according to the color of the real bodies. The result was as follows: ● White Shooting Star: There were seven observations. On average the DAX stood 1.5 points lower after three days. ● Black Shooting Star: It provided a very positive result. There were ten observations and each timeprices were around 13 points lower during the following three days. ● Black Inverted Hammer: The 13 formations led to a price advance of an average 2.5 points after three days. ● White Inverted Hammer: It occurred nine times. On average, the DAX increased by 11 points and was able to gain substantially in the time to follow. Chart 8 Shooting Star

Based on this analysis it becomes clear, at least for the DAX, that the color of the real body is of crucial importance for performance. A black Shooting Star for instance, has a very high statistical significance as far as accuracy and performance are concerned. The same applies to the white Inverted Hammer. It is obvious that the colors of the real bodies equal the trend to be expected. This statement does not, of course, lay claim to completeness and general validity, but it encourages the scrutiny of the currently valid theory that the color does not play a decisive role in formations with one candle. 2. STATISTICAL ANALYSIS OF CANDLESTICK FORMATIONS WITH TWO CANDLES

2.1 Trend Reversal Formations 2.1.1a The Positive Engulfing Pattern Positive Engulfing plays a key role among formations with two candles. The formation consists of one small black candle immediately followed by a white candle. Here it is important that the white body completely engulfs the black body: in other words, the following day opens below the previous day’s close. At the end of the day

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IFTAJOURNAL the prices will then be in the positive zone. The formation appears at the likely end of a downtrend and is a clear sign that optimists are gaining the upper hand. Chart 9 Positive Engulfing Pattern

Statistically, the Positive Engulfing Pattern can be easily determined. From 1988 until 1996 the DAX had this formation 22 times. All in all, prices were in 14 cases higher in the next days and lower in eight of the cases, so that 64% of the time, the Positive Engulfing Pattern had correctly indicated the direction. On average, the DAX was 8 points higher in the three following days; this implies a reliable quality of the forecast. If the subsequent day is taken as a measure, the result slightly deteriorates to 7 points. Within the framework of this study it seemed to be important to answer the question as to how far the signal would carry such a formation. This is shown in the following table.

However, the most dramatic result was to be seen between the third and the tenth day on average. 2.1.1.b The Positive Doji Engulfing Pattern The Positive Doji Engulfing Pattern is a special kind of Positive Engulfing. Here the body of the first black candle becomes as small as a line and thus forms the Doji. A Doji is a very important figure in the candlestick analysis, as some uncertainty can be recognized during this period of observation. The form of the candle shows (open and closing prices are equal or near each other [Chart 11]) that neither optimists nor pessimists have succeeded in moving the market in “their direction.” Thus a Doji intensifies the structure of a formation substantially. A Doji Engulfing Pattern appeared during the primary intermediate uptrend of the DAX in early 1995. After four falling days in the uptrend (tertiary consolidation), a Doji Engulfing Pattern on April 19 and 20, 1995, indicated the end of the tertiary consolidation and a renewed start of the primary intermediate movement. This formation occurred 18 times during the period under observation. All in all, 12 increases in prices were registered; only 6 times were the prices lower in the following days. Chart 11 Positive Doji Engulfing Pattern

Table 4 Profit Length of the Positive Engulfing Pattern Days

Hit Ratio

1 2 3 4 5 6 7 8 9 10 11 12 13

68% 59% 64% 64% 64% 63% 65% 65% 64% 60% 58% 53% 51%

Median Performance

7.2 7.6 8.0 14.0 15.7 13.2 13.5 13.3 19.9 13.3 7.4 3.1 0.5

2.1.2.a The Negative Engulfing Pattern The Negative Engulfing Pattern is the inversion of the Positive Engulfing Pattern. It includes a white small candle which is embraced by a black candle following behind it. Thus the opening of the second day is above the closing price of the first day. The second day’s close is below the opening of the first day. Chart 12 Negative Engulfing Pattern

Chart 10 Profit Length of the Positive Engulfing Pattern

The pattern shows that the effects of the Positive Engulfing Pattern were on average noticeable up to the 13th day inclusively.

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The Negative Engulfing Pattern clearly shows a change in sentiment on the market. At the beginning, prices still open positive, but on the close of the day they are decisively in the negative zones. The statistical predictive ability of Negative Engulfing is as follows. Thirty one Negative Engulfing Patterns were seen during the period under study. In 65% of these cases, the DAX was lower three days later. Looking at the 31 selling signals, the DAX was on average 7 points lower after three days. Here the high accuracy is impressive. As already mentioned before, the DAX was in a primary uptrend during the period of analysis. This corresponds to a positive upward momentum and thus increases the risk of a short position. For the Negative Engulfing Pattern an extension statistic can also be calculated.

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Table 5 Profit Length of the Negative Engulfing Pattern Days

Accuracy

Median Performance

1 2 3 4 5 6 7 8 9 10

58% 55% 65% 63% 63% 59% 58% 57% 57% 56%

4.9 3.3 7.0 7.8 7.2 3.8 4.7 4.9 -0.2 -3.5

was in a primary uptrend during the period under study and the bear cycle represented only secondary corrections. 2.1.3 Harami The Harami is also one of the important formations of the candlestick analysis. It is made up of two candles. • In case of the Positive Harami, first day’s black body engulfs the white body following on the second day. • In case of the Negative Harami, first day’s white body engulfs the black body following on the second day. 2.1.3.a The Positive Harami Chart 15 Positive Harami

Chart 9 clearly shows that the profit length of the Negative Engulfing Pattern is shorter than that of the Positive Engulfing. The downtrend is already over after an average of nine days and another uptrend begins. Chart 13 Profit Length of the Negative Engulfing Pattern

2.1.2.b The Negative Engulfing Doji Pattern The Negative Engulfing Pattern is also intensified by a Doji. Here the small white candle of the first day shrinks to a Doji. Chart 14 Negative Engulfing Doji Pattern

In the period under study, the Negative Doji Engulfing Pattern occurred 20 times. For instance, a Negative Doji Engulfing Pattern on September 19 and 20, 1995, led to a correction phase of the 1995 bull market and corrected 50% of the previous uptrend. However, the DAX lost on average only 5 points after three days. In around 60% of the time, lower prices had to be expected. If we calculate the Negative Doji Engulfings according to the hit ratio of Negative Engulfing Patterns as laid down in 2.1.2, median performance improves substantially. Then the average loss after three days markedly increases from 7 to 11.5 points. In contrast to the assumption that a Doji intensifies the formation, the performance of the Negative Doji Pattern was disappointing. Both the accuracy of 60% and median performance were worse than that of the “normal” Negative Engulfing Pattern. This anomaly is probably – as in other cases, too – due to the fact that the DAX

The first day is characterized by a gloomy mood. Prices fall continuously. On the second day, there is a change in sentiment, prices open already higher and close in the positive zone, although below the previous day’s opening price. In the second phase of the 1993 uptrend of the DAX, after the secondary consolidation, which lasted from early 1994 to the fall of 1995, a Positive Harami appeared on November 23 and 24, 1995. After this formation, the DAX succeeded in surmounting its secondary line of resistance at 2,120 points for a sustained period of time and in finishing the secondary consolidation. In the next few months, the equity market continued to rise and reached the current 2,650 points. The Positive Harami appeared 26 times during the period under observation. However, the statistical predictive ability was not very significant. Only in 54% of the observations, was the DAX to close higher in the next three days. An extension calculation was not able to deliver a statistically significant assumption. Therefore, a closer analysis is here dispensed with. Thus the Positive Harami obviously was less reliable than the Engulfing Pattern. 2.1.3.b The Positive Harami Cross When the second white body shrinks to a Doji, the pattern is referred to as a Positive Harami Cross, thus putting the downtrend, which has so far been intact, into question. Chart 16 Positive Harami Cross

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IFTAJOURNAL The DAX in August 1992 is a good example of the fact that the Doji of the Positive Harami Cross signals a change in sentiment. At that time, the Doji indicated an apparent improvement in market sentiment. The formation appeared in the last week of August . A sharp price increase which helped the DAX break its secondary resistance line at 1,525 points followed. The signals of the Positive Harami Cross are more unambiguous than those of the Positive Engulfing Pattern. For instance, 65% of the 20 formations during the period under study announced rising prices in the next three days. Prices were on average 20 points higher. 2.1.3.c The Negative Harami A Negative Harami shows a large white candle of the first day followed by a smaller black candle on the second day (see chart 17). Here too, the body of the black candle must be completely engulfed by the body of the white candle.

