CAIA level 1 Secret Book 2018

March 2018

Exam Prep

Lev Le vell

Schweser's Secret Sauce® eBook

©

KAPLANx UNIVERSITY

)

SCHOOL OF PROFESSIONAL AND CONTINUING EDUCATIO EDUCATION N

SCHWESER

Le v e l I S e c r e t Sa u c e

Foreword...........................................................................................................................iii Topic 1: Profes Professional sional Standards and Ethics................................................................. Ethics ................................................................. 1 Topics Topi cs 2.1 2 .1-2 -2 .9 .9:: Introdu Introduction ction to Alternative Investments........................................ In vestments........................................ 4 Topics Top ics 3.1 3 .1-3 -3.6 .6:: Real Assets.......................................................................................... Assets...................................... .................................................... 48 Topics Top ics 4.1 4. 1 -4 .6 .6:: Hedge Fun F unds ds.................................................... ..................................................................................... ................................. 78 Topics Top ics 5 .1 .1-5 -5.3 .3:: Private Equit Eq uity.............................. y.................................................................................. .................................................... 112 Topics Topi cs 6.1 6 .1-6 -6 .4 .4:: Structured Prod Products ucts................................................................... ....................................................................... .... 128 Topics Top ics 7.1 7 .1-7 -7 .4 .4:: Risk Managem M anagement ent and Portfo Portfolio lio M an anag agem em en ent........................ t........................152 152 Essential Exam Strategies

...........................................................................................

177

Index................... Ind ex............................................................................................ ............................................................................................................ ................................... 188

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CAIA® 2018 MARCH LEVEL I SCHWESER’S SECRET SAUCE® ©2018 Kaplan, Inc. All rights reserved. Published in 2018 by Kaplan Schweser. Printed in the United States of America. ISBN: 978-1-4754-6428-3

Kaplan Schweser products are written and edited by well qualified professionals who are committed to providing clear, concise, and accurate study materials to prepare candidates for the CAIA Exam. Additional Addi tional informa information tion regardin regardingg our facul f aculty ty can be found on our website: www. schw schweser. eser.com com/help /help/facu /faculty, lty, php ?group= up=caia. caia. If this book does not have the hologram with the Kaplan Schweser logo on the back cover, it was distributed without permission of Kaplan Schweser, a Division of Kaplan, Inc., and is in direct violation violat ion o f global copyright copyrig ht laws. Your assistance in p ursu ursuing ing potential p otential violators o f this law is greatly appreci appreciated. ated. CALAA does not endorse, promote, review or warrant the accuracy of the products or services offered by Kaplan Schweser, nor does it endorse any pass rates claimed by the provider. CALAA is not responsible for any fees or costs paid by the user to Kaplan Schweser nor is CALAA responsible for any fees or costs of any person or entity providing any services to Kaplan Schweser. CAIA®, CAIA Association®, Chartered Alternative Investment AnalystSM, and Chartered Alternative Investment Analyst Association® are service marks and trademarks owned by CHARTE CHARTERED RED ALTERNATI ALTERNATIVE VE INVESTMENT ANALYST AS SOCIATION , INC., a Massachusett Massachusettss n on-profit corporation with its principal place place o f busines businesss at Amherst, Massachusetts, and are used by permission.

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Fo r e w o r d

This book will be a valuable additi addition on to the study stu dy tools of o f any CAIA candidate. It offers a concise summary of the Level I CAIA curriculum. However, this book does not cover every Learning Objective. Because it is a summary, it cannot and should not cover every concept in the Level I curriculum. It is a review tool designed to solidify the most important areas of the curriculum. We suggest you use this book as a companion compa nion to your othe other, r, more comprehensive study materials. It is easy to carry with you and will allow you to study key concepts, definitions, and techniques over and over. Repetition is an important part of mastering the material. When you get to topics where the coverage here appears too brief or raises questions in your mind, this is your clue to go back to your SchweserNotes™ to fill in the gaps in your understanding. For the great majority of you, there is no shortcut to learning the very broad array of subjects covered by the Level I curriculum, but this volume should be a very valuable valuab le tool for reviewing the materi material al in the last few weekss of your studies bef week before ore exam day. day. Do not underestimate the task at hand. You must study intensely in order to prepare for the Level I CAIA exam. Our study materials, practice exams, question bank, videos, and Secret Sauce are are all designed to help you study as efficiently as possible, grasp and retain the material, and apply your knowledge with confidence on exam day. Best regards, ‘Sun&ett

Derek Burkett, CFA, FRM, CAIA VP V P, Product Manageme Man agement nt Kaplan Schweser

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Page iii

Pr o f e s s i o n a l St a n d a r d s a n d Et h i c s Topic 1

Ethics is 15—20% of the Level I CAIA exam exam and is highly hig hly impo i mporta rtant nt to your you r overall success (remember, you can fail a topic area and still pass the exam, but we wouldn’t recommend failin failingg Ethics). Ethics can be tricky, and small details can be important on ethics questions. Be prepared. In addition to starting early, study the ethics material more than once. Ethics is one of the keys to passing the exam. Standa ndard rdss o f Practice Handbook , which is available We recommend recomm end you read the Sta for free in electronic form on the CAIA Association website. Although we are very proud prou d of o f our reviews of the ethics material, ma terial, most of the ethics questions willl likel wil l ikelyy come directl d irectlyy from the text and examples in the Handbook. Handboo k. You wil willl be much better off if you read both our summaries of the Standards a n d the Handbook and all the examples presented in it.

S t a n d a r d s o f P r o f e s s i o n a l C o n d u c t Questions about the Standards will most likely be procedural questions, but do not neglect to study the details pertaining to violations and compliance with the Standards. Yo You u will be asked to identify ide ntify the course of action that th at an individual or firm should take to comply with the Standards. You are not required to know the Standards by number, just by name. The following is intend intended ed to off offer er a useful summa su mmary ry of o f the Standards of Practice, but certainly does not take the place of careful reading of the Standards themselves, the guidance for implementing the Standards, and the examples in the Handbook. 1.

Know the law relevant relevant to your position. • Com Comply ply with the most strict law or Standard that applies to you. • Do not solic solicit it gifts. • Do not compromise your objectivity or independence. • Use reaso reasonable nable care. • Do not lie, cheat, or steal. ©2018 Kaplan, Inc.

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Topic 1 Professional Standards and Ethics

• • • •

2.

Do not conti continue nue association wit with h others who are break breaking ing laws, rules, or regulations. Do not use others others’’ work or ideas witho without ut attributi attribution. on. Do not guaran guarantee tee investment results or say that past results wi willll be certainly repeated. Do not do things outside of work that reflec reflectt poorly on your integrity integri ty or professional competence.

Do not act act or or cause other otherss to act on material nonpublic nonpub lic information. • Do not manipu manipulate late market price pricess or or tradin tradingg volume with the intent to mislead others.

3. Act solely for for the benefit of your client and know to whom a fiduc fiduciary iary duty is owed with regard to trust accounts and retirement accounts. • Trea Treatt clients fairly by attempt attempting ing simultaneous dissemination of investment recommendations and changes. changes. • Do not person personally ally take shares in oversubscribed IPOs. • Whe When n in an advisory relationship: ♦ Know your client. ♦ Make suitable recommendations and take suitable investment action (in a total portfolio context). ♦ Preser Pre serve ve confidential client cl ient information i nformation unless it conce concerns rns illegal activity. ♦ Do not try to mislead with performance presentation. ♦ Vo Vote te nontrivial prox proxies ies in clients’ best interests interests.. o f your employ employer. er. 4. Act for the benefit of Do not harm your employer. Obtain written permission to compete with your employer or to accept additional compensation from clients contingent on future performance. Disclose (to employer) any gifts from clients. Do not take material with you when you leave employment (you can take what is in your brain). Supervisors Superv isors must take action to ensure compliance with wit h rules, laws, Standards, etc. Do not take supervisory supervisor y responsibility i f you believe procedures procedures are inadequate. 5. Thoroug Tho roughly hly analyze investments. • Have a reasonable basis. • Keep recor records. ds. • Tell clients about investm investment ent proc processes. esses. • Dist Distingui inguish sh between fact factss and opinion opinions. s. Page 2

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Topic 1 Professional Standards and Ethics

• •

Review the qu qualit alityy of thirdthird-party party research research and the the serv services ices of external advisers. In quantitative models, models, consider consider what happens when their inputs are are outside the normal range.

6. Disclose potentia potentiall conflicts of interest (let others judge the effec effects ts of any conflict for themselves). • Disclose referral arrangem arrangements. ents. • Clie Client nt transactions transactions come bef before ore employer transactions which come come before personal transactions. • Treat clients who are are family members members just like any other clients. 7.

Do not cheat on an y exams exams (or help others to). • Do not reveal reveal CAIA exam questions or disclose what topics were tested or not tested. • Do not disclose wha whatt concepts were tested or not tested.

My goo goodne dness! ss! What Wh at ca n you you do? • • • • • • • • • • • •

You can use infor You informatio mation n from recognized statis statistical tical sources wit withou houtt attribution. You Yo u can be be wron wrongg (as (as long as you had a reasonable basis at the time) time).. You Yo u can use several pieces of nonm nonmateri aterial, al, nonpublic nonpu blic information informati on to construct your investment recommendations (mosaic theory). You Yo u can execute large trades that may affect affect marke markett prices as as long as the intent of the trade is not simply to mislead market participants. You Yo u can say that Treasury securities are wi witho thout ut defau default lt risk. You Yo u can always seek the guid guidance ance of your supervisor, compli compliance ance officer, officer, or outside counsel. You Yo u can get rid of record recordss after seven years. You Yo u can accept gifts gifts from client clientss and referral fees fees as long as proper properly ly disclosed. You can call your biggest clients first (after (after fair distribution of investment recommendation or change in recommendation). You Yo u can accept compensation from a comp company any to writ writee a research report if you disclo disclose se the relationship and nature of compensation. compensation. You can get drunk when not at work and commit misdemeanors that do do not involve fraud, theft, or deceit. You Yo u can accu accurate rately ly describe the nature of the exami examinatio nation n proce process ss and the requirements to earn the right to use the CAIA designation.

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In t r o d u c t i o n t o A l t e r n a t i v e In v e st st m e n t s Topics 2 . 1 - 2 . 9

This topic introduces alternative investments and set setss a framework for analyzing these investments using statistical methods. Many of the analysis techniques are similar to those found in traditional investment analysis, but they are applied in a different manner to suit the requirements of alternative investments. There are many definitions and formulas in this topic. Be ready to do some number crunching on the exam. i c 2.1: W h a t i s a n A l t e r n a t i v e I n v e s t m e n t ? T o p ic

Categories of Alternative Investments

There are four categories of alternative ass assets ets you must m ust know for the CAIA exam, including real assets, hedge funds, private equity, and structured products. 1. Real assets are associated with investments that directly control nonfinancial assets and represent actual rights to consumption. Within real assets, investors may invest in real estate, infrastructure, natural resources, commodities, and intangible assets. 2.

Hedge funds are private investment vehicles that are subject to minimal regulation and therefore able to pursue unique investment opportunities using derivatives, leverage, short positions, and other strategies.

3.

Private equity investments include debt and equity securities that are not publicly traded. Within private equity, investors may invest in venture capital (senior equity financing for small, high-risk startup companies unable to obtain public equity), leveraged buyouts (funds that privatize a public company by purchasing its equity eq uity using a large amount amou nt of debt), debt), mezzanine debt (privately held convertible debt, debt with equity options or warrants, and preferred stock), and distressed debt (debt issued by companies in or about to enter bankruptcy).