2.2 Examination of Trend Reversal and Trend Consolidation Formations 2.2.1 Formations with Positive Implications 2.2.1.a The Positive In-Neck Pattern As a rule, this formation appears at the end of a downtrend. The first day is usually still marked by a negative sentiment. The second day of the formation is characterized by an extreme initial weakness. However, during the session the situation changes considerably and prices start to rise again (see chart 19). At the close of the market, they have again reached the previous day’s price level. Normally, this initiates a short-term trend reversal. Chart 19 Positive In-Neck Pattern

Chart 17 Negative Harami

The Negative Harami sets off a selling signal and indicates the end of a euphoric mood. The DAX had 26 Negative Haramis during the period under study. In 69% of these cases, prices fell in the next three days. Prices were on average 16 points lower. This formation has so far been the only one which showed high accuracy on both the buying side and the selling side during the course of these examinations. The other formations mentioned so far were mostly only convincing and statistically significant from a one-sided view, i.e. either as a buying signal or a selling signal.

2.2.1.b The Positive Thrusting Pattern If prices continue to rise on this day, but do not exceed the midpoint (Thrusting Line) of the black body, a Positive Thrusting Pattern will result, which has the same implications as the In-Neck Pattern (see chart 20). Chart 20 Positive Thrusting Pattern

2.1.3.d The Negative Harami Cross Chart 18 Negative Harami Cross

2.2.1.c The Positive Piercing Pattern The Piercing Pattern is an intensification. Here the midpoint (Thrusting Line) is pierced and the white body ends somewhere in the upper half of the preceding black candle (see chart 21). Chart 21 Positive Piercing Pattern

The Negative Harami Cross is similar to the Negative Harami, the only difference being that the second day is a Doji. On the one hand, this shows a certain uncertainty on the market and on the other, optimists also lose a lot of their strength. The statistical reliability was 55% in those 11 cases which appeared during the period under observation. Thus it has to be considered to be not as significant, but rather more as a coincidence. The ideal extension of the forecast is here also three days. After ten days, the influence of this formation can no longer be felt.

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As the above-mentioned formations can appear at the end of a trend (trend reversal) or during a trend (trend confirming), it is hard to determine the statistical reliability. A consistent analysis of the market situation is thus very important so that a context-related integration of the formation should then be made. This is also

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proved by the author’s statistical examinations. All in all, the Positive In-Neck Patterns, Positive Thrusting Patterns and Positive Piercing Patterns appeared with a frequency of 96 during the period under observation. In 51% of these occurrences the DAX was higher in the next three days, in 49% the DAX was lower in the following three days. This highlights its low statistical reliability and its high degree of randomness.

Chart 24 Dark Cloud Cover

2.2.2 Formations with Negative implications 2.2.2.a The Negative In-Neck Pattern This formation has a negative implication. The first candle has a white body. The second day initially opens in a euphoric mood and prices continue to rise. But the sentiment changes during the trading day and prices begin to fall. At the end of the session, the previous day’s close is more or less reached (see chart 22). This can be seen as a first sign of a shift in market assessment so that selling may take place in the next few days. Chart 22 Negative In-Neck Pattern

The forecasting effect of these three formations is also not very concrete. They can all occur as both a consolidation formation or a trend reversal formation. Here too, individual candle formations should be judged only within their context. The statistical examination does also not allow any significant statement. In the period under observation 106 cases of these formations were recognized in all. In 52% of these occurrences the DAX was lower in the next three days and in 48% it was higher. Here too, it has to be assumed that the sole observation of formations can provide only a random result. 3. STATISTICAL EXAMINATION OF CANDLESTICK FORMATIONS WITH THREE CANDLES

2.2.2.b The Negative Thrusting Pattern However, if prices fall even below the neck line on the second day and hit the Thrusting Line, a Negative Thrusting Pattern results. Consequently the implication of this formation is slightly more negative.

3.1 The Morning Star The Morning Star is made up of a large black candle, a lowerplaced smaller black candle followed by a higher-placed larger white candle (see chart 25). The formation clearly shows the turnaround in sentiment within a few days. The bearish sentiment is still very high on the first day. The second day also opens weak, but during the session pressure noticeably eases. Finally the third day opens more buoyant and ends much firmer.

Chart 23 Negative Thrusting Pattern

Chart 25 Morning Star

2.2.2.c Dark Cloud Cover If the second day drops below the Thrusting Line and closes in the lower half of the preceding black candle, a Dark Cloud Cover results. This formation shows very clearly that the sentiment seems to be changing, and has thus the most negative effects.

The Star can be black or white; in principle, this does not have any influence on the Morning Star’s message. 3.1.1 The Morning Doji Star It is also possible that the Star appears as a Doji. According to the theory, this leads to an intensification of the signal (see chart 26).

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IFTAJOURNAL Chart 26 Morning Doji Star

at 51% during the period under study and thus not statistically significant. 3.3 Three White Soldiers This formation shows that market players’ confidence is on the rise. There are positive price changes every day compared with the previous day. The positive momentum increases and each individual day closes very near to its high. Chart 29 Three White Soldiers

Sixty five Morning Stars and Morning Doji Stars occurred in the period under examination. In 61% of these cases prices were higher within three days. The DAX was able to gain 7 points on average. Although the statistical significance was not very high, very good results could be achieved with the help of consistent trend and indicator analysis. 3.2. The Evening Star This is the counterpart of the Morning Star and leads to a selling signal after the formation has been completed. Market players’ psychology is similar to that with the Morning Star. The first day is determined by much optimism, prices are still rising strongly. The second day also shows its best side, prices start somewhat higher, but then they lose a considerable amount of strength and close only slightly higher. On the third day the sentiment changes, as prices open lower and close noticeably weaker. Chart 27 Evening Star

Statistically, this formation is of great significance. It occurred 35 times in the period under examination (1/1/88-8/31/96). In 59% of these cases it had positive implications and led to a DAX gain of 7 points on average. 3.4 Three Crows This formation shows that investors’ confidence is declining. After an uptrend, prices begin to fall and drop to a closing low. Ideally, prices fall below the open of the previous (white) candles. In the following two days, prices continue to fall and close near their allday low and below the previous day’s closing prices (see chart 30). These three candles with the long black bodies point towards a clear deterioration in market sentiment and signal a further drop in prices. Chart 30 Three Crows

3.2.1 The Evening Doji Star The more intense form of the Evening Star occurs when the Star shrinks to a Doji. Chart 28 Evening Doji Star

The statistical predictive power of the Three Crows is also significant. The Three Crows occurred 19 times in the period under study. In 62% of these cases, the DAX lost after three days and was on the average of overall events 10 points lower. 4. STATISTICAL ANALYSIS OF WEEKLY CANDLES

Since Monday’s opening price and Friday’s close is enough for the analysis of the weekly candle, it was possible to analyze the DAX over a longer period of time. The analysis thus goes back to 1959. The statistical significance of Evening Stars is very low. Some cases have precisely indicated the trend reversal towards a corrective movement after a longer uptrend. But the formation of the Evening Star was very often only a short period of consolidation, which lasted only one to two days. The hit ratio of Evening Stars was

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4.1 General Statistical Data From 1959 to 1996 the DAX gained 1,693 points, giving an increase of an average of 0.9 points per week. All in all, 1,864 candles could be drawn; 884 of them were white, 751 were black. After a white candle the DAX rose by around 1.9 points in the following week, and after a black candle it fell by 0.3 points on average. But there were also weeks in which prices remained nearly unchanged,

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in other words when Doji candles appeared. 234 Dojis of the DAX were registered in the period under examination. On average, the DAX rose by 1 point afterwards; this comes very close to the median rise of the DAX of 0.9 points over the whole period. 4.2 Consequences of the Body Height of Weekly Candles As already mentioned, as far as daily candles were concerned, the height of the body allows assumptions concerning the further development of the DAX. 4.2.1 Weekly White Candles Examinations have shown that the length of the candles’ bodies should be at least 28 points for a statistically significant statement. With a body length of 28 points, the DAX rose on average by 5 points, with a body of 40 points, the increase was 7.5 points and with a body of 50 points, the increase was around 10 points in the following week. Table 6 Dependence of the Weekly Performance of White Candles on the Height of the Body Body Height Daily Performance

28

30

35

40

45

50

55

5

6.2

7.5

8

8.9

10

11.4

Chart 31 Dependence of the Weekly Performance on the Height of the Body

Table 7 Profit Length of the Positive Engulfing Pattern (Weekly) Weeks

1 2 3 4 5 6 7

Hit Ratio

Median Performance

66% 68% 68% 69% 62% 60% 58%

1.9 5.4 4.1 8.2 8.5 9.0 12.0

Table 7 shows that the maximum of the Positive Engulfing Pattern’s statistically positive effect is reached after four weeks on average. 4.3.2 The Weekly Negative Engulfing Pattern The predictive ability of this formation was much worse. A positive performance can on average only be found during the first two weeks after the appearance of this formation. The DAX lost after one week around 2 points on average, after two weeks only 0.5 points, and in the following weeks prices started to rise again. Up until the second week, the hit ratio stayed in significant regions with 63%, but then it sank rapidly and reached very unsatisfactory results. This also statistically confirms the secondary correction of the Dow Theory. 4.4 The Weekly Haramis Haramis play a major role on a weekly basis as well. Obvious differences between the Positive and the Negative Harami were also to be seen here. 4.4.1 The Positive Harami (Weekly) The predictive power of the Positive Harami is not as good as that of the Engulfing Pattern. In the first one to two weeks, the DAX fell on average 2 to 4 points, then in the following four to seven weeks, prices rose by 18 points on average. Table 8 Profit Length of the Positive Harami (Weekly)

4.2.2 Weekly Black Candles As far as black candles are concerned, there is no statistically significant size of the body which forecasts further trends. The black candles’ trend mostly only continues for a few weeks. Relatively long black candles for a short period of time are characteristic, but they do not deliver any sustained indication for further price movements. This result seems to be obvious if one is aware of the fact that the German equity market was in a primary uptrend during the whole period under study so that black candles were mostly secondary corrections. According to the Dow Theory, it is well-known that those candles are of a short-term nature. 4.3 Weekly: Engulfing Pattern Similar to the daily candles, the Engulfing Pattern provides a high statistical significance in its weekly version, too. There is also a clear difference between the Positive Engulfing and the Negative Engulfing Patterns. 4.3.1 The Weekly Positive Engulfing Pattern This formation has a high hit ratio of 68%. The resulting high statistical significance makes this formation an important weekly structure.

Weeks

Hit Ratio

Median Performance

1 2 3 4 5 6 7 8 9 10

44% 46% 46% 60% 62% 63% 68% 62% 60% 51%

-2 -3 -1 5 8 12 18 16 16 11

Table 8 shows that the Positive Harami needs up to three weeks start-up time to have a statistically significant impact. Then, however, the effect is very positive and the DAX rises for a sustained period of time. It is important to mention that during the first one to three weeks, prices do not fall significantly. As a rule only a “basis formation” develops. 4.4.2 The Negative Harami (Weekly) The statistical effects of the Negative Harami were only very small. Prices fell slightly only in the first week after the appearance

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IFTAJOURNAL of this formation, on average by 0.6 points. Prices advanced in the following weeks so that the DAX stood on average 5.7 points higher after four to seven weeks. The Negative Harami proved to be only a rather “slight” brake during the uptrend and thus showed sideward tendencies. It is interesting that prices declined sharply after some individual Negative Haramis despite their statistically weak predictive power. This can be seen, for instance, in the second week of April 1975 and 1976. This shows clearly the importance of the first following week. Only if this particular week confirms the Negative Harami, with a window or with larger price decreases (dropping below the support lines), can it be assumed that further strong declines will follow. This was the case for the DAX in over 85% of the heavy price declines. 4.5 Hanging Man, Hammer, Shooting Star and Inverted Hammer The predictive power of these single candle formations was more evident. In the years from 1959 to 1996, 220 Hammer, Hanging Man, Shooting Stars and Inverted Hammer formations could be counted. All in all, a significant movement was to be recognized only after five to six weeks. 4.5.1 Hammer and Inverted Hammer When the Hammer occurred, the DAX was around 12 points higher five weeks later. The hit ratio stood at a significant 72%. The forecasting effect of the Inverted Hammer was not that high. After five weeks the DAX had only increased by 2.7 points on average. The hit ratio was 56%. 4.5.2 Shooting Star and Hanging Man Shooting Star and Hanging Man did not produce any statistically significant forecast. Prices were on average 2.6 points higher so that the predicting effect was negative. The positive momentum of the primary uptrend is probably the major reason here, too. 4.6 Formation of Series The first observation of weekly candles already makes it clear that they tend to form series. A white candle mostly does not occur alone; it is normally followed by several other white ones, leading to a trend. The creation of a trend can most easily be proved by means of the normal distribution. From 1959 until 1996, 1,092 weekly white candles or weekly Dojis occurred. 201 appeared as a series of one, i.e. black candles were in front and behind them. However, according to normal distribution, there should have been 273 series of one. This shows clearly that series of one emerge less frequently (-35%) than in the normal distribution. A similar result was produced by the series of two. 137 would have been likely overall, but there actually were only 96. The series of three occurred only 62 times instead of 68. The picture changed considerably from series of four upwards. Here 44 appeared, although only 34 were to be expected according to the Gaussian distribution. Table 9 shows that this trend continues.

Table 9 Formation of Series of White and Doji Candles (Weekly) Number of Candles

Real Occurrence

1 2 3 4 5 6 7 8 9 10 11 12 13

201 96 62 44 23 11 6 5 3 2 1

Normal Distribution

273 137 68 34 17 8 4 2 -

Just the fact that the candle events are always above normal distribution from the series of four on, contradicts the random walk hypothesis and shows that the market is very “trendy.” Of course, it is possible to take advantage of this insight. The result is as follows: Table 10 Probability of the Series Formation of White and Doji Candles (Weekly) Number of Candles After 1 After 2 After 3 After 4 After 5 After 7

Probability of Another White Candle 56% 62% 54% 56% 62% 68%

Thus, the probability that prices will rise one more week is highest after the seventh week. From this week on, the probability of prices climbing up further falls rapidly. It seems, therefore, to be logical that more than 66% of the corrections took place between the seventh and the eleventh week. For the DAX, the seventh week is a good opportunity to take profits and to wait for a secondary correction. Such an analysis cannot be carried out for black candles. The normal distribution of these candles is too strong and statistically not very predictive. It can only be seen that black candles apparently occur more coincidentally and more vehemently, in other words “only” as correction periods during the primary uptrend. 5. STATISTICAL ANALYSIS OF MONTHLY CANDLES

Due to the very meager basis of monthly figures for the DAX, the author was not able to make a significant statement about the forecasting effect of the 427 monthly candles (1959-1996). The examination of the predictive effect of individual formations such as Haramis or Engulfing Patterns always proved to be statistically nonsignificant. It must be assumed that the parent population of 427 candles is not enough for a statistical examination. However, it is also possible that the psychological factors, which build the foundation of the candlestick analysis, lose their effects during a period of one month so that other factors influencing the market (fundamental situation, political environment, cyclical fluctuations, portfolio-based considerations of fund managers) gain more weight and give the market the decisive stimulus in one direction. Within this overall framework the market moves within a certain fluctua-

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tion range, which can then be explained on a weekly and daily basis by means of the candlestick analysis. III. CONCLUSION

This statistical examination shows that the following criteria are of great importance for the candlestick analysis:

IV. BIBLIOGRAPHY ■ ■ ■

1. Context Dependence of the Candlestick Analysis In the wake of these examinations, it becomes evident that only a selection of candle formations has a really significant and statistically provable forecasting accuracy. For the DAX, all of the positive candle formations had a high hit ratio (average 70%). However, candle formations which signaled falling prices showed a bad or negative performance overall. This can be attributed to the fact that the DAX was in a primary uptrend during the whole period analyzed, and thus followed a positive upward momentum. Those candle formations which predicted falling prices only showed good results in secondary consolidation periods. Signals of candle formations should only be analyzed and evaluated in connection with the market context. 2. Confirmation of Formations Another important insight of this study is the fact that all candle formations should be confirmed by the trend in prices on the following day. Such confirmation increased the hit ratio for the DAX even further to between 63% and 70%. All signals of candle formations should be confirmed on the following day. 3. The Period Under Observation The performance of candle formations also depended to a large extent on the observation period. On a weekly basis the results were only significant for some of the candles, for instance, Engulfing Patterns, Haramis and Hammers. A new additional aspect is the high statistical predictive ability of uniform candle series, which cannot be found in such a distinct form in daily analysis. If the period under study is enlarged in a month, the significance of many candle formations – at least for the DAX – will be minimized to a random level. This seems to be logical, if one is aware of the fact that candle formations are nothing but direct positive and negative market forces. The “clearest form” of these forces is included in one full trading day, whose two most important points are the opening and the closing price. Around these points, not only the highest daily trading activity can be noticed, but the relationship between these two “fixed points” helps to derive conclusions about the strength of the optimists and the pessimists. The more the daily relationship is left to one side, the more distorted the above-mentioned factors become, so that the informative value of candle formations decreases on average from the daily to the monthly observation. The same applies also to intraday analyses. Here too, a rapid fall in the reliability of formations can be seen. It must be considered that signals of candle formations are dependent on the observation period.