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Topics 2.1 2. 1 -2 .9 Introduction to Alternative Investments

4.

Structu red products, such as collateralized debt obligations (CDOs) and Structured credit derivatives, create a specific risk, return, tax, or other profile by segmenting the cash flows of traditional investments or linking the returns to one or more market values.

Structures Struct ures o f Alternative Inve Investme stments nts

Alternative investments can be described by several interconnected interco nnected structures. • • •

•

•

Regulatory structures include government regulation and taxation. Securities structur structures es include methods of cash cash flow flow securitization and the resulting tradable units. Trading structures include the development and execution of trading strategies utilized by investment managers and the resulting performance impact of the strategies. strategies. Compensation structures include arrangements that impact a managers fees, fee s, exposure to the investments investmen ts performan performance, ce, and conflicts of o f interest interest with investors. Institutional Institut ional structures include financial institutions and markets that affect the ownership and trading of a particular investment.

Return Characteristics

Alternative investments are often viewed as diversifiers since the y frequently freq uently have low or no correlation with traditional assets, allowing investors to reduce risk without hurting return expectations. Alternative investments also tend to be illiquid (infrequent or low-volume trading) and lumpy (difficult to divide), meaning that immediate transactions occur at lower prices than for an equivalent liquid asset. Many alternative investments trade at inefficient prices due to fewer participants, lower competition, higher transaction costs, and an inability to establish both long and short positions. Finally, the return distributions for many alternative investments are not normal due to infrequent trading, nonlinear payoffs, and leverage. Altern Alt ernativ ativee Investin Investing g Goals

The prim primary ary goals associated with investing in alternative ass assets ets include active management, absolute and relative return generation, arbitrage, return enhancement, and return diversification. Alternative investment managers are evaluated in terms of o f active management manageme nt systems, which incur active risk (deviation from the benchmark) to obtain active return (average portfolio return above the benchmark). Managers may

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generate absolute returns (evaluated against a standard of zero or the risk free rate) or relative returns (evaluated against a risky benchmark return) by engaging in arbitrage, return enhancement, or return diversification strategies. i c 2.2: T h e E n v i r o n m en e n t o f A l t e r n a t i v e In v e s t m e n t s T o p ic

Market Participants Buy-side institutions are asset managers that focus on acquiring appropriate securities for their investment portfolios. •

•

• •

•

•

•

• •

Plan sponsors are organizations that fund a health care or retirement plan for qualified members. The plan sponsor manages the plan ass asset etss to meet its obligations and determines the membership requirements and plan structure. Foundations and endowments. Foundations are are nonprofit funds established to support specific charitable activities on a continuing basis while maintainin main tainingg the real value of the portfolio assets assets.. E nd ow m en ts are are funds dedicated to providing financial finan cial support on an ongoing bas basis is for a specific specific purpose.. Foundations and endowments typically purpose typic ally have long investment horizons, high-risk tolerance, and low liquidity needs. Family office and private wealth institu institutions tions are investment firms whose client base consists consists of high net worth families. Sovereign Soverei gn wealth funds are pools of assets owned by a government and typically managed by its central bank. Their purpose is to stabilize the economy, to provide a potential resource for future crises, and to provide future goods and services to citizens. Private investment pools include hedge funds, funds of o f funds, private equity funds, and commodity trading advisers. These funds are typically structured as limited partnerships and utilize sophisticated trading strategies. Performance-based fees are used to reward top-performing general partners. A separat separately ely managed account (SMA (SMA)) is a portfolio owned by a single investor and managed according to that investors preferences. No shares are issued because a single investor owns the entire account. Mutual funds and ’40 Act funds. These funds fall under unde r the scope scope of the U.S. Investment Company Act of 1940. A recent innovation in this 4 0 Act Act fu n ds , which utilize alternative investments category is altern ative ’40 and alternative investment strategies within withi n the confines confines of the the ’40 Act. Private limited partnerships operate similar to other limited partnership structures. Limited partners experience favorable tax treatment. Master limited partnerships (MLPs) are essentially the same as a private limited partnership but offer the advantage of being publicly traded.

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Sell-side institutions focus on selling investment research and transaction execution services rather than managing accounts. •

•

Large dealer banks underwrite and trade securities and derivatives; often operate their own hedge funds and private equity funds; and engage in proprietary trading, off-balance sheet financing, and over-the-counter derivatives derivat ives trading. Dealer banks also may offer offer account management services to buy-side institutions and may serve as prime brokers. Large dealer banks have the potential to influence the overall health of the financial markets because because of actions actions that t hat can increas increasee systemic risk. Retail brokers generate investment research and execute securities trades for their customers. customers. Retail brok brokers ers also engage engage in proprietary propr ietary trading. Fron Frontt office off ice responsibilities include includ e client c lient meetings to decide investment strategy. strategy. Middle office responsibilities include managing risk and linking front and back offic officee communication. communicati on. Back office office responsibilities include account maintenance, information technology, and clearing and settling trades.

Outside service providers provide professional professional services vital to the formation and continued operation of alternative investment funds. •

Prime brokers execu execute te trades on behalf of investment managers; managers; lend securities to short; and provide research, account statements, other documentation, and financing. Prime brokers allow managers to transact with multip multiple le broker dealers dealers and transact in multip multiple le investment types within with in a single account. • Auditors/accountants review all documentation for accounting issues and provide tax advice advice to managers creating creati ng funds. The accountant accountan t audits fund records, provides tax and compensation advice, and prepares financial statements once the fund is operational. • Attorneys provide legal advice regarding optimal fund structure; maintain regulatory registrations; and prepare documents including private-placement memoranda, offering documents, partnership agreements, subscription agreements, and management company operating agreements. • Fund administrators verify operational controls, ass assets ets under management, and performance figures, and may also be a key figure with regard to tax issues and audit preparation. • Hedg edgee fund infrastruct infrastructure ure service providers reduce the complexity of operating a hedge fund by providing platforms, software, software, and data. • Consultants provid providee portfolio allocation and investment manager selection advice and may also help identify client investment objectives and provide ongoing monitoring mon itoring of portfolio portfolioss and an d managers. • Depositories/custodians hold client assets and provide information services, trade clearance, and trade settlement. • Banks. Investment banks focus focus on investment activities, while wh ile commercial banks focus focus on capital management and provide loans, lines of credit, and external credit enhancement. Non-U. S. banks may ma y be structured differently and provide a different set of services. ©2018 Kaplan, Inc.

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Typess o f Financial Markets Type Primary markets relate to the sale of new security issues. New equity issues involve initial public offerings (IPOs) and seasoned issues or secondary issues. Securitization is is the process of pooling assets and then issuing new securities that derive their cash flows from the pool. The pool assets may be publicly listed or unlisted and vary in terms of liquidity. Primary markets are often used as an exit strategy for alternative investments. Secondary markets are where securities trade after their initial issuance. Secondary markets provide liquidity and price/value information. Welldeveloped secondary markets lower the cost of capital for firms raising external capital in the primary market. In secondary markets, dealer banks serve as intermediaries and trade for their own accounts with other dealer banks and also with broker-dealers. Dealers generally do not charge commissions on bid-ask k spread. transactions. Instead, they make their profit from the bid-as Third marke markets ts refer to regional exchanges where nonmember firms can both make markets in and trade exchange-listed securities without the exchange, thereby reducing transaction costs. Fourth markets allow private electronic exchange of securities between investors without using using a broker as an intermediary. Members avoid the bidask spread by submitting orders that are matched to other outstanding orders through crossing. This market is used by institutions that trade very large (HF7), which involve trades volumes of o f securities. H igh-frequency tradin g (HF7), that are executed in milliseconds and positions that are held for only seconds, private ate typically occurs in fourth markets. Third and fourth markets are both priv markets. Regulations

U.S. financial regulations for hedge funds include: •

• •

Securities Securit ies Act of 19 1933 33:: governs new securities issues and requires the company to disclose relevant information, register new issues, issues, and disseminate a prospectus. Investmen Inve stmentt Company Act of 1940: instituted to regulate investment pools. Hedge funds often utilize exemptions to avoid registration. Investmen Inves tmentt Advi Advisers sers Act of 19 1940 40:: requires that investment advisers register with the SEC. Exemptions Exemptions are related to the total value of managed funds and state registration requirements. The Act also subjects advisers to antifraud regulations.

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Pertinent European financial regulations include: •

•

•

The Undertakings for Collective Investment of Transferable Securities (UCITS) Directive allows hedge funds to be more easily marketed to retail investors throughout the European Union. The Markets in Financial Instruments Directive (MiFID) established more uniform regulations throughout the European Union. MiFID II eliminates many of the loophole loopholess that th at allowed dark pools to exist under the original MiFID. Alternative ative Inves Investme tment nt Fund Fund Man Manag ager erss (A (AIF IFM M) Directiv Directivee requires The Altern fund managers operating in the European Union to meet minimum capital requirements and obtain local regulatory approval. However, funds covered under the UCITS Directive are excluded from this law.

Key hedge fund regulations for several other countries are summarized in the following figure figures. s. Figure 1: European Regulators and Regulations C o u n tr y United Kingdom

France

R e g u la t o r y I n s t it u t i o n s

R e g u l a to r y S u m m a r y

Financial Conduct Authority

80% of European hed ge fund assets assets

(FCA) and P rudential

are located in the U .K. F CA focuses focuses

Regu latory Auth ority (PRA)

prim arily on large hedge funds. funds.

A u to ri te s de s M ar ch es Financiers (AMF)

T h e A M F al lo w s fo r fu n d s o f hed h ed ge funds, unleveraged hedge funds, and leveraged hedge funds. T h e B aF in en fo rc es ru le s re la te d to redemption procedures, subscription

Bundesanstalt fiir Germany

Finanzdienstleistungsaufsicht (BaFin)

limits, custody procedures, and disclosure requirements. In addition, it allows for funds of funds funds to be distributed distributed both p ublicly and privately, while regular hedge funds can only be distributed privately.

Swisss F inancial Market Swis Switzerland

Supervisory Au thority (FINMA)

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33% of all all funds o f hedge funds assets ass ets are located located here. Th is m ay be attributable to minim al regulations regulations for funds of hedge funds.

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Figure 2: Global Regulators and Regulations C o u n try

R e g u l a to r y I n s ti tu ti o n s

R e g u l a t o r y S u m m ar ar y Hed ge funds are subject to the same

A u st ra li a

A u s tr a li an S ec ur it ie s a n d

regulations as managed funds. In general, domestic funds used as unit

In v es tm en t C o m m is si o n

trust structures and foreign funds are classified as foreign classified foreign investm ent funds. A u s tr al ia n ta x at io n p o li ci es fo r h ed ge

(ASIC)

funds are complex. Funds are required to adhere to .. B r“ ' 1

the classification claimed in their

Securities Co m m ission

investment policy. policy. The C VM regul regulates ates

(C V M )

investor types, required reporting, and allowable asset valuation methods. T h e m a jo ri ty o f fu n d s ar e so ld u si n g linked products, such as principal protected notes. D ealers, portfolio portfolio managers, and advisers must register

r

, Canada

Can adian Securiti Securities es A d m i n is is t ra ra t o rs rs ( C S A )

w it h th e C S A a n d ar aree s u b je ct to compliance reviews. Most funds can on ly be sold to accredited investors. Disclosure Disclosu re of audited annual (and in some cases, semiannual) financial statements is required.

T

F in a n ci a l Se rv ic ices es A g e n cy

T h e FS A pl ac es m in im a l re g u la to ry

J l p a n

(F SA )

requirements require ments on hedge funds. Governmental desire to increase

M onetary Authority of

alternative alter native investment trading has

Singapore (MAS)

caused deregulation and lower taxes for hedge funds. Hedge fund managers must register as financial service providers and are not

South Africa

Finan cial Service Servicess Board

allowed to ma rket to retail investors. investors. However, hedge funds remain unreg ulated. Taxation rules of hedge funds are not yet finalized. Hedge funds m ust register register w ith the

TT . . A . Um ted Arab h m i ra r a te te s

G u lf C o o p e ra ti o n C o u n c il ; UA£ Bank. ^ 0 . A . Financial Services Authority

UAE Central Bank or the Dubai Financial Services Authority. Funds are subject subject to m arketing lim itati itations, ons, risk assessment requirements, audit requirements, and regulatory oversight. Hedge funds are not taxed. taxed.

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Liquid Alternatives Liquid alternatives utilize private placement investment strategies within a retail fund. Regulatory constraints include leverage limits, diversification requirements, require ments, and liq uid uidity ity requirements. requirements. Liquid alterna alternatives tives can be divided divided into five categories:

1. Skill-based replication products —atte —attempt mpt to earn comparable compar able returns to alternative funds that rely on managers skills by using a more basic strategy that may use a mathematical or system approach. 2. Liquidity-based replication products —uti —utilize lize liq liquid uid investments that hav havee similar chara characteri cteristics stics to illiqu id securities securities used in illiqu illiquid id alternative funds. funds. 3. Constrained clones —atte —attempt mpt to follow similar simila r strategy str ategy as an existing exi sting alternative investment product but modified due to investment limitations (e.g., liquidity, leverage, diversification). 4.

Unconstrained clones —at —attempt tempt to follow a near-iden ne ar-identical tical strategy as an existing alternative alternative investment product that is relatively liqu id.

5. Diversified/absolute return products —focus on creating creati ng returns that have low correlation with traditional investments but do not pattern strategy after existing alternative investments. The fact factors ors responsible for the difference in risk-adju risk-adjusted sted returns for liquid liq uid alternatives and private placements are that liquid alternatives have: (1) no incentive fees, (2) less skilled managers, (3) an inability to capture illiquidity premiums, and (4) a narrower set of permissible investment strategies. Taxation

Countries tax investment returns differently depending on whether the returns are in the form of interest, dividends, or capital gains. Interest and dividends may be taxed at a reduced rate or at ordinary rates after exceeding a threshold. Long-term capital gains are often taxed at a lower rate than short-term capital gains, and generally taxes are paid only when gains are realized. Hedge funds often seek out locales that tha t offer offer income tax relie r elieff at the corporate level. In addition to income taxes, other forms of taxation should be considered, including real estate taxes (used to fund local services), wealth taxes (annual tax on net worth), estate taxes (charged when estate assets transfer heirs), transaction taxes, (charged on security transactions), and foreign investment income taxes taxes (charged on foreign investment profits).

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Topics 2.1 2. 1 -2 .9 Introduction to Alternative Investments i c 2.3: Q u a n t i t a t i v e F o u n d a t i o n s T o p ic

Compounded Returns Compounding refers to the growth in value realized on a reinvested asset. Compounding recognizes interest earned on reinvested interest. Compounding increases overall return, but when calculating a return for a set beginning and ending dollar amount, the realized compounded return will be lower than the simple interest return, all else equal. Over discrete time periods, the simple holding period return equals:

R = 1+ V

R

2

2 -1

--------

2

/

In finance, we often are interested in continuously compounded returns. Continuous compounding refers to the continuous reinvestment of interest, in which whic h case the simple return wil willl equal:

Logarithms can be used to calculate the continuously compounded rate. Taking the natural logarithm of both both sides sides of o f the continuous compounding equation and using the property of natural logarithms: logarithms:

ln(l + R) R) = ln(eR1™ ) = R m^° °

In the the previou previouss equation, l n (l + R) is the the log return return or continuously compounded return. Log returns greatly facilitate the calculation of the geometric mean return. We can calculate the geometric mean return using ordinary returns as follows: 1/T

geometric mean

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n a + R . ) lt=l J ©2018 Kaplan, Inc.

-1


Another method m ethod is to use log returns, in which whi ch cas casee the geometric mean return ret urn is calculated as: geometric mean =eM In the equation above, M is the arithmetic mean log return:

In(l + R j ) + In(l +

~~

) + ...+ .. .+ In (l + Rq Rq^)

T

There are a couple of key points regarding rega rding the normal distr distributio ibution n and compounded returns. Assume we are compounding monthly returns to create a quarterly compounded return. If monthly returns are normally distributed, the quarterly retur returns ns using discrete compounding are not normally distributed. However, if monthly log returns are normally distributed, the quarterly log returns are also normally distributed. This is why log returns are often preferred for statistical analysis.

R e t u r n s B a s e d o n N o t i o n a l P r i n c i p a l A forward contract contract is a bilateral contract that obligates one party to buy and one party to sell a specific quantity of an asset, at a set price, on a specific date in the future. The initial value of a forward contract is zero to both parties at contract initiation. This initial zero value creates a problem that requires us to use notional principal to determine investment returns. Notional principal is the face amount on the underlying asset upon which cash flows on a derivative instrument (e.g., forward or swap) are based. The return on notional principal equals the gain or loss on a forward contract divided by the notional principal. However, this measure is misleading because the initial cash outflow does not equal the notional principal. A better method is to express the return on a fully collateralized basis, in which the forward contract is matched with capital equal to its notional principal.

Rfc fco oii = ln( n(ll + R) + Rf collater terali alized zed bas basis is,, in Alternatively, the return can be expressed expressed on a partially colla which the forward contract is matched with w ith capital equal to a percentage, p , of

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the forward forward contracts notional principal. A partially collater collateralized alized return is a leveraged return, where the leverage factor L equals equals 1 / p p..

Rpcoll

= [£ x ln ln(l (l + R)] + Rf

I n t e r n a l R a t e o f R e t u r n The internal rate of return (IRR) is the discount rate that equates the present value of an investments invest ments cash inflows inflows with wi th the present value of o f the investments inv estments cash outflows. In other words, the IRR is the return associated with a zero net present value. IRR is calculated using an iterative process with the following formula. Note that using the IRR function on your financial calculator will save you time on exam day. c f 2 _ s _ + + (l + IRR) (l + IRR)2 IRR)2

•••

+

CFj (1 + IRR)t

The IRR is the standard measure of performance in the private equ equity ity and private real estate markets in which regular valuations of assets are not available. The IRR accounts for both the tim timing ing and magnitud m agnitudee of cash cash flows flows into and out of the investment. •

•

• •

Lifetime IRR (overall IRR) assumes all of the cash flows are available from start to finish of the investment. investment. No terminal appraised value is needed since all cash flows are known. In a lifetime IRR calculation, period T signifies the end of o f the the investment. Interim IRR utilizes an assumed terminal value. In an interim IRR, period T occurs occurs prior to the end of the investment and an appraised value is used for the period T cash cash flow. Point-to-Point Point-to-P oint IRR assumes that the time 0 and time T cash flows are appraised values values or are other cash cash flows flows during du ring the investments investmen ts lifetime. Since-Inception Since-Inceptio n IRR is the IRR used to assess the performance of a fund (rather than an investment) since the date of its formation. Each periods cash flows are the aggregate cash flows of all portfolio holdings. Similar to the interim IRR, an appraised portfolio value is used for time T.

IRR is a highly useful method to calculate returns. However, IRR is subject to several problems stemming from its assumptions and cash flow patterns. •

(i.e., positive initial cash flow) changes the Borrowing typ typee ca cash sh flow patterns (i.e., interpretation of the IRR. In this case, a high IRR reflects the effective cost of borrowing, borrowing, not the return on investment.

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• • • •

•

may create multiple IRR solutions and M u lt ltip ip le s ig ignn ch a n g e cas c ashh f l o w p a tt er n s may the number of solutions may ma y equal the number of o f sign changes. changes. Scale differences , which are differences in the timing of cash flows or differences in investment size. arise when one investment lasts longer than another. Differences in tim ing arise the result resultss o f several investments . IRRs also are prob problemat lematic ic when aggregatin g the The combined IRR of two two investments might not equal the ave average rage of the two individual investment IRRs. IRR calculations IRR calculations assume th at all cash flow s are reinvested at a rat ratee eq ual to IRR. In cases where the reinvestment assumption is invalid, the modified

IRR can be used, in which the investments cash inflows are compounded at an assumed reinvestment rate and the investments cash outflows are discounted at an assumed financing rate. dollar-weighted eighted return, meaning it is an average return that depends IRR is a dollar-w on the timing of cash distributions and withdrawals. In contrast, a time weighte wei ghted d return (or g e o m e t r ic m ea n re tu turn rn ) is an average return that ignores the effects of the timing of cash distributions or withdrawals. The use of the time weighted weighte d return rem remove ovess the distortions caused by the tim timing ing of cash cash flows flows and thus provides a better measure of a managers ability to select investments over the period. Conve Conversely, rsely, i f the manager has complete control ove overr money flows flows into and out of an account, the money-weighted return is the more appropriate performance measure.

C a s h D i s t r i b u t i o n W a t e r f a l l In a limited partnership structure, the cash waterfall sets the rules and procedures for the distribution of profits among the providers of capital and investment managers. The cash waterfall is determined by the hurdle rate, carried interest, and management fees. preferred rred return return,, is the return that must be distributed to The hurdle rate, or prefe the limited partners before general partners can earn any incentive fees. A soft hurdle rate allows allows the general partner to share in all profits if the performance of the fund is above the hurdle rate. A hard hurd le rate allows the general partner to share only in profits in excess of the hurdle rate. Carried interest is an incentive fee equal to the percentage split of profits that general partners earn after meeting the minimum hurdle rate and is paid on top of management fees. Carried interest may be subject to catch-up provisions that temporarily allocate a larger distribution of the profits to catch up to the incentive fee. A deal-by-deal carried interest arrangement (i.e., paid on each investment) is better for the general partner but not for the limited partner. A fund-as-a-whole carried interest arrangement (i.e., paid on the entire fund) protects limited partners but might not attract the most talented general partners. Note that incentive fees are similar to the payoffs of a long ©2018 Kaplan, Inc.

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call option. Incentive fees fees become more valuable as greater risk is experienced vesting ing (i.e., the process and timing by the fund. Incentive fees are subject to vest the receipt of fee fees) s) and clawbacks (i.e., clauses giving limited partners rights to reclaim fees due to poor performance). Management fees are fees paid to the general partner to cover basic fund operating costs such as salaries, research, travel, rent, and utilities and are paid regardlesss of the performance of regardles o f the the fund. i c 2.4: S t a t i s t i c a l F o u n d a t i o n s T o p ic

Summarizing Data

Summarizing data is an important im portant component of statistical statistical analysis. Data postt are often described according to a distribution of observations. Ex pos distributions summarize historical or realized values of the random variable. Ex ante distributions summarize possible future values of the random variable. Ex post distributions can be used to approximate ex ante distributions if the distribution has a constant mean and variance (i.e., it is stationary) and a large number of historical data points are available. The normal distri distributio bution n is frequently frequ ently used in statistical analysis. The Th e bell shape of the normal distribution makes it very useful for analyzing data from both an empirical and theoretical point of view. Empirical tests show the normal distribution approximates real world data very well. Figure 3: The Normal Distribution

Th e no norm rmal al curve is sym s ymme metri trical cal.. Th e two halves are ide ident ntica ical.l.