■ ■ ■ ■ ■

Sherry, Clifford J., Mathematics of Technical Analysis, Chicago, Illinois, Probus Publishing Company, 1992. Morris, Greg, East Meets West: Candlepower Charting, Technical Analysis of Stocks and Commodities, September 1991. Murphy, John J., Technical Analysis of the Futures Markets, New York: New York Institute of Finance, 1986. Neter, John, Applied Statistics, Boston, Allyn and Bacon, 1993. Nison, Steve, Japanese Candlestick Charting Techniques, New York: New York Institute of Finance, 1991. Pring, Martin, Technical Analysis Explained, New York: McGraw Hill, Third Edition, 1991. Shimzu, Seiki, The Japanese Chart of Charts, Tokyo Futures Trading Publishing Co., 1986. Wagner, Garry S., Pattern Recognition and Candlesticks, Stocks & Commodities, September 1991. BIOGRAPHY

Reza Montassér is Chief Technical Analyst and Market Strategist with Bankhaus Reuschel & Co., a German private bank in Munich. He began his career at Merrill Lynch in Munich. Reza received his undergraduate degree and his Master’s Degree at Ludwig Maximilians University, Munich and is currently doing Doctorate studies in the field of technical analysis there. His early education was received in schools in Munich, Cairo, Teheran and Bern. Reza has appeared on German news television and has published articles for financial magazines. He is writing a book about the theoretical evolution of technical analysis. He can be reached at [email protected], or log onto his website: www.markttechnik.com.

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Predicting the Exchange Rate: A Comparison of Econometric Models, Neural Networks and Trading Systems Giampaolo Gabbi, Ruggero Colombo, Riccardo Bramante, Maria Paola Viola, Paolo de Vito, Alberto Tumietto INTRODUCTION AND PURPOSE

Financial literature offers a number of papers in which trading systems, econometric or neural network models [Zhang, Patuwo, Hu, 1998] are applied. The purpose of the paper is to find out whether these methodologies applied to high frequency financial time series can generate “good” forecasts [Gabbi, 1999]. The DEM/USD high frequency time series (recorded during 1998 every 5, 10, 20, 30 and 60 minutes) show, among their properties tested with ADF, Ljung-Box, correlation dimension, BDS and Lyapunov exponent, the existence of non linear dependence not explained by deterministic chaos. This result allows us to apply different econometric models (ARCHGARCH and state-space) and neural networks (feed-forward backpropagation and general regression), both to in-sample and out-of-sample data and compare outputs with an algorithmic trading system. The best forecasts, for each model category, are “good” if compared with random walk, but statistical errors remain too high to consider them useful in trading. Outcomes are more interesting when the expected output is a signal for position taking. For all the frequencies, forecasting models generate better results than Monte Carlo simulations; in terms of reward/risk index, econometric outputs over-perform neural networks. Non linear and non-chaotic properties of financial time series seem to be theoretically coherent with the inability to fit the statistical pattern and the goodness of directional outputs. We will try to give answers to the following questions: 1. can structural and black box models be applied in forecasting financial high frequency data characterised neither by random walk nor by chaotic patterns? 2. are technical analysis indicators useful in predicting time series dynamics? DATA DESCRIPTION AND PROPERTIES

High frequency time series examined are recorded on “minute by minute” data for the exchange rate Deutsche Mark – US Dollar (DEM/USD) during the period January 12, 1998 to May 8, 1998. From the original data we have then obtained lower frequency time series (5, 10, 20, 30 and 60 minutes). For all the cases (Table 1), in order to exclude the weekend effect, we consider a period of “business time,” withholding the observations included in the time span from Friday at 22.30 GMT to the following Sunday at 22.30 GMT. Table 1 Time Series Number of Observations Frequency DEM/USD n° observations 5’ 21,769 10’ 11,513 20’ 5,962 30’ 4,012 60’ 2,035

All our models are estimated using daily logarithmic returns (r t) of the exchange rate. For all the time series we verified the presence of unit roots, through the τ ADF test (Augmented Dickey-Fuller), also considered for the case τµ (with constant term) and τt (with constant term and trend). Results show it is always possible to reject the null hypothesis of non-stationary data.

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Table 2 displays some properties (coherently with Muller, Dacorogna, Pictet, 1995): time series are characterised by asymmetry and high leptokurtosis (even if decreasing for lower frequencies). The normality hypothesis has been refused through the JarqueBera tests. Data Independence and Autocorrelation Analysis The evaluation of the existence of serial correlation among data, essential for the phase of the model specification through AR and/ or MA components, has been achieved with the autocorrelation coefficients, computed for the first five lags and for time difference of 50, 100, 150, 200 periods: results allow to underline a significant first-order autocorrelation, with increasing intensity as frequency decreases. Comparable results are obtained through the Ljung-Box Q statistic which confirms the presence of serially correlated observations. We also computed Q’ statistics in order to avoid the risk to undervalue the phenomenon in case of conditional heteroskedasticity [Diebold, 1988]. The test values have not changed for any of the frequencies of DEM/USD. Table 2 Descriptive Statistics for DEM/USD Frequency

5’

10 ’

20 ’

30 ’

60 ’

Min

-0.9400

-0.9093

-0.9093

-0.8338

-0.7803

Max

0.2451

0.4273

0.4296

0.4073

0.5307

Average

0.0000

0.0004

0.0010

0.0000

0.0019

Std. Dev.

0.0316

0.0412

0.0547

0.0662

0.0924

Skewness

-2.2841

-1.9290

-1.4091

-1.3531

-0.8715

Kurtosis

62.8194

42.9152

24.6106

21.4675

12.3715

Jarque-Bera 3,264,662

771,426

117,989

58,236

7,704.5

(0.000)

(0.000)

(0.000)

(0.000)

(0.000)

Finally, the analysis of the coefficients for the squared time series (ρxx) and in absolute value (|ρ|) allows to confirm the presence of ARCH components and of asymmetrical reaction functions. Coefficients (ρxx) and (|ρ|) are generally higher than the original series and remain significant for different lags; moreover, the statistics Qxx and Q|x| are larger than the corresponding Q' (particularly in the case of DEM/USD for lag > 5). Chaotic and Non-Linear Dynamics We know that time series generated by a chaotic process, if studied through conventional statistical methods like auto-correlation function or spectral analysis, come into view apparently random. Brock et. al. [1987] proposed a methodology useful to distinguish stochastic and deterministic processes through a statistics able to verify the hypothesis of a series identically and independently distributed (IID). Ashley and Patterson [1989] and Hsieh [1991] demonstrate that the independence of a variable from its past values does not necessarily imply a white noise process. The alternative reason for the IID are: chaos, non-stationarity and conditional heteroskedasticity. Therefore, we adopted opportune tests [Barnett and Chen (1986);

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Frank and Stengos (1988a/b)] like the dimension of correlation, the BDS test and the Lyapunov exponent, in order to evaluate possible chaotic behaviours. The dimension of correlation, independently by the time frequency, increases linearly with m, and this suggests that the underlying data process generation are primarily stochastic. Besides, the dimension assumes relatively low values, between 1 and 2 (with the exception of DEM/USD 5 minutes for m=10) and they are always below the random model values. The BDS tests [Brock, Dechert and Scheinkman, 1987] allow to verify whether time series are identically and independently distributed, both for series produced by chaotic systems and for non linear stochastic systems. The high BDS values point out that it is not possible to accept the null hypothesis of IID data, while they suggest that the generating process is non linear. Besides, the BDS test disconnects the random model N(0,1) from the chaotic one. The empirical evidences bring us to conclude that time series are non linear even though not necessarily chaotic. A peculiar characteristic of the chaotic systems is the dependence from the starting conditions, with trajectories that diverge exponentially, despite very similar initial values. The most important tool to quantify the dependence from the initial conditions in a dynamic system is the Lyapunov exponents [McCafferty et al., 1992 and Dechert and Gencay, 1993]. Our results are consistent with those previously obtained through the dimension of correlation and seem to exclude the presence of a chaotic regime. In fact, being that the Lyapunov exponents are negative for all the currencies examined and all the frequencies, is indicative of a stable generating process. All the empirical results show a strong evidence of the existence of linear and non linear dependencies for all the examined financial time series, even though deterministic chaos is not an explanation. These considerations are coherent with the implementation of econometric models and neural networks, in order to fit the linear and non linear components here observed. Data properties authorise some conclusions: 1. our time series are asymmetrical and leptokurtic, therefore non normal distribution is a coherent result with that traditionally obtained for daily and weekly observations; 2. dependencies found in data are not linked with a white noise generating process; however, as well underlined by Hsieh [1991], it is opportune to treat this conclusion with extreme caution, since the higher the frequency the greater the probability of false dependencies, linked to the market microstructure; 3. the possibility to describe the exchange rate dynamics through a little dimension chaotic model has been clearly refused. This result is in contradiction with a large part of financial literature which found a strong chaotic component for daily and weekly time series. FORECASTING METHODOLOGIES