Th e me mean, an, me media dian, n, and mode are equal. Page 16

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The lognormal distribution is generated by the function ex, where x is is normally distributed. Since the natural logarithm, In, of ex is x, the logarithms of lognormally distributed random variables variables are normally distributed, thus the name.. Characteri name Characteristics stics of the the lognormal distribution include: • • • •

Log returns, ln (l + R), are are norma normally lly distributed, or, or, equivalently, (1 (1 + R) are lognormally distribute distributed. d. The distribu distribution tion is continuous. The distribu distribution tion is skewed to the right. The distribu dist ribution tion is bound bounded ed from below by zero so it is useful for for mode modeling ling asset prices, which never take negative values.

The Mom Moments ents o f a Distr D istribu ibution tion

The shap shapes es of o f proba probability bility distribu distributions tions are described by the moments of the distribution. These include both raw and central moments. Generally we are interested in the first raw moment and the second, third, and fourth central moments. The first raw moment is the mean of the distribution. n E(R) -M- == E p ;R l i=l varian iance ce.. :cond central moment is the var varia va rianc ncee = a2 = E [ ( R - m )2 )2]]

The square root of the variance is the standard deviation, a, and is often used to measure the volatility of the data. The skewness statistic is the standardized third central moment.

E e h p T i m p e e ----bKCWIlCbo —

-

r

1

_ _ _ _ _ _ _ _

1

— ~ —

i

a3

Skewness measures the departure from symmetry. The tails of a skewed distribution will be elongated to the right for a positively skewed distribution and elongated to the left for a negatively skewed distribution. For positively skewed distributions, there are more outliers to the right of the mean than to the left of the mean. For negatively skewed distributions, there are more

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outliers to the left of the mean than to the right of the mean. Alternative investments often exhibit exhib it skewness. skewness. The kurtosis statistic is the standardized fourth central moment of the the distribution. Kurtosis refers to the degree of peakedness and, for the normal distribution, equals 3. Therefore, the excess kurtosis for any distribution equals:

excess kurtosis

A mesokurti mesokurticc distribution has zero excess kurtosis. A leptokurtic leptokurtic distribution has a peak that extends above that of a normal distribution and tails that are fatter than those of a normal distribution. Relative to a normal distribution, a leptokurtic distribution has a greater percentage of small deviations from the mean and a greater percentage of extremely large deviations from the platykurtic distribution has a peak that lies beneath that of a normal mean. A platykurtic distribution. Relati Relative ve to a normal normal distribution, a platykurtic distribution has a smaller percentage of small deviations from the mean. Correlation

Covariance and correlation are extremely important concepts in finance. Covariance is an unsealed statistical measure of how two assets move together. It is the expected value of the product of the deviations of the two random variables from their th eir respec respective tive mean values. Covariance is calculated calculate d from a sample as follows:

The key component c omponent of o f the covariance is the cross-product (i.e., (i .e., the numerator num erator in the previous equation). The cross-product is positive if both assets perform well at the same time or perform poorly at the same time. The T he cross-product willl be negative if wil i f one asset asset performs performs well while the other performs poorly poor ly and vice versa. versa. The correlation coefficient is a statistical measure of the linear relationship between two variables. When applied to asset returns, the correlation measures

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the strength of the relationship of the returns for two assets. The correlation coefficient is calculated as follows:

Cov(Ri 5Rj)

There are three key results of interest when calcu calculatin latingg the correlation corr elation coefficient between the returns of two assets. • • •

If corre correlation lation equals 1.0, asse assets ts are perfect perfectly ly and posit positively ively correlated. Asset Asset returns move move proportionally propor tionally in i n the same direction with w ith each other other.. If correlation equals equals -1 .0 ass assets ets are perfectly and negatively negatively correlated. Asse Assett returns move proportionally in the opposite direction from each other. If correl correlation ation equals 0, assets assets are indep independen endent. t. There is no relat relation ion in the movements of the returns of the two assets.

Correlation plays an important role in portfolio diversification. To demonstrate this point, consider the equations for portfolio standard deviation:

Note that correlation is a significant component of the portfolio standard deviation calculation. If the correlation of returns between assets i and and j equals one, then: (T = W; O; +W + W; (TP

1 1

J

J

If the the correlation is less less than one, then:

a

P

< w - aa- + w ; a J J 1 1

Thus, low or negative correlations have the power to significan signi ficantly tly decrease portfolio standard deviation.

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Outliers have a large effect on the correlation and will drive the correlation estimate away from its true value. To address the outlier problem, we can calculate the Spearman rank correlation, which is the correlation of the asset asset returns ranks. 1.

Ran k the observations Rank observations for for each each variable with the largest being one and the smallest being be ing Af Af (i.e., the sample size) size)..

2. Compute Compu te the difference in the ranks of each paired observation Y- (i.e., Xj, Yi as di =Xj — (i.e., X and and Y are ranks of the original observations). 3. Calcu Calculate late the the Spearman rank correlation coefficient as as::

Beta is closely related to the correlation. While correlation measures the strength of linear relationship between two assets, beta measures the slope of the linear relationship. In the context of the CAPM, the formula for beta is: _ Cov(R Co v(Rii ,R m) _ CTi,m _22 _ Var(R Va r(Rm) m) If an assets returns are correlated over time, we can conclude there is predictability in the returns. The correlation over time for an asset is called autocorrelation. The formula for the bo rd rder er autocorrelat autocorrelation ion is:

If the variance of returns is constant over time, autocorrelations will diminish over time. A test for the existence of o f serial correlation (i.e. (i.e.,, first-order autocorrelation) can statistic, tic, which test be conducted using the Durbin-Watson statis testss the hypothesis:

H o: Pt,t- l “ 0^ a : Pt,t - i ^ 00-

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The formula for the Durbin-Watson Durbin -Watson statistic is:

If the sample is large, the Durbin-Watson statistic can be approximated using the following: D W « 2 ( ll - p tjt. 1)

Standard Deviation and Variance

Depending on the distribution, we can make assumptions about how much of the data will fall within a certain distance from the mean. In the normal distribution, approximat approximately: ely: • • •

68% of the data lie with within in plus or minus on onee standard deviation of the mean. 95% of the data lie withi within n plus or minus two two standard deviations of the mean. 99% of the data lie withi within n plus or minus three three standard deviations of the mean.

To find find these boundaries for a portfolio, we must calculate ca lculate the portfolio mean and variance. The variance of returns of an 72-asset portfolio equals:

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The variance varian ce can be calculated using regular or log returns. Using log returns allows for some simplification in the calculation. If log returns are uncorrelated over time, then the variance of a multi-period log-return simply equals the sum of the inter-period log-return variances. Taking this one step further, if the variance variancess of daily log-returns log-returns are identical, and if i f returns returns are independent (i.e., zero autocorrelation), then the T-period log-return variance is simply T times the variance of a daily log-return where T is the number nu mber of days. Var[l Va r[ln( n(ll + R ^ )] =T x Var[ln Var [ln(l (l + R^] Therefore, the standard deviation of a multi-perio multiperiod d log-return equals the square root of T times the standard deviatio deviation n of daily log-re log-returns. turns. Autoc Au tocorre orrelatio lation, n, Illiquidity, and No Nonlin nlinear earity ity

The normal distri distributio bution n is highly hig hly useful, but b ut alternative investment returns often exhibit non-normality. The main causes of non-normality include autocorrelation, illiquidity, and nonlinearity. •

•

•

Autocor relation Autocorrelatio n occu occurs rs when the return in one period is is directly related to the return from the prior period. Autocorrelation will cause more extreme outcomes than predicted by the normal distribution. Manyy alternative investment Man investmentss suff suffer er from ill illiqu iqu id idity ity,, in which transactions do not take place on a regular basis and require appraisal valuations. Appraisals Appraisa ls often exhibit positive autocorrelation that produces non-normal returns. Alternative investments may als also o exhibit non nonline linear ar return patterns. Per Perhap hapss the best example example of nonlinearity nonlinea rity is the distribution distrib ution of returns returns associated associated with a call option. Beca Because use of these these issues, issues, alternative investments may m ay need to be modeled without relying on the normal distribution.

Tests Te sts o f Norma Nor mality lity

Wh ile it may be tempting tempt ing to conclude that a sample that th at has either ei ther skewness skewness or excess kurtosis is indicative of a non-normal distribution, this is an incorrect conclusion. This is because a sample, by definition, is an incomplete set of data. Therefore, we need to utilize a normality test that utilizes the sample size, sample skewness, excess kurtosis, and a confidence level.

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Jarque-B ue-Bera era stati statistic stic is used to test data for departures from the normal The Jarq distribution. The Th e formula for the Jarque-Bera statistic is:

The Jarque-Bera Jarq ue-Bera statistic is used to test the hypothesis that th at a set of returns follows a normal distribution. The statistic follows a chi-square distribution with 2 degrees of freedom. freedom. The hypothesis of o f norm normality ality is rejected if i f the Jarque-Bera Jarque-B era statistic statis tic for the sampled data exceeds exceeds the critica criticall value. Forec Fo recast astss o f Future Future Return R eturn Volatility Vo latility

Two popular Two popul ar time-series models used to foreca forecast st risk are the ARCH ARC H (autoregressive conditional heteroskedasticity) and GARCH (generalized autoregressive conditional heteroskedasticity) models. ARCH model modelss are used to forecast variances based on recent volatility in prior periods. An example of an ARCH(l) model is as follows:

variance forecast forecast in period t +1

a0 + al £?

GARCH models are used to forecast variances based on recent unexpected returns and past variances. GARCH is a more robust method for forecasting volatil vol atility ity because it i t allows volatil vo latility ity to change based on the histor historyy of o f the variable, eve even n if i f the price level for the variable has not changed. An example of a GARCH(1,1) model is as follows:

variance forecast forecast in period t +1

QLq T

2

2

T o ^ O ’t

i c 2.5: M e a su s u r e s o f R i s k a n d P e r f o r m a n c e T o p ic

Altern Alt ernativ ativee Measures o f Risk

Standard deviation may not be the appropriate risk measure for all investments. Alternative investments may m ay be analyzed using a different set of o f risk measures to form a more complete picture of risk exposure. exposure.

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Semivariance measures only downside risk and is computed as the average squared deviations below the mean.

semivariance

for Rt
for Rt
sample semivariance

T —1 —1

Semistandard deviation (or semideviation) is the square root o f semivariance.

semistandard deviation

Rt-E(R)f E for Rt
E (R. - E(R)f

sample semistandard deviation =

forr R t
T —1 —1

Targe t semivar Target se mivariance iance measure measuress the averag averagee squared deviations below a target level (rather than the mean). Target semistandard deviation is the square root of target semivariance. Shortfall risk is defined as the probability that the investment return will fall below the target return. Trac king error measu Tracking measures res the extent to which the investment investmen t returns deviate from the benchmark returns over time.

tracking error

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Maximum drawdown is the worst percent loss experienced from peak to trough over a specified period of time. Inve Investors stors concerned with worstcase scenarios may find drawdowns to be more intuitive than volatility risk measures. Valuee at risk (V Valu (VaR) is a measure of potential loss. VaR is interpreted as the worst possible loss under normal conditions ov over er a specified period for a given confidence level. The strengths of VaR are that it is simple to apply, can be applied across segments within a fund or across funds, and is useful when it makes no sense to examine the worst-case scenario. A major weakness of VaR is that it can be misleading for non-normal distributions. Conditional VaR (CVaR), also known as expected shortfall or expecte d tail loss loss , is the expected loss given that the portfolio return already lies below the pre specified worst-case quantile return. Estimation o f Value at Risk

A common method m ethod of o f calcu calculatin latingg VaR is the parametric param etric VaR approach. Parametric VaR assumes returns are normally distributed and is calculated as follows:

The VaR model can be adapted to accommodate the more complex assumption that security returns are generated by normally distributed economic factors. Using a factor model, VaR is calculated as a function of variances and covariances covari ances of the factors factors and of the exposure exposuress of the security returns to the factors. A key statistical stati stical inpu inputt used to calculate calculat e the parametric parame tric VaR is the volatil vo latility ity of the asset. Volatility can be estimated based on historical data or implied option volatility. Analysts must m ust be careful when wh en using VaR for analyzing analyz ing investments with leptokurtic distributions. In these cases, the suggestion is to use a distribution that allows for fat tails, such as a mixed distribution or the Student ^-distribution. An alternative and simpler solution is to increase the number of standard deviations. Historical VaR uses past return data and ranks the returns to determine which fall below a given confidence level. ©2018 Kaplan, Inc.

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Monte Carlo analysis for VaR simulates values for risk factors and estimates how changes in risk factors might affect the fund s returns. A model is used to randomly generate possible future outcomes for the fund, and those simulated outcomes indicate indi cate what wh at types of losse lossess are possible for the fund.

Note that caution must be exercised when aggregating VaR measures of individual investments at the portfolio level. The only case in which the portfolio VaR equals the sum of the individual asset VaRs is if the individual asset outcomes are perfectly and positively correlated. Performance Measures

The Sharpe ratio equals the expected excess return (i.e., the mean portfolio return less the risk-free rate) earned per unit of total risk: E(Rp) E(R p) —Rf —Rf

The Sharpe ratio is the appropriate appr opriate performance measure if i f portfolio p is the total portfolio owned by the investor. The Sharpe ratio should not be used for components of the total portfolio, unless the components themselves are welldiversified portfolios. The Sharpe ratio is sensitive to the return computation interval and should not be used to compare portfolios with different levels of skew and kurtosis. Treyno ynorr ratio equals the expected excess return (i.e., the mean portfolio The Tre return less the risk-free rate) earned per unit of syste ma tic risk risk.. Like the Sharpe ratio, the Treynor ratio is sensitive to the return computation interval and should not be used to compare portfolios with different levels of skew and kurtosis.

E(Rp)~ R f Pp The Sortino ratio equals the portfolio excess return (i.e., the mean portfolio return less the target return ) divided by the target semistandard deviation (a downside risk measure): . . E( R ) —R t E(R Sortino ratio = 1 TSSD -----

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The information ratio equals the portfolios excess return (i.e., the mean portfolio return less the mean benchmark return) divided by the portfolio’s tracking error. E(Rp)

■^benchmark

The return on VaR, is the expected return on the portfolio divided by its VaR.

RoVaR =

E(Rp) VaR

Jensens alpha Jensens alpha,, also known simply as alpha , is the difference between the portfolio mean return and CAPM ex post mean return:

M2 is a risk-adjusted measure of the portfolio return. Using leverage, the portfolio standard deviation is adjusted to the point where it equals the standard deviation of the market index. M2 equals the expected return on the leveraged portfolio that has the same standard deviation as the market index. The following fo llowing figure illustrates illustrate s the M 2 method. Figure 4: The M2 Approach

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M2 is calculated using the following equation:

The average tracking error is the difference in mean returns between the portfolio and the portfolios benchmark. It is the numerator of the information ratio. i c 2 . 6 : F o u n d a t i o n s o f F i n a n c i a l E c o n o m i c s T o p ic

Informational Market Efficiency

In efficient markets, investors are unable to earn abnormally high returns. Forms of informational market efficiency include: • •

•

efficie ienc ncy, y, markets already capture all past price and volume In weak form effic information (i.e., technical analysis will not earn abnormal returns). In semistrong form efficiency, markets capture not only all past price and volume information, inform ation, but also all public information, (i.e., systematic or discretionary trading strategies will not earn positive risk-adjusted returns). for m efficie efficiency, ncy, not even private information is useful in In strong form creating profitable trading strategies, implying that neither technical nor fundamental analysis is useful.

Factors that cause improved informational market efficiency are: (1) larger asset values, (2) higher h igher frequency of trades, (3) little l ittle or no trading tra ding frictions, (4) low levels of regulatory constraints, (5) easier access to quality information, and (6) lower levels of uncertainty about asset valuation. Assett Pricing Models Asse

Asset pricing pricin g models generall ge nerallyy include incl ude three primary prim ary components: (1) the risk-free rate of return, (2) factor risk premiums, and (3) factor sensitivities for the asset. Asset pricing models can be used to separate risks and returns into diversifiable (idiosyncratic) and non-diversifiable (systematic) components and to quantify the compensation expected to be received for risk. Ex ante asset pricing models are important for developing frameworks to analyze investment performance. A single-factor example of this model type is the ex ante form of the capital asset pricing model (CAPM).

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E(R (Rll) = R f + p,[E ,[E(R (Rm m) - R f] According to the CAPM, the expected return retu rn on any asset is solely determined determi ned by its systematic risk (beta). The CAPM also states that no additional expected return will be earned by bearing non-systematic or idiosyncratic risk. Systematic risks are driven by non-diversifiable market factors. Idiosyncratic risks are driven by diversifiable investment-specific factors that can be offset by combining assets within a portfolio. An ex post asset pricing model descri describes bes “after-the-fact” historical returns. The ex post form of the CAPM is:

According to the ex post post CAPM CAP M realized excess excess returns are the result of o f two factors: systematic returns, (3 (3(R (R —Rf) attribu attr ibutab table le to broad mar market ket effec effects, ts, and idiosyncratic returns, e . If the assumptions underlying the CAPM are valid, then empirical tests of the time series CAPM-based regression should indicate that: the intercept estimate is not significantly different from zero, indicating that the excess return for the asset equals the expected return described by the CAPM; the beta estimate equals the true beta of the asset; the estimates of e reflect the effects of idiosyncratic risks. A weakness weakness of o f the the CAPM C APM is that it assum assumes es abnormal abn ormal performance doe doess not exist. This creates an internal inconsistency when using the CAPM to measure superior performance. Another weakness is that the CAPM assumes that all m ), which investors hold the market portfolio ( m w hich is unobservable. For traditional investment frameworks in which it might be logical to assume investors will invest in the market portfolio and can easily diversify idiosyncratic risk, the CAPM might work well. However, for alternative investments, many assets are not publicly traded or trade infrequently, meaning that idiosyncratic risk is not easily diversified away. If investors can earn positive returns on idiosyncratic risks, we must find factors that capture those risks and will explain future returns well.

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Benchmarking Benchmark ing W ith Multifactor Asset Pricing Models Models Multifactor asset pricing models describe the relationship between expected returns of assets and the assets’ exposures to multiple risk factors. The equation for a general K -factor -factor ex ante model is:

The ex post version version of the multifactor mu ltifactor model is:

Risk factors are derived based on theory or on empirical observation. The main weakness with emp empirica irically lly derived multifa multifactor ctor models is that the factors factors may m ay have been identified from spurious correlation or or may have explained the past well with w ith little abi ability lity to explain the future. The step stepss to derive an empirical em pirical multi multifactor factor model are: Step 1: Derive excess excess returns for the security. potentiall factors. factors. Step 2: Identify a set of potentia Perform orm ttests ests of significance to identify identif y the important importan t priced factors factors.. Step 3: Perf

Assumi ng the facto Assuming factors rs are tradable trada ble assets (rates of return can be observed, observed, from which whic h the risk premiums can be calcul ca lculated) ated),, then the intercept inter cept of the ex post post multifactor model reflects the abnormal performance of the security. The Fama-French model is an empirical multifactor asset pricing model:

E(Rj) - Rf = (31( 1(RmRm- Rf) + |32E(SMB) + p3E p3E(HML) (HML) The Fama-French-Carhart four-factor model adds a fourth factor based on the difference in returns between the prior year’s winning and losing stocks (i.e., the momentum factor, UMD):

E(R (Rj) j) - ^ = P1(Rm P1(Rm-- Rf) +p2 + p2E(SM E(SMB) B) + p3 p3E(H E(HML ML)) + p4 p4E(UMD E(UMD))

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The Fama-Fre Fama-French nch and Fama-French-Car Fama-French-Carhart hart models have found wide wi de application for traditional equity inves investments, tments, but application to non-equity non-equ ity alternative investments has been limited. W ith regard to empirical With emp irical multif multifactor actor models, three cave caveats ats are in order when derivin derivingg factors. factors. First, we should not indisc in discrim riminat inately ely test a mul multitud titudee of factors. Second, we should avoid identifying factors based on spurious correlation. Third, the CAPM does not work well for alternative assets, which could have large idiosyncratic risks that are not easily diversified away. Arbitrage-Free Arbitrag e-Free Financial Models Arbitrage-free Arbitragefree mode models ls are pricing models that assume arbitrage opportunities are short-lived or nonexistent. According to the simplest arbitrage-free models, futures price curve curvess are only o nly an expre expression ssion of current variables.

In the spot market (or cash market), where trades are for immediate immedia te delivery, the only two criteria for the arbitrage-free pricing model are that: (1) two economically identical assets exist, and (2) their prices and returns are equal. A basic carry trade is unhedged and involves borrowing in a currency with a low interest rate (e.g., Japanese yen) and lending in a currency with a high interest rate (e.g., Australian dollar) in order to profit from the interest rate differential between the two currencies. Derivatives may be used to hedge away the exchange risk, resulting in an arbitrage trade. A forward contract contract is a bilateral contract that obligates one party to buy and one party to sell a specific quantity of an asset, at a set price, on a specific date in the future. Cost of carry is a measure of the financial difference between holding a spot position and holding a forward position. Any difference between the spot and forward price is due to the cost of carry, which causes the term structure of forward prices to have a slope or curve.

F (T) =S +carrying costs If at any point in time the forward price does not equal spot price plus carrying costs, arbitrage will ensue to restore the relationship. Financial forw ards include include contracts on stock indices, U.S. Treasury bond

futures, and Eurodollar CD futures. With financial assets, there may be a

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monetary benefit to holding the underlying asset, which will decrease the no-arbitrage futures price because the net cost of holding the asset is lower. Accounting Accou nting for a known dividend div idend or coupon yield yiel d results in the following forward forwa rd pricing relationshi relationship: p: F(T)) =S x e(rF(T e(r- d)x d)xT T A binom bi nom ial tree mode modell is often used for option pricin p ricingg and show showss the possibl possiblee values an option can take at each given time period. It reflects reflects the uncerta un certainty inty in outcome by modeling an upward and downward movement at each state. Term Stru Structur cturee and Pricing o f Forward Forwar d Contr C ontracts acts

Two factors that differentiate forward and spot trades are interest costs and Two dividend yields. Alternative investments, and commodities in particular, are driven by three additional factors: (1) forecasts for changes in supply and demand, (2) storage costs, and (3) convenience yield. There are four cost-of-carry model scenarios for financial securities. 1. In a simp simple le scenario wi with th no inter interest est costs costs and no divide dividends, nds, there ther e are are no differences in forward prices and all forward prices equal the spot price. This results in a flat term structure of forwards. forwards. 2.