The trading system we tested has been introduced by Saidenberg [1997]: it is based on the levels of maximum and minimum experienced during the previous day which generate the trading levels [Appendix]. Besides the algorithmic trading system, we wish to describe the behaviour of our time series by estimating different kinds of structural models and different neural network architectures. The identification of the structural component is made on the basis of alternative models, characterised by different structures, and of the selection of the most useful variables through stepwise regression. Besides the classical causal formulations, obtainable from the most general autoregressive distributed lags and state space models, three

autoprojective models were estimated in order to verify possible autoregressive and/or moving average structures (ARIMA). Moreover, we compared the models’ performance to extremely simple structures, such as random walk. As regards the state space model, we considered using a multivariate state space representation of an autoregressive moving average process. The investigation is aimed at the best fitting for every model, in line with an acceptable error distribution. With reference to rt volatility, and in line with techniques broadly proposed in literature, we used ARCH models [Engle, 1982] which are able to model the conditional variance, according to an autoregressive scheme. More complex GARCH models were then estimated: I-GARCH, M-GARCH and E-GARCH. AIC index was then used in model selection. The types of neural network architectures used in forecasting rt are as follows: 1. Standard connections: a) with three layers; b) with four layers; c) with five layers. 2. Recurrent networks: a) input layer back into input layer; b) hidden layer back into input layer; c) output layer back into input layer. 3. Feature detectors: a) with two different activation functions; b) with three different activation functions; c) with two different activation functions plus jump connection. 4. Jump connections: a) with three layers; b) with four layers; c) with five layers. 5. General Regression Neural Network. Back propagation networks utilise various activation functions, such as linear, logistic, Gaussian and tangent and were tested using several learning rates and momentum. Optimal average values are 0.1 for both parameters. General regression neural network is tested in the 20-300 range of genetic breeding pool size and with Euclidean and city block distance metric. THE ECONOMETRIC RESULTS

The study is aimed at evaluating the opportunity to use technical indicators as inputs into state-space and ARCH-GARCH models. The indicators we used as input are the following: 1. Lower and upper Bollinger Bands 2. Differenza fra medie mobili ponderate lineari (Linearlyweighted moving average difference) 3. Linear extrapolation 4. Linear regression 5. Linear regression slope 6. Linear weighted moving average 7. Differential moving average 8. Exponential moving average 9. Lagged exponential moving average 10. Wilder’s RSI Besides, we found out the goodness of outputs as financial “signals” produced by the single model in a trading system. Our trading system is based on the following rules: every forecast is a signal and the trader is assumed to take a position (long, short, hold) Pt∈{-1;+1} of constant magnitude. Forecast is exact if it equals the observed sign of r t, otherwise it produces a loss. In order to compare structural and black box returns, we computed the perfect trading system, i.e. the result we could obtain by taking all the right positions in every period t. Trading System Outcomes Empirical results generated by the algorithmic trading system underline the stability of the model for the different frequencies. On average, the system introduces a good reliability (60.7%). If we analyse long and short signals, the former show a lower reliability

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IFTAJOURNAL (50.5%) than the latter (71.2%). The following conclusions can be formulated (Table 3): 1. the model furnishes both long and short indications; 2. winning trades are relatively high (around 60%); 3. the average performance of the single operations is low (0.0021); 4. the system does not lose the big movements of market; 5. equity lines are very similar, independently from the time frequency. Table 3 Trading System Report for DEM/USD (10 minutes) Total net profit

0.0947

Open position P/L

Gross profit

0.2087

Gross loss

47

Percent profitable

Number winning trades

24

Number losing trades

0.0394

0.0000

Table 5 State-Space Trading System DEM/USD

-0.1140

Total # of trades

Largest winning trade

The trading purpose allows to improve significantly the estimation quality of the model (Table 5), since the magnitude of forecasting error becomes less important [Dacorogna, Muller, Jost, Pictet, Olsen, Ward, 1996]. 1. We do not see a performance improvement as the time frequency decreases; 2. the percentage with respect to the perfect model is not high if compared with the trading system functioning; 3. the reward-risk index, which is decreasing with the frequency, points out the presence of risk premia (spread), especially for the highest frequencies.

Largest losing trade

51% 23

Frequency

Simulation number

60’

1,151

596

401

203

979

609

266

176

66

2.82

3.42

3.79

1.34

161.12

138.76

175.78 204.14

48.96

Correct signals number (%)

50.25

52.30

51.51

57.61

57.71

Turning Points (%)

44.73

51.97

40.94

44.57

26.14

-0.003

-0.260

-0.342

Reward Risk Index

11.64

10.84

9.99

12.78

3.28

Perfect Model (%)

6.59

19.55

16.50

23.32

12.15

Average losing trade

-0.0050

Ratio avg win/avg loss

1.7544

Avg trade(win & loss)

0.0020

Annual return

Max consec. Winners

7

Max consec. Losers

5

Avg # bars in winners

71

Avg # bars in losers

46 1.8307

State-Space Model Identification The multivariate ARMA model estimation written in a statespace form implies the following steps: 1. preliminary fitting of a sequence of autoregressive models based on Yule-Walker equations in order to identify the order of the model corresponding to the minimum AIC index value; 2. identification of the technical indicators as input in the state vector through canonical correlation analysis; 3. estimation of the model parameters by maximising the likelihood function. The model identification has been realised testing, for all the frequencies of our two currencies, alternative models by explicative variables and by autoregressive structure. Empirical results (Table 4) show how the pattern is not adequately captured by the models; in addition, passing from higher frequencies (5 and 10 minutes) to lower ones (30 and 60 minutes), the interpretation of the phenomenon does not improve, both in-sample and out-of-sample. Table 4 Estimation Fitting Freq.

In-sample fitting N° obs. M.A.E. M.S.E.

5’

19,592

0.02178

0.00101

2,177

0.02058

0.00082

10’

10,362

0.02814

0.00170

1,151

0.02589

0.00131

20’

5,366

0.03750

0.00294

596

0.03531

0.00236

30’

3,611

0.04422

0.00433

401

0.03976

0.00329

60’

1,832

0.06386

0.00848

203

0.05481

0.00667

Out-of-sample fitting N° obs. M.A.E. M.S.E.

The analysis of the error component exhibits the presence of an asymmetry associated with a significant leptokurtosis already found for the original variables; the Jarque-Bera test allows us to conclude that we deal with non normal distributions. The Lyung-Box test values, with particular reference to (ρxx) and (|ρ|), point out the presence of a notable heteroskedasticity degree. Performance improvement can be obtained through volatility information [Bramante, Colombo, Gabbi, 1998, and Timmer, Weigend, 1997].

40

30’

2.94

0.0087

Profit factor

20’

Operations number

Average winning trade

-0.0457

2,177

10’

-0.0240

Period return

Max drawdown

5’

Max-Drawdown

-0.296 -0.410

Monte Carlo Simulations Period return Correct signals number (%)

2.90

2.79

3.44

3.83

1.32

51.31

52.75

51.68

57.9

57.72

1. the number of correct signals is superior than 50% both for insample and out-of-sample estimates; 2. the operational degree is coherent with the different level of volatility found for the time series; 3. the number of current signals is significantly higher than Monte Carlo simulations. Identification and Estimation of ARCH-GARCH Models The identification of ARCH and GARCH models has been conducted by testing four alternative models, characterised by different complexity levels, through the application of stepwise regressions: the general polynomial model with distributed delays; the ARMA model; the random walk; the random walk plus drift. The error analysis of M.A.E., M.S.E., SIC and AIC, shows little descriptive ability of the single econometric structures. This means that technical indicators used as inputs are not explanatory variables able to recognise the pattern of exchange rate. The identification of the conditional variance model has been led up experimenting alternative structures (ARCH, GARCH, IGARCH, GARCH-M and E-GARCH), with different number of parameters, and comparing the indicators (AIC and SIC) generally used to select competitive models. The implementation of the ARCH component has made possible an improvement of the phenomenon interpretation and the statistical characteristics of errors (leptokurtosis, symmetry, serial autocorrelation). The data generating process seems to be characterised by an increasing “memory” by time frequency. Among all the alternative models, E-GARCH and GARCH-M seem to be preferable, since they minimise AIC and SIC indicators. Very meaningful is the risk premia (spread) (d) incorporated in the scheme GARCH-M. This parameter assumes more elevated values