The interest rate equals the dividends rate, but both are positive. This also results in a flat term structure of forwards.

3. The interest rate exc exceed eedss the the dividend rate. Wh When en that happens, the noarbitrage forward price must exceed the spot price and the term structure of forward prices is upward sloping. 4.

The dividend rate exce exceeds eds the interest rate, rate, and the no-arbitrage forward price is lower than the spot price. The term structure of forward prices is downward sloping.

Option Characteristics, Spreads, and Combinations

Options are contracts that give the option holder the right, but not the obligation, to enter into a specific transaction in the future. • •

A call option gives gives the option option holder the right to buy a security or or a particular particu lar asset in the future at a specifi specified ed price. A pu putt option gives gives the holder the the right to to sell sell a particul particular ar security or or asset asset in the future at a specified price.

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An option spread involves: (1) either calls or puts (but not both) and (2) both long and short positions on the underlying security. • •

A bull spread combines a long position in a lower strike price option with a short position in a higher strike price option. A bear spread combines a long position in a higher strike price option with a short position in a lower strike price option.

Option combinations involve a combination of both calls and puts on the underlyingg sec underlyin securit urity. y.

•

•

•

•

•

An option straddle is a position in a call and a put (either both long or both short) short) on the same underlying underly ing security, same expiration date, and an d same strike price. An option strangle is a position in a call and a put (either both long or both short) on the same underlying security and expiration date, but with diffe ren t strike strike prices. A risk reversa reversall combines a long out-of-the-money call combined with a

short out-of-the-money put on the same asset asset and with the same expiration. An option collar is a long position in an out-of-the-money put and a short position in an out-of-the-money call. The option collar is therefore the same as the short position in a risk reversal, and has the same payoff diagram as a bull spread. A collar includes a long position in the underlying security, which is combined with a long put option and a short call option. The collar investor expect exp ectss only onl y modest volatility volatil ity and is looking to protect against downside risk but is willing to forgo upside potential beyond a certain point.

Put-call parity is a no-arbitrage relationship between two sets of positions with identical payoffs: (1) a long position in an underlying asset and (2) a long call, short put, and long risk-free bond positions.

call +risk-free +risk-free bond bond - put = underlyin underlyingg asse assett Option Prici Pricing ng Models

T he fou The fourr op optio tion n p ri rici cing ng mo models dels are as follo follows: ws: 1 . The basic option pricing model values an option on a portfolio that th at contains both long and short positions. The option gives the option holder the right to either purchase the entire portfolio or walk away and let the option expire. Po =P1 =P1N( N( d) -P N( d- v)

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2.

The Black-Scholes call option formula values a call option as a function func tion of the price of the underlying security, the option strike price, the volatility of security returns, the options time to expiration, and the risk-free rate: c =SNfdj =S Nfdj)) - e" e"rrTKN(d2 KN(d2))

3. The Black forward option pricing model replaces the underlying security in the Black-Scholes call option formula with the forward contract. c =e- ^ fF N ^ ) - KN KN((d2)]

4.

In the currency option pricing model, there are two risk-free interest rates that correspond to the two currencies that are exchanged. In other words, the model prices an option that gives the right to exchange S* units units of one currency with its associated r* risk-free risk-free interest rate, for S units units of another another currency at r risk-free risk-free interest in terest rate: option optio n price = e“ e“r* r*TS*N TS*N(d (d11) - e-rT e-rTSN SN(d2) (d2)

Option Price Sensitivities

Option Greeks measure option sensitivities to four underlying factors: the underlying security, the return volatility of the asset, time to expiration, and the risk-free interest rate. The most widely used sensitivities include: • • • • •

Delta meas measures ures the sensitivity of o f the option price to changes changes in the price of the underlying security. Vega measu measures res the sensitivity of the the option price to changes changes in the price volatility volat ility of the the underly un derlying ing security. Theta measures the sensitivity of the option price to changes in time to expiration. Rho measures the sensitivity of the option price to changes in the risk-free interest rate. Gamma measures the rate of change in delta relative to changes in the price of the underlying security.

i c 2.7: B e n c h m a r k i n g a n d P e r f o r m a n c e A t t r i b u t i o n T o p ic

Benchmarking Benchmarking is the process of identifying the appropriate index against which a portfolio’s portfolio’s performance performance is evaluated. Benchmarks might m ight be formed based on on Page 34

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group p is a group of funds with objectives and peer groups or on indices. A peer grou constraints that are similar to the fund under examination. Many indices exist, but most are value-weighted averages of the index components. Typess o f Asse Type Assett Pricing P ricing Models

Asset pricing models describe relationships between risk and a nd expected return r eturn and can be classified as follows: • •

•

•

A normative model attempts to explain how investors should behave. A positi po sitive ve model model attempts to explain how investors actually do behave. Theoretical Theoret ical models are based on assumptions and logic that presumably capturess underl capture u nderlying ying beha behavior vior.. Empirical models are based on historically observed behavior. Applied Appl ied models are designed to address real-world problems, such as how to achieve efficient diversification, and therefore, are often used for alternative Abstract act mod model elss are theoretical models designed to describe investments. Abstr behavior under hypothetical, often unrealistic, circumstances. Cross-sectional Cross-s ectional asset prici pricing ng models are used to identify key sources of return differentials across across assets assets and aid in the identification of peer peer Time me-se -serie riess asset asset pri pricin cing g mod models els are used to identify key sources groups. Ti of return differentials over over time for an individua indiv iduall asset or portfolio. portfolio. Panel data sets refer to data spanning multiple time periods and multiple assets (a combination of cross-sectio cross-sectional nal and time-series data).

Performanc Perf ormancee A ttributio ttribution n Return attribution (or perfo performa rmance nce attributio attribution) n) is the process of ascribing returns to different components of the assets performance. The active return equals the difference between the managed funds return and its benchmark.

Using the ex post single-factor CAPM equation, the active return equals the deviation of the realized return from the expected return. The CAPM fails to account for common alternative investment characteristics such as multiperiod non-stationarity, non-stati onarity, non-normality of returns returns distributions, and investment illiquidity. Using the Fama-French and Fama-French-Carhart multifactor models, a funds incremental performance equals the difference between the historical excess return earned by the fund versus the return generated by the ex post model. Relative to single-factor models, multifactor models provide a superior methodology for determining the skill of a fund manager.

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Topics 2.1 2. 1 -2 .9 Introduction to Alternative Investments i c 2.8: A l p h a , B e t a , a n d H y p o t h e s i s T e s t i n g T o p ic

Alph Al pha a and Beta Beta is a measure of an assets systematic risk. Beta is useful in traditional and alternative investment analysis as a measure of single or multiple sources of systematic risk in asset valuation and as a benchmark in performance evaluation of a fund or portfolio. An investor seeking a higher expected return may seek portfolios with higher betas. Alternatively, an investor might be interested in matching the beta of a benchmark but with a higher return produced by the skill of the portfolio manager. Alpha is the incremental return earned by the asset relative to a risk-adjusted benchmark. Alpha is useful in security selection as a method in determining whether ass assets ets are underpriced underpri ced or overprice overpriced. d. Alpha Alp ha is also useful in measuri measuring ng investor skill in that positive alpha may indicate superior performance relative to a risk-adjusted benchmark. Ex Ante vs. Ex Post Alpha

Ex ante alpha is the anticipated incremental incremental return on an investment, after adjusting for the time value of money and systematic risk effects. Ex ante alpha often indicates skill on the part of a manager. Ex ante alpha is calculated as:

a i =E(Ri =E(Ri))- { R f+ (3i[E i[E((Rm) - R f]} postt alpha is the realized incremental Ex pos incremental return after adjusting for the time value of money and systematic s ystematic risk effects. effects. Ex post alpha measures portfolio performance relative to a risk-adjusted benchmark over a specific period. Ex post alpha is calculated as:

ex post alpha = e. = Rj - [Rf +(3i(Rm- Rf) Rf)]] There are two steps to performance evaluation: Calculate late the ex ex post alpha after approp appropriately riately controlling controll ing for for Step 1: Calcu systematic risks. Step 2: Determine how much of the ex post alpha was attributable to skill or luck.

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Ex ante alphas may be identified through due diligence analysis and empirical analysis. In due diligence analysis, an investor qualitatively assesses a analysis, sis, an investor managers investment procedures and style. In empirical analy quantitatively analyzes the statistical properties of the ex post alpha and its predictive ability for the ex ante alpha. There are two steps when using empirical analysis to analyze the ex post alpha to estimate ex ante alpha: Step 1: Identify the appropriate ex post asset asset pric pricing ing model or benchmark. Step 2: Test Test the statistical properties of the the ex post alpha to determine what

portion of alpha is attributable to luck or skill. Determining ex ante alpha using empirical analysis may be problematic as a result of invalid inferences, non-normality, and sample selection biases. Return Retur n Attribution

The prim primary ary goal of return attrib attribution ution analysis is to properly proper ly attribute attr ibute returns to systematic risk (i.e., beta), ex ante alpha (i.e., skill), and idiosyncratic risk (i.e., luck). However, empirical return attribution analysis is susceptible to errors stemming from three different types of model misspecification: 1. M is es titim m at ed betas betas.. If systematic risk (beta) of the return series is overestimated (underestimated), then the ex ante alpha from the return attribution will be underestimated (overestimated). rela latio tio ns hi hips ps.. An asset pricing model may assume a linear 2. N on lilinn ea r re relationship between risk and return when, in fact, the true relationship is quadratic or exponential. In this case, the estimate of systematic and idiosyncratic return components will be biased. Alternative investments often have nonlinear risk-return relationships.

3.

Om itt itted ed or misidentifi misidentified ed fact factors. ors. If any part of the investment return is

attributable to omitted or misidentified factors, then it might be incorrectly attributed to either skill or luck. Beta nonstationarity refers to the tendency for beta to shift over time. For instance, if the leverage of the asset changes over time, then the systematic risk of the asset also will change over time. Types of beta nonstationarity include:• include: • • •

Beta creep refers to gradual increases in beta over time. Beta creep might occur as more funds compete for expected returns. Beta expansion refers to increases in beta as market conditions change. Betas increase as the correlation of the fund’s returns with the markets returns increase.

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•

Ma rket timing Market tim ing refers refers to attempts of the fund manager to to alter beta in anticipation of changes in market conditions (i.e., positive risk exposure in anticipati an ticipation on of o f upward movements movements and negative risk exposure exposure in anticipation of downward market movements).

Alph a and beta effect Alpha effectss are difficult di fficult to disentangle. disentangl e. In most cases, cases, performance is attributable to a commingling com mingling of o f alpha and beta. Performance Persistence

Abno rmal retu Abnormal return rn persi persistence stence ref refers ers to the tendency ten dency for idiosyncr idio syncratic atic performance to be positively correlated over time. As mentioned earlier, a major issue in estimating ex post alpha and inferring ex ante alpha is the separation of the estimated idiosyncratic return into skill and luck components. We can attribute idiosyncratic returns to skill or luck as follows: 1.

Calculate Calcu late the ex post alpha for for time period t.

2.

Calculate Calcu late the ex post alpha for for time period t+1 .

3. Test whet whether her the ex post alphas are correlat correlated. ed. Driverss o f Alpha and Beta Driver

Beta drivers are exposures to market risk factors that compensate investors for bearing nondiversifiable market risk. In a CAPM model, beta drivers provide exposure to a single risk factor: the market risk factor. In a multifactor framework, beta drivers may provide exposure to more than one factor. Alpha drivers (e.g., most alternative assets) are exposures to active return factors that are unrelated to benchmark exposures. Investment strategy, as opposed to asset class or geographic location, determines if an investment is an alpha driver. Product innovators are alpha drivers that create new investment opportunities, while process drivers d rivers are beta drivers that deliver beta as cheaply che aply and efficiently as possible. Hypothesis Testing Steps

The four steps in hypothesis testing are are:: Step 1: State the hypothesis. The first component is the null hypothesis, which

usually is the statement that the analyst attempts to reject. The second component is the alternative hypothesis, which is the opposite claim of the null hypothesis and represents the behavior that exists if the null hypothesis is false. Page 38

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Step 2: Formulate an analy analysis sis pla n. Choose a test statistic, which is a function

of the observed observed values of the random variables of interest, based on distributional assumptions for the data. Large test statistic values provide evidence against the null hypothesis and in favor of the alternative hypothesis. Establish a significance level for the test, which denotes the probabi pr obability lity that a significant significan t result may be due to random chance. Common significance levels are 1%, 5%, or 10%. The confidence level equals 100% minus the significance level. Step 3: Analyz Analyzee sam ple data . The next step is to derive the value of the test

statistic, which is used to test the null hypothesis. The test statistic is calculated from the data and is compared against the predetermined critical value to make a reject or fail to reject decision regarding the null hypothesis. The test statistic is often standardized, such as:

test statistic =

estimated value - hypothesized value standard error

Step 4: Inte rpre t the resul results. ts. The decision rule is to reject the null hypothesis if

the calculated test statistic exceeds its critical value or if the Rvalue is less than the significance level. Inferential Statisti Statistics cs

A result is statistical stati stically ly significant sign ificant if it is unlikel un likelyy to have occurred merely m erely by chance. Common errors in the interpretation of statistical significance relate to: • • •

Strength Stren gth o f relati relationshi onship. p. Outcomes with lower ^-values (or higher ^-statistics)

often ofte n are mistaken to indicate stronger relationships. E co no m ic sig s ignn ifific ican an ce . Economic significance describes the extent to which a variable has a meaningful impact. Level o f confidenc confidence. e. Another common error is to confuse the confidence level for the probability that a relationship exists.

Type pe I error occ A Ty occurs urs when rejecting a true null hypot hypothesis. hesis. The probability o f a Type I error is usually denoted by a . The confidence level or specificity of the test is is 1 - a . Type pe II II error occurs when failing to reject an untrue null hypothesis. The A Ty probability of a Type II error is usually denoted by (3. The statistical power power of thee test th te st is 1 - |3.

Increasing the specificity of the test (i.e., lowering the significance level) leads to a decrease in the Type I error but leads to an increase in the Type II error. The erro errors rs can be reduced r educed by b y increasing increasi ng the sample siz size. e. ©2018 Kaplan, Inc.

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Sampling and Testing Issues

Collecting and testing data is subject to several biases and other issues. Selection bia biass refers to the exclusion of certain observations from the sample, causing distortions in the relevant characteristics of the population. Survivorship bias occurs when funds or companies no longer in existence are excluded from the sample. Self-selection bias occurs when fund managers make the decision to report or not report performance. As a result of survivorship bias and self-selection bias, most hedge fund and private equity databases underrepresent poorer-performing funds, causing upward performance bias. In some cases, analysts are overzealous when searching for relationships in data, leading to practices that may compromise the validity of the results. •

•

•

• • • •

Data mining ref refers ers to the practice of vigorously testing data until u ntil valid relationships are found. The premise is that th at vigorous vigorous testing is justified to identify previously uncovered uncovered relationships. Data dredging refers to the practice of overusing statistical tests to identify significant relationships without considering economic rationale, which places too much confidence on the results. Backtesting is the process of applying models on historical data to determine how well the models would have explained the actual result results. s. Backtesting combined with data dredging can lead to false predictions. Overfitting occurs when too many parameters are used to fit a model to historical data. Backfilling occurs when a fund includes returns that pre-date the date of entry in a database, creating an upward return bias. Cherry pick picking ing is the process of selectively reporting results to support a particular particu lar view. view. Chumming involves distributing vastly different investment predictions and then luring investors with marketing material focused only on the correct predictions.

Alp ha and Beta: Iss Issues ues W it ith h A ttr ttrib ibut ution ion

If returns are normally distributed and the null hypothesis of zero alphas is correct, then the percentage of abnormal performers should equal the significance level. However, if returns are non-normal, then the percentage of funds with abnormally high alphas may be higher or lower than the percentage predicted by the normal distribution. Spurious correlation is correlation that does not result from a true or direct relationship. Causality refers to a reliable and direct cause-and-effect relationship among variables.

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Models that do not properly account for nonlinearities are misspecified and can lead to erroneous conclusions regarding correlation and causality. If a nonlinear relationship exists, the correlation between the untransformed variables will be low due to the misspecified linear model. Beta estimation is affected by the choice of factors used in the model. If thousands of tests are performed, hundreds of factors might seem statistically significant merely by chance. The tests may find significant factors where no true relationship exists. Alp ha and Beta: Estimat E stimation ion Fall Fallacie aciess

Lessons regarding alpha estimation include: • • •

Returns should be compared against a proper risk-adjusted benchmark rather than against each other. Alphaa calcula Alph calculations tions are onl onlyy as reliabl reliablee as the asset pri pricing cing model used to estimate performance. The probability probabilit y that a fund alpha is is nonz nonzero ero is generally unknown, even even if the test indicated a statistically significant alpha.

Lessons regarding beta estimation include: • • •

The probability probabili ty that a fund beta beta is non nonzero zero is generally unknown, even even if the test indicated a statistically significant beta. Using a linear regression regression model, a zer zero o beta doe doess not necessarily impl implyy a lack of relationship; only a lack of linear relationship. A statistical statistically ly significant beta do does es not necessarily impl implyy causal causality ity beca because use two variables variables might migh t be linked through another common fac factor tor..

i c 2.9: R e g r e s s io io n , M u l t i v a r i a t e , a n d N o n l i n e a r T o p ic Methods

Single-Factor Regression Models A regres regressio sion n is a statistical method that describes the relationship between a dependent variable and one or more independent variables. Independent variables also are known as explanatory variables .

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A simple sim ple lin linear ear regression is a statistical statisti cal method that models a linear li near relationship between a dependent variable and a single independent variable. A simple linear regress regression ion fits a line to a scatter of o f paired observat observations ions for the dependent and independent variable. variable. The equation for a simple simple linear CAPMbased regression is:

R it - R f = a i + B i( i ( R mt - R f) + ei e it

where: where: Rj =s =stock tock return for asset i in in period t =risk-free rate Rmt =market portfolio return for period t ai = regression inter intercept cept estimat estimatee for asset i Bi = regression slope estimate for for asset i eit = regression residuals for for asset i in in period The following figure illustrates a CAPM-based CAPM-b ased regres regression. sion. Figure 5: CAPM-Based CAPM -Based Regression

The regressio regression n equation eq uation for the figure above above is: regression regres sion estimate of asset ex exce cess ss return = 0.02 + 1.50 1.50(Rm (Rmtt - Rf)

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Ordinary least squares (OLS) is a statistical method that derives estimates that minimize the sum of squared residuals. The regression equation just mentioned is an example of OLS. The residuals are the differences between the dependent variable and the regress regression ion estimate of the dependent variable (i.e., the vertical distances between the scatter points and the regression line). The regression line minimizes the residuals.

The OLS method is most likely li kely to generate accurate, unbiased estimates if i f the regression residuals are normally distributed, uncorrelated, and homoskedastic. •

N or m al dis d is tr ib u ti tioo n . The normality assumption often is violated when data

contain outliers. • A Aut utoc ocor orre rela latio tio n. The OLS method assumes that regression residuals are uncorrelated with their lagged values. The consequence of autocorrelation (also known as seria l correlation) correlation) is that the standard errors and /-statistics estimated by the regression will be invalid. The Durbin-Watson test statistic is used to check for serial correlation. • Homoskedasticity. If the variance of the residuals in an OLS regression is constant, the residuals are said to be homoskedastic. The OLS model assumes homoskedasticity. Heteroskedasticity refers to a violation of the constant error variance assumption. Fo Forr example, if i f the variance of the the residuals gets larger as the values of the independent variable gets larger, there is evidence of con ditio na l heteroskedasti heteroskedasticity city.. Estimates derived from a regression often are tested for statistical significance Estimates using a /-statisti /-statistic. c. Another way w ay to assess assess the qual q uality ity of a regression regression is to examine the goodness of fit statistic, or 7?-squared value of o f the the regression, which equals the percent of the variation in the dependent depend ent variable explained by the independent variables. The i?-squared ranges from 0 to +1. In a simple linear regression, the i?-squared equals the square of the correlation between the dependent and independent variable. The percent of the assets variation attributable to idiosyncratic risk equals 1 minus the /^-squared. Multifactor Regression Models Multifactor regression models describe relationships between asset returns and the returns on multiple risk factors. The equation for a general £-factor regression model is: R it - R f - ai + Bi lF lt + Bi2F2t +‘ •'+ BikFkt BikFkt + eit

where: Rit =return on asset i in in time for period t Rf = risk-f risk-free ree rate EL = beta of asset i relative relative to factor j Fjt = return on risk factory’ for period t

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Fama-Fr a-French ench three-factor three -factor model is an example of a multifactor asset The Fam pricing model:

R it i t - R f - ai + Bm (Rmt “ R f) + B i ( R t - R bt) + B2^ B2^R R ht “ R lt^

where: R = return on the market index for period / R = return on a portfolio of small firms firms for period / Rbtt = return on a portfolio Rb portfol io of big firms firms for period / R^ = retur return n on a portfolio of o f high book-to-ma boo k-to-market rket firms for for period / Rj = return on a portfolio of low book-to-market book-to-market firms firms for for period /

Fama and French contend that small firms are riskier than large firms, and high book-to-market firms are riskier than low book-to-market firms. The FamaFrench three-factor model predicts that stock returns will be high for firms with high market beta, small market capitalization, and high book-to-market ratio. B1will be positive for small firms and B2 will be positive for high book-tomarket firms. Multicollinearity refers to the condition in which two or more of the independent variables are highly correlated with each other. When independent variables are correlated, cor related, the intercept interce pt and slope standard error errorss are biased Type pe II upward, which, in turn, biases the /-statistics downwards. This leads to Ty errors (i.e., there is a greater probability that we will incorrectly conclude that a variable is not statistic sta tistically ally sign significan ificant). t).

Multicollinearity has a downward biased effect on the /-statistics of the intercept and slopes but does not affect i?-squared or the ^-statistic. High i?-squared and low //--s -sta tatis tisti tics cs provide provide evidence of multicollinear multico llinearity. ity. Transforming the independ in dependent ent variables can solve solve the problem of of multicollinearity. Choosing the correct variables to include in a regression can be difficult. The stepwisee regression method cho stepwis choose osess indepen i ndependent dent variables based on each variables varia bles explanat explanatory ory power. power. The first independent indepe ndent variable vari able chosen is the one with wit h the highest /-st /-statist atistic ic for its slope. Then, addi additiona tionall variables are added sequentially depending on the size of their /-statistics. A criticism of stepwise regression is that it is fishing; there is no economic theory behind the variable choices.