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as frequency decreases. Likewise, it is considerable the effect of asymmetrical answer (υ in E-GARCH), even if the relative value seems to be independent by the time frequency. Estimated models can be used for interesting applications, such as: 1. accurate forecasting of exchange rates for all the frequencies; 2. finding out forecasting intervals more accurately, especially with volatility cluster and using theoretical measure of volatility to improve the trading rules [Zhou, 1996]. Forecasting accuracy and trading system. Results have been operationally experienced into the trading system previously described. Simulations emphasize that all the models are characterised by positive performance, especially if compared with Monte Carlo outcomes. Similar findings are offered by quality indicators such as “number of correct signals” and “percentage of turning point.” ARCH-GARCH models, better than Monte Carlo simulations, distinguish the periods in which markets offer higher economic returns. Operational degree and economic annual return worsen as time frequency decreases. In fact, annual return should be compared to the perfect model, to quantify the quality of forecasting activity: it emerges that the trading system increases its accuracy for lower frequencies, both for in-sample and for out-of-sample time periods. Trading system and operational filters. Since the availability of efficient forecasting intervals is usually more interesting than the instant prediction, we can use ARCH component to build these kinds of intervals. In our case, the particular dynamics of our financial time series makes this criterion excessively discriminating, allowing the trading system to operate in few occasions only. Alternatively, volatility indications can be used as tracking signal to find the moments of “excessive noise,” during which it is more convenient to apply a stand-by strategy [Bramante, Colombo, Gabbi, 1998]. By the comparison of results with the two trading rules, the inclusion of a “trace signal” leads to a significant improvement of the risk/return indicator. There are still many aspects that deserve opportune deepening: a. firstly, our estimations do not allow us to verify the existence of a threshold level valid for all the considered time series; b. secondly, the individualisation step requires terms hardly compatible with the normal operational demands. ARCH and GARCH models do not demonstrate a good ability to define the structural component; in all the cases, the use of the technical analysis indicators do not generate a considerable progress in the interpretation of the single events. The inclusion in the model of an ARCH component allows to improve the fitting of the experimented models, reducing the level of leptokurtosis and asymmetry of the error terms. The existence of a risk premium guides us to a partial superiority of the GARCH-M scheme. Moreover, the knowledge of a theoretical measure of volatility improves the reliability level of the trading system, through the use of a tracking signal able to distinguish periods of excessive volatility when it should be more convenient not to operate. Empirical Verification with Neural Networks A first evaluation of the results altogether reached with neural networks shows a modest performance in statistical terms. The only remarkable difference between BPNN and GRNN is the value of the coefficient of determination (R2). The data analyses show a meaningfully better result for the general regression neural networks (Table 6).

IFTAJOURNAL Table 6 Statistical Results of the Neural Networks (generalisation set) Frequency

MSE

MAE

Min R2

Max R 2

5’

0.001

0.021

0.0018

0.0069

10’

0.002

0.028

0.0000

0.0103

20’

0.002

0.036

0.0029

0.0252

30’

0.005

0.048

0.0176

0.0387

60’

0.007

0.059

0.0561

0.0910

Errors generated by the application of neural networks to the generalisation set can be analysed using symmetry and normality tests already used in the econometric evidences. With reference to the skewness, results (Table 7) are close to the expected value (equal to 0, in the case of perfect symmetry of the observations) only for the frequencies 5 and 20 minutes, both for the back-propagation and for the general regression. Similar considerations can also be made for the kurtosis, which should assume a value equal to three in case of normality. Table 7 Error Properties (generalisation set) Frequency Skewness

Kurtosis

Jarque-Bera

Q|x|

Qxx

2,177

73.715

251.61

(0.000)

(0.016)

(0.000)

27,864

65.667

21.294

(0.000)

(0.068)

(1.000)

381

36.206

38.210

(0.000)

(0.928)

(0.889)

3,609

57.390

9.773

(0.000)

(0.220)

(1.000)

5’

-0.304

4.882

10’

-2.218

23.826

20’ 30’

60’

0.455 -2.034

1.146

3.867 14.365

4.640

210

64.630

56.623

(0.000)

(0.080)

(0.242)

With reference to the financial meaning of results (Table 8), an elevated annual performance is observed meaningfully. Table 8 Financial Results of Neural Networks (generalisation set) Frequency Results

5’

10’

20’

30’

60’

Annual Trading (%)

216.30

148.88

90.00

170.11

140.74

Perfect trading (%)

6.98

8.89

8.42

16.97

24.45

Correct signals (%)

50.80

50.84

76.35

53.90

56.56

0.27

0.57

0.34

0.66

0.63

12.08

4.70

5.16

4.92

4.70

Max drawdown Reward/Risk Index

Out of 60 back-propagation networks estimated (Table 8), only five generate negative results with a range characterised by a maximum of 379.6 and a minimum of 13.1% per year. The higher performances are referable to the trading realised on the 5 minutes frequency, while the lower average is corresponding to the hourly frequency. This result is different by the percentage incidence of the correct movements: the BPNNs record 57% of good signals, while GRNN records only 54%. A meaningful outcome is related to the frequency of the BPNN with more good than bad signals: out of 60, 54 neural networks. The wide number of architectures here applied to forecast the two

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IFTAJOURNAL currencies over the five time frequencies allows us to draw some useful considerations for the ex-ante choice problem. Although we do not have elements for a generalisation, all the results show that the network typology is indifferent for M.S.E. and M.A.E., which assume the same values for all the BPNN. The choice rule, therefore, can be the training duration. The most rapid architectures are the jump-connection types and the two and three hidden layers standard connection networks. In all the different cases, the highest duration of training is recorded by the Jordan-Elman architectures. If measured by the coefficient of determination (R2), statistical quality shows that architectures are very different with each other: for the DEM/USD exchange rate recorded every 20 minutes, the architecture n.7 records an R2 eight times higher with respect to the network n.2. The reliability of these results can be synthetically calculated through the RI index proposed by Bramante, Colombo and Gabbi [1998]:

where O1 and O2 are the first and the second objective. RI index varies between 0 (least reliability) and 100 (maximum reliability). Crossing the results of the coefficient of determination and the financial trading result (performance and number of the correct signals) we obtain the Table 9. Data show how the reliable neural networks for statistical purposes become less reliable when financial trading is the final goal. Empirical results allow to make some considerations on the architectures choice: 1. the preferable standard connections neural networks has only one hidden layer; this is true both for statistical error and for trading performance optimisation. Training duration is, on average, short (especially in the case of two and three hidden layers), like the jump-connection networks which show higher performance; Table 9 Reliability Index O1 O2

DEM/USD

Performance R2

Correct signals R2

Performance Correct signals

41.67

50.00

72.22

1. with reference to the jump connection neural networks, the choice of the hidden layers number does not depend on the purpose but, at least in our estimates, on the phenomenon we studied; 2. relative to the networks with multiple activation functions, statistical results show a meaningful homogeneity of all the three types of the architectures; simpler is the choice if the objective is constituted by the financial result, which is maximised by the three activation functions networks; 3. finally, in the case of the Jordan-Elman networks, a notable volatility behaviour is recorded, by frequency, by objective and by market; the only clear indication is the outcome generated by the net with feedback between output and inputs for the finality of the coefficient of determination optimisation. Financial results produced by the application of neural outputs to the trading system depend on the nature of the entry and exit rules and on the filters eventually applied. Table 10 shows that all the 12 financial outcomes have positive values and always higher than random results simulated with a Monte Carlo method. Although in two cases (10 and 20 minutes) Monte Carlo simulation is preferable, similar considerations apply to correct signals (Table 10).

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Table 10 Neural Networks and Monte Carlo Simulations Results Trading

Correct Signals

Freq.

BPNN

GRNN

BPNN

GRNN

M-Carlo

5’

216.3

376.4

M-Carlo

6.20

50.80

53.06

48.95

10’

139.4

219.5

-15.32

50.84

50.04

51.90

20’

90.0

203.2

-20.64

56.35

54.29

57.08

30’

170.1

204.1

-17.17

53.90

52.87

49.83

60’

140.7

155.1

3.07

56.56

61.39

49.93

A useful indicator to evaluate this result is the maximum drawdown, that presents the best payoff for the most elevated frequency (Table 11). Table 11 Results Order in Terms of Return/Risk by Time Frequency Maximum Drawdown

Reward/Risk Index

Frequency

BPNN

GRNN

BPNN

5’

1

1

1

1

10’

3

3

4

3

20’

2

2

2

2

30’

5

5

3

5

60’

4

4

5

4

GRNN

This result is substantially confirmed by the indicator that compares the output to the loss (reward/risk index). The worse values are referable to the lowest frequencies (60 and 30 minutes). Empirical and Methodological Comparison

Statistical Outcomes In order to verify the statistical quality of the study, we compare all the results among them: firstly, we consider the optimisation of the differential between expected and real output; in second place, we evaluate residuals properties. Econometric and neural network results can be measured up by different indicators: we choose M.A.E., since it is less influenced by the underlying methodology. M.A.E. computed on out-of-sample data emphasises the preferred aptitude of GARCH models (Table 12). In fact, only GARCH models perform error values significantly lower than random walk. State-space estimations do not diverge remarkably from random decisions that often exhibit better M.A.E. than neural networks. Table 12 M.A.E. (out-of-sample) Random Walk

ARCH GARCH

State-Space

BPNN

GRNN

5’

0.022

0.002

0.021

0.021

0.022

10’

0.028

0.003

0.026

0.028

0.028

20’

0.037

0.006

0.035

0.036

0.037

30’

0.044

0.009

0.040

0.048

0.043

60’

0.062

0.020

0.055

0.059

0.060

Frequency

With regard to error characteristics, the first evaluation is symmetry approximated by skewness (Table 13).

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IFTAJOURNAL Table 13 Skewness (in-sample) Random Walk

ARCH GARCH

StateSpace

BPNN

GRNN

5’

-2.269

-0.642

-2.303

-2.269

-2.823

10’

-1.917

-0.534

-1.959

-1.928

-1.986

20’

-1.312

-0.355

-1.235

-1.263

-0.834

30’

-1.275

-0.522

-1.267

-1.402

-1.404

60’

-0.871

-0.367

-0.878

-0.931

-0.869

Frequency

Only ARCH and GARCH models provide symmetrical errors. Neural networks, above all GRNN, give results not too different from the random walk. Results based on data kurtosis (Table 14), only in the case of the ARCH-GARCH models assume lower values than the random walk. Positive results show that outputs are distributed with tails thicker than the normal distribution. Table 14 Kurtosis (in-sample) Frequency

Random Walk

ARCH GARCH

State-Space

BPNN

GRNN

5’

60.63

11.08

59.30

59.25

74.68

10’

40.47

6.45

40.22

40.77

40.96

20’

21.58

5.12

20.68

20.96

15.63

30’

18.19

6.44

18.38

19.04

18.90

60’

9.46

4.80

9.30

10.06

9.49

Values improve when frequency reduces and E-GARCH model is able to gather better than the alternative methodologies. In fact, errors produced by neural networks show inadequate characteristics of kurtosis, even worse than random walk. The estimation comparison shows that black-box findings are rarely useful to learn the underlying pattern of time series, even though, among them, we appreciate a moderate preference for GRNN outcomes. Econometric schemes are preferable, but the choice is for the ARCH-GARCH type; especially E-GARCH and GARCH-M give a better performance for the extraction of non-linear components in the time series.

Financial Outcomes In first place, we compare output quality of our trading systems. The rate of occurrence of signal correctness is a proxy for reliability of the system. Table 15 compares these results with Monte Carlo simulations. Table 15 Correct Signals (out-of-sample) Freq.

Monte Carlo

Trading Systems

ARCH GARCH

StateSpace

BPNN

5’

48.97

-

51.99

50.25

52.66

53.06

10’

49.57

61.29

53.64

52.30

52.26

50.04

20’

49.84

61.96

52.06

51.51

57.31

54.29

30’

49.75

58.24

54.81

57.61

55.25

52.87

60’

49.99

61.80

55.56

57.71

58.42

61.39

GRNN

All the trading systems based on econometric and neural network outputs perform levels higher than 50 percent. The most remarkable difference in respect with statistical analysis is the heterogeneous distribution of the best performances: neural networks show seven bests, while econometric models dominate in three cases only.

Our results demonstrate that econometric and black box models are competitive only on lower frequencies. An interesting way to evaluate the forecasting quality is quantifying models’ capability to intercept the most extensive differences. Table 16 % Perfect Model for DEM/USD (out-of-sample) Trading System

ARCH GARCH

StateSpace

BPNN

GRNN

5’

-

12.44

6.59

10.75

8.38

10’

13.23

12.20

19.55

10.55

24.87

20’

13.78

15.49

16.50

13.39

20.99

30’

19.04

14.25

23.32

12.32

29.66

60’

18.48

21.64

12.15

18.71

15.45

Frequency

Table 16 shows the percent ratio of profitability calculated comparing results with the perfect trading model. In this case, neural networks exhibit the best outcome in six cases out of ten. In order to consider the risk component we present the reward/risk index, computed as the ratio between the total net profit of the system and the maximum drawdown. Table 17 shows that ARCH and GARCH models, despite the low percentage of correct signals, are able to record an index value on average higher than neural networks and state-space schemes. Table 17 Reward/Risk Index for DEM/USD (out-of-sample) Trading System

ARCH GARCH

StateSpace

BPNN

GRNN

-

25.82

11.64

18.11

8.27

10’

3.57

14.45

10.84

7.37

7.92

20’

3.51

11.75

9.99

10.31

8.89

30’

9.06

7.33

12.78

5.90

9.13

60’

3.04

5.76

3.28

5.41

8.87

Frequency

5’

The comparison of financial forecasting results allows one to underline an high competitiveness of the alternative models to the ARCH-GARCH ones, especially if the analyst’s purpose is based on signals reliability. Generally speaking, if we consider altogether profitability and risk, econometric methodologies appear the most efficient, although it is impossible to determine a universal using rule. CONCLUSIONS

Non-linear and not-chaotic characteristics of time series are hardly consistent with the possibility to explicit their structure through econometric models so to obtain a reliable forecast. This conclusion comes out from the ARCH-GARCH and statespace schemes: an autoregressive component does not exist (but a modest third order factor) to justify the exchange rate behaviour, at least during the period examined and for the analysed time frequencies. The results are, therefore, coherent with this outcome: our research shows that errors tend towards an asymmetric and non normal distribution. However, non linearity offers the opportunity to produce meaningful output in financial terms, especially to evaluate: a) volatility; b) turning points; c) position taking. Comparison between econometric models and neural networks architectures suggests a supremacy of the former: GARCH solutions, in particular, are able to fit the high volatility found in the market. The algorithmic trading system shows better performance in terms of correct signals.

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IFTAJOURNAL Our results contribute to acceptance of the empirical hypothesis that, knowing the properties of the series, analysis phase is possible to find out the forecast quality. If a chaotic component is not found it is hard to model the pattern structure of time series, but non linearity helps to generate useful signals for financial applications. GLOSSARY

AIC ADF ARCH ARIMA BPNN GARCH E-GARCH I-GARCH M-GARCH GRNN MAE MSE RI SIC

Akaike Information Criterion Augmented Dickey Fuller Autoregressive Conditional Heteroschedasticity Autoregressive - Integrated - Moving Average Back-propagation neural networks Generalized Autoregressive Conditional Heteroschedasticity Exponential GARCH Integrated GARCH Mean GARCH General Regression Neural Network Mean Absolute Error Mean Squared Error Reliability Index Schwarze Information Criterion APPENDIX

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Algorithmic Trading System (TradeStation©) input: f1(0.05),f2(0.35),f3(0.55),reverse(0.006); vars:ssetup(0),bsetup(0),senter(0),benter(0),bbreak(0),sbreak(0), ltoday(0),htoday(9999),startsys(0),div(0), Sell1(0),Sell2(0),Sell3(0), Buy1(99999),Buy2(99999),Buy3(99999); if currentbar=1 then startsys=0; if Date>Date[1] then begin startsys=startsys+1; bsetup=ltoday-f1*(htoday-close[1]); ssetup=htoday+f1*(close[1]-ltoday); senter=((1+f2)/2)*(htoday+close[1])-(f2)*ltoday; benter=((1+f2)/2)*(ltoday+close[1])-(f2)*htoday; bbreak=ssetup+f3*(ssetup-bsetup); sbreak=bsetup-f3*(ssetup-bsetup); htoday=h;ltoday=l; end; if high>htoday then htoday=high; if low=2 and Date>entrydate(1) then begin if marketposition=-1 then Buy1=entryprice+reverse; {BUY LEVEL STOP AND REVERSE} if marketposition= 1 then Sell1=entryprice-reverse; {SELL LEVEL STOP AND REVERSE} (BUY REVERSAL LEVEL) if ltoday<=bsetup and marketposition<> 1 then Buy2=benter-(bsetup-ltoday)/ 3; {SELL REVERSAL LEVEL} if htoday>=ssetup and marketposition<>-1 then Sell2=senter+(htodayssetup)/3; if marketposition=0 then Buy3=bbreak; {BREAKOUT BUY LEVEL} if marketposition=0 then Sell3=sbreak; {BREAKOUT SELL LEVEL} end; IF (Sell1>=Sell2 AND Sell1>=Sell3) THEN SELL at Sell1 stop ELSE IF Sell2>=Sell3 THEN SELL at Sell2 stop ELSE SELL at Sell3 stop; IF (Buy1<=Buy2 AND Buy1<=Buy3) THEN BUY at Buy1 stop ELSE IF Buy2<=Buy3 THEN BUY at Buy2 stop ELSE BUY at Buy3 stop; REFERENCES ■

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Ashley R.A., Patterson D.M., 1989, Linear versus Nonlinear Macroeconomics: A Statistical Test International Economic Review, 30 (3), 685-704. Barnett W., Chen, P., 1986, The Aggregation-Theoretic Monetary Aggregates are Chaotic and Have Strange Attractions, in W. Barnett, E. Berndt and H. R White (eds), Dynamic Econometric Modelling. Cambridge: Cambridge University Press.

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Bramante R., Colombo R., Gabbi G., 1998, Are Neural Network and Econometric Forecasts Good for Trading? Stochastic Variance Model as a Filter Rule, in A.-P. N. Refenes – A. N. Burgess – J. E. Moody (eds), Decision Technologies for Computational Management Science, Kluwer Academic Publishers, Boston. Brock W.A., Dechert W.D., Scheinkman J.A., 1987, A Test for Independence Based on the Correlation Dimension, Working Paper, University of Houston and University of Chicago. Dacorogna M.M., Muller U.A., Jost C., Pictet O.V., Olsen R.B., Ward J.R., 1996, Heterogeneous Real-time Trading Strategies in the Foreign Exchange Market, in C. Dunis (eds.) Forecasting Financial Markets, John Wiley, New York. Dechert W.D., Gencay R., 1993, Lyapunov Exponents as a Nonparametric Diagnostic for Stability Analysis, Journal of Applied Econometrics, 7, S41-S61. Diebold F.X., 1988, Lecture Notes in Economics and Mathematical System, Springer-Verlag, New York. Engle R.F., 1982, Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation, Econometrica, 50, 987-1008. Frank M.Z., Stengos T., 1988a, Chaotic Dynamics in Economic Time Series, Journal of Economic Surveys 2, 103-133. Frank M.Z. Stengos T., 1988b, Some Evidence Concerning Macroeconomic Chaos, Journal of Monetary Economics 22, 423-438. Hsieh D. A., 1991, Chaos and Nonlinear Dynamics: Application to Financial Market, The Journal of Finance, No.5. McCafferty D.F., Ellner S. Gallant A.R., Nychka D.W., 1992, Estimating the Lyapunov Exponent of a Chaotic System with Nonparametric Regression, Journal of American Statistical Association, 87. Muller U.A., Dacorogna M.M., Embrechts P., Samorodnitsky G., 1995, How Heavy are the Tails of a Stationary HARCH Process? A Study of the Moments, Internal document O&A Research Group. Saidenberg R., 1997, Trading with a 100% Mechanical Approach, Workshop Proceedings, Milan. Timmer J., Weigend A.S., 1997, Modelling Volatility Using State Space Models, in International Journal of Neural Systems, Vol. 8, No. 5. Zhang G., Patuwo B. E., Hu M. Y., 1998, Forecasting with Artificial Neural Networks: The State of the Art, International Journal of Forecasting, vol. 14. Zhou B., 1996, Forecasting Foreign Exchange Rates Subject to Devolatilization, in C. Dunis (ed), Forecasting Financial Markets – Exchange Rates, Interest Rates and Assets Management, John Wiley & Sons, Chichester, England. THE AUTHORS

Giampaolo Gabbi graduated in Economics at University of Parma, Ph.D. in Financial Economics at Bocconi University Milan, Associate Professor of Banking and Management Department, University of Siena, Italy and in the Credit Area, SDA Bocconi, Milan Ruggero Colombo graduated in Economics at Catholic University of Milan, Professor of Statistics at Institute of Statistics, Catholic University, Milan Riccardo Bramante graduated in Economics at Catholic University of Milan, Professor of Statistics at Institute of Statistics, Catholic University, Milan Maria Paola Viola graduated in Economics at Catholic University of Milan, Risk Manager at RAS, Milan Paolo De Vito graduated in Information Technology at University of Turin, CEO of IT Trading, Turin Alberto Tumietto graduated in Economics at Bocconi University, Milan; Private Banking Manager at Banca Nazionale dell’Agricoltura, Milan; President of SIAT, Italian Technical Analysts Association

2000 Edition

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IFTAJOURNAL

1999-2000 IFTA Board of Directors

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Finance Committee Chairperson

Public Relations

Bruno ESTIER (SAMT) Lombard Odier & Cie Phone: (41) 22 709 2041 Fax: (41) 22 709 2911 E-mail: [email protected]

Joerg SCHREIWEIS (VTAD) DG Bank Phone: (H) (49) 6174 61116 Fax: (49) 69 7447 7980 E-mail: [email protected]

Robin GRIFFITHS (STA/MTA) HSBC Securities Inc Phone: (1) 212 658 4304 Fax: (1) 212 658 4480 E-mail: [email protected]

Vice-Chairperson – The Americas

Membership & New Development Committee Chairperson

Academic Interface

Nina COOPER (MTA) Pendragon Research Inc Phone: (1) 815 244 4451 Fax: (1) 815 244 4452 E-mail: [email protected]

Carl GYLLENRAM (STAF) S E B Kapitalförvaltning Phone: (46) 31 62 18 48 Fax: (46) 31 62 18 50 E-mail: [email protected]

Vice-Chairperson – Europe & Africa Julius De KEMPENAER (VTA) AMSTGELD NV Phone: (31) 20 528 2867 Fax: (31) 20 624 3358 E-mail: [email protected]

Education Committee Chairperson

Vice-Chairperson – Pacific Region

Accreditation Committee Chairperson

Hiroshi OKAMOTO (NTAA) Phone: (81) 3 5542 2257 Fax: (81) 3 5542 2258 E-mail: [via] [email protected]

Tony REEVES (ATAA) Kaplin Reeves & Co. Phone: (61) 29 299 6797 Fax: (61) 29 299 6069 E-mail: [email protected]

Claude MATTERN (AFATE) BNP Paribas Phone: (33) 1 43 16 98 39 E-mail: [email protected]

Treasurer

Data Committee Chairperson

Bill SHARP (CSTA) Valern Investment Management Phone: (1) 905 338 7540 Fax: (1) 905 845 2121 E-mail: [email protected]

Adam SORAB (STA) Credit Suisse First Boston Phone: (44) 171 888 7240 Fax: (44) 171 888 7498 E-mail: [email protected]

Secretary

Communications Committee Chairperson

Bronwen WOOD (STA) Phone: (44) 1932 850282 Fax: (44) 1932 850282 E-mail: none at present

Len SMITH, CMT (MTA) Phone: (1) 360 834 3021, ext. 3590 Fax: (1) 360 244 6449 E-mail: [email protected]

Immediate Past Chairman & Body of Knowledge Chairperson

IFTA Conference 2000 Committee Chairperson

John BROOKS, CMT (MTA) Yelton Fiscal Inc. Phone: (1) 770 645 0095 Fax: (1) 770 645 0098 E-mail: [email protected] ○

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Administration/ Business Manager Michael SMYRK Town House, High Street Haslemere, Surrey GU27 2JY, England Phone: (44) 1428 643310 Fax: (44) 1428 641080 E-mail: [email protected]

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Hartmut SIEPER (VTAD) Phone: (49) 6127 5921 Fax: (49) 6127 5978 E-mail: [email protected]

Conference Advisory Committee Chairperson Frank VLUG, CEFA (VTA) IRIS/Robeco Nederland B.V. Phone: (31) 10-2242833 Mobile: (31) 651268322 E-mail: [email protected]

Bernardino BRANCA (SIAT) FIBRA SPA Phone: (39) 02 945 99801 Fax: (39) 02 945 99973 E-mail: [email protected]

Directors at Large Ralph ACAMPORA, CMT (MTA) E-mail: [email protected] Larry BERMAN, CTA, CMT (CSTA) E-mail: [email protected] Patty BERRY (AMAT) E-mail: [email protected] Gerry BUTRIMOVITZ (TSAASF) E-mail: [email protected] Loic De GALZAIN (AFATE) E-mail: [email protected] David KRELL, CMT (MTA) E-mail: [email protected] Colin NICHOLSON (ATAA) E-mail: [email protected] Ian NOTLEY (MTA) E-mail: none Alberto TUMIETTO (SIAT) E-mail: [email protected] Anne WHITBY (STA) E-mail: [email protected] Adri WISCHMANN (VTA) E-mail: [email protected] ○

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World HQ – (Banking, Legal etc.) Shelley LEBECK c/o Market Technicians Association, Inc. One World Trade Center, #4447 New York, NY 10048 USA Phone: (1) 212 912 0995 Fax: (1) 212 912 1064 E-mail: [email protected]

IFTA UPDATE & Journal Production Barbara GOMPERTS Financial & Investment Graphic Design 41 Hawkes Street Marblehead, MA 01945 USA Phone: (1) 781 639 0169 Fax: (1) 781 639 0187 E-mail: [email protected]

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2000 Edition

IFTAJOURNAL

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INTERNATIONAL FEDERATION OF TECHNICAL ANALYSTS, INC. A Not-For-Profit Professional Organization Incorporated in 1986