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Nonlinear Return Models

Alternative investment returns retu rns often are nonlinea non linearly rly related to market fact factors. ors. Nonlinear models examine nonlinear relationships between dependent and independent variables. Dynamic risk exposure models examine nonlinear relationships caused by factor risk exposures that change over time. For example, fund managers might attempt to time the market by targeting higher betas as the market index improves.

Three dynam dynamic ic risk r isk exposure methods include: inclu de: Dummy variable regression model: The fund beta takes one of o f two two values: an up-market beta and a down-market beta. The dynamic risk exposure model is:

where: b-i ,d , = down-m down-market arket beta D1 =dummy va vari riab able le;; equ equal alss 1 wh when en R - Rf is po posi siti tive ve,, and equals equals 0 when R - Rf is ze zero ro or negative dif ifff = difference between up-m up-marke arkett beta and downdown-marke markett beta Separate regressions model: The analyst runs separate non-overlappin non-overlappingg regressions to estimate betas for each regression period. Several different time periods are examined, and several periodic betas are derived for the asset. Quadratic curve regression model: The ex exce cess ss returns for the asset are are regressed regressed against the square of the market excess returns, resulting in a quadratic curve regression:

A positive value for Bim indicates that the fund manager con continu tinually ally adjusted the beta higher as the market return increased, and adjusted it lower as the market return fell. A negative value for Bim is indicative of a bad markettimer and the intercept measures the skill of the manager after controlling for market-timing ability.

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Time-Vary Time -Varying ing Corr Correlati elations ons

Alternati ve investment Alternative in vestment returns are typic t ypically ally non-stationary, implying that key parameters such as means, variances, and correlations are not constant over time. Conditional correlation is the correlation between two variables conditional on a specified set of circumstances (e.g., the correlation between the returns of two assets during up markets only). •

•

A positive conditional correlation refers to situations where the correlation between a funds returns and the markets returns are more positive during up-markets than during down-markets. A negative conditional correlation refers to situations where the correlation is lower during up-markets than during down-markets.

Both time-varying correlations and regression estimates can be derived based w indow app approac roach, h, in which a moving window of time is used to on a rolling window derive periodic correlations. Multifactor Mu ltifactor Applications Applications

Multifactor models are applied to explain fund returns relative to: •

Return Ret urnss o f asset clas classes ses he ld by the fu n d (sty (style le analysis) analysis)..

Portfolio returns are regressed against asset class index returns. Slope coefficients measure the extent to which the portfolio is exposed to each asset class included in the regression. asset et class class indices ♦ The i?-squared indicates the degree to which the ass explain the funds returns. One minus the /^-squared indicates the degree to which the returns are attributable to manager skill or to luck. Return Ret urnss o f fu fu n d s w it ithh si m ililaa r stra st ra te tegi gies es . Returns can be compared against portfo portfolios lios that tha t follow similar strateg strategies ies ♦ (e.g., long-only equity, long/short, market neutral, global macro). ♦

•

•

M ar arke kett fa c to r s th at d r iv e as asse sett return ret urn s. Principal components analysis is a multivariate statistical method that ♦

♦

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helps identify funds with similar strategies, without the need to observe fund holdings. The factors, called principal components, are derived statistically by grouping funds that have high return correlations. The Fama-French three-factor model can be used to examine the relationship between the returns of o f a stock or or fund and the returns on market-wide factors. Similar models have been developed for hedge funds. Factors that have been identified for hedge funds include: • Ex Exces cesss retu return rn on the S&P 500. • Small cap minus big cap stock return. ©2018 Kaplan, Inc.


• • • • • •

Ten-year Treasury bond return minus the risk-f risk-free ree return. Baa-rated bond return minus 10-year Treasury bond return. Portfolio of bond call and put options. Portfolio Port folio of currency call and put option options. s. Portfolio Portf olio of commodity call and put option options. s.

Fund replic replication ation using specialized market factors. Hedge fund replication is a proces ♦ processs of o f identifying an investment

strategy that mimics a particular fund’s returns. In fund replication, a model is derived that uniquely identifies specialized factors factors for each fund. In the case of fund replication, the model identifies factors for a specific fund, rather than market-wide factors for a broad cross-section of funds. Some caveats are in order for applications of multifactor models for hedge funds. •

•

•

•

Returns Retur ns explained by returns returns o f asset clas classes ses held by the fun d. This method does

not apply well to hedge funds. Tests show that hedge fund returns are not explained well by passive asset class returns. Returns explained by returns on fu nd s w ith sim ilar strate strategies gies.. This method does not apply well to hedge funds. Hedge funds often are unique, driven primarily by idiosyncratic risks, and, therefore, may not correlate highly with other funds funds that th at employ seemingly se emingly similar sim ilar strategies. Returns explained by ma rketwide factors. This method does not apply well to hedge funds. For example, a merger arbitrage fund correlates more highly with probabilities of the the mergers suc succes cesss than with w ith market-wide factors. Returns explained by specializ ed market fac tor s . This method may work for hedge funds. Market-based factors might be identified uniquely for each fund.

Performance Persistence

Results of empirical testing regarding the performance persistence of hedge funds are mixed largely due to inadequate measures. Methods used to test for perform ormance ance pers persist istenc encee include: the existence of perf include:•• •

Regression tests. Regress current hedge fund returns on past returns. If the

•

slope coefficient is positive, there is evidence of performance persistence. measuress of skill are positively correlated over time, Mea M easu su re ress o f skill test tests. s. If measure there is evidence of performance persistence.

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R e a l A s s e t s Topics 3 . 1 - 3 . 6

Topic 3 is relatively r elatively straightforward. Real assets, assets, incl includi uding ng natur natural al resources, land purchased for development, commodities, timberland, farmland, infrastructure, and intellectual property are considered. Keep in mind that in real assets, we are really only exploring two types of investments: direct (e.g., purchasing actual properties or indices of actual properties) and indirect (i.e., ownership of o f vehicles, such as REIT REITs, s, that t hat purchase properties). The commodities sections cover cover a wide range of o f materi material, al, incl includi uding ng forward and futures contracts, rolling contracts, forward price term structure, valuation of commodities, diversification issues, , types of commodity investments, roll return propositions, and commodity risks and returns. Much of the material is qualitative, but you may see some calculations on the exam related to margin accounts, futures pricing, or the roll yield. An unders u nderstandin tandingg of o f mortgages, mortgage-backed securities, and RE REIT ITss is also important. You should also understand the issues associated with both appraisals and market prices when valuing real estate. i c 3.1: N a t u r a l R e s o u r c e s a n d L a n d T o p ic

Natural Resources

At any a ny point po int prior p rior to expiration, an option has both time value and intrin intrinsic sic value. The Th e intrinsic option value equals the maximum of the value of immediate option exercise and zero. The time value of an option equals the option premium (price) less the intrinsic value of the option. option price =intrinsic value +time value An exchange option is an option to exchange one risky asset for another risky asset. The option to convert natural resources to commodities can be

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Topics 3. 1- 3 .6 Real Assets

considered an exchange option. In option terminology, the inputs to the strike price would be considered the deliverables (i.e., mineral rights, equipment, labor, and materials) and the resulting output (i.e., commodities) would be the receivables. Moneyness refers to whether an option is in the money or out of the money. The lack of o f expiration date for a natural natu ral resourc resourcee perpetual perpetu al option increa increases ses the complexity of the decision of when to exercise the option. While the option must be in the money for exercise, the amount it must be in the money in order to exercise is more complicated to determine and relies on correlation, input price volatility, volatility, and output price volatility. volatility.

A change in the price of the resulting resulti ng commod co mmodity ity is the primar pr imaryy short-term risk factor of in-the-money natural resource options. Long-term out-of-themoney options have a greater sensitivity to changes in the costs of the options deliverables. Undeveloped Land Undeveloped land is a real asset that is not currently being used to generate a scarce resource, such as recreation, crops, or shelter. The value of undeveloped land arises from development opportunities. Land investing is a long-term strategy as it may take years before a property is fully developed.

Investors may purchase undeveloped land for the purpose of developing the land in the future. This is called land banking. Historically, builders bought land and banked it themselves, but increasingly they rely on institutional investors and other third parties to provide lots for building. Both the type of undeveloped land and the location of the land are important risk factors. The more potential uses a property has, the less risky the investment. Land is categorized based on the level of existing improvements that have been made. Lots that may be purchased for investment are classified as:• as: • • •

•

Paper lots. These lots are vacant but have have zoning approval for for development. Blue top lots. The process process of development development has begun for these these lots including rough grading of the property and interim drainage and erosion controls. Finished lots. These lots are ready for construction with all development fees paid.

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Topics 3. 1 -3 .6 Real Assets

Raw land is a risky investment because it requires a long holding period and does not provide the investor with an annual cash flow. The expected return of raw land is a probability-weighted average of the expected returns if the land is developed or not developed. When evaluating the historical returns of raw land, investors must account for the nega tive survivorship that occurs due survivorship bias that to the most desirable properties being developed. Land as a Call Option

Investors in undeveloped land are in essence buying a call option on development devel opment.. A single or multiperiod binomial option pricing model m ay be used to value land as an option. In a binomial option pricing model, there are only two possible outcomes, an upward movement or a downward movement. Assuming Assumi ng a 0% risk-free rate and a one-period model simplifies the analysis. The components of o f the call option are: • • •

•

•

•

Strike or exercise price. The strike price includes construction and other costs required for developing the land. Timee to expira Tim expiration. tion. The option typica typically lly doe doess not have an expiration date. The time to develop develop the land is generally unlimi unlimited. ted. Underlyi Und erlying ng asset. asset. The under underlying lying asset asset is a combination of the land and the improvements that are made to develop the land (e.g., a duplex and the land on which the duplex sits). Option payoff. The payoff of the option is the differen difference ce between between the value of the completed project (i.e., the value of the underlying unde rlying ass asset) et) and the cost of developing and constructing the project (i.e., the strike price). Exercising the option. The option will be exerc exercised ised (i.e., the property will be developed) when the expected income from the developed property exceeds the value of retaining the option to develop the property. Moneyness of o f the option. If the value of the underlying asset asset is greater than the strike price, the option is in the money and if the value of the underlying asset is less than the strike price, the option is out of the money.

Timber Tim ber and Tim Timberla berland nd

Tim ber berlan land d investments are long-term investments in wood via existing existin g forestland. There is private (i.e., institutional and individual investors) and public (i.e., government) ownership of forest land. Historically, firms dealing in wood products were high highly ly integrated. Th That at changed in the late 1970s. Firm Firmss sold off timber holdings for large profits. Recently, there has been a significant increase in Timberland Investment Management Organizations (TIMOs). TIMOss manage timberl TIMO ti mberland and owned by investors for a fee. fee. They Th ey also share in profits when timber is harvested. As a result, ownership is now dominated

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by institutional investors such as pension funds, insurance companies, and endowments. Advantages Advantag es of investing in timber timberland land include: • • • • • •

Low correlation with stock and bond returns. Mayy act as a hedge against inflation. Ma Investors Investo rs are mak making ing an investm investment ent in land land,, a real asset. Timber Tim ber is a renewable resource resource alth although ough it has a long growth cycle. There is is some some flexibility with respec respectt to harvesting and tree treess gain value if harvesting is postponed. Timber can be used for a variety of products, which adds significant value.

Disadvantages of investing in timberland include: • • • • •

Trees can be destroyed by fire, disease, drought, and other natu Trees natural ral disasters. Values are tied to cyclic cyclical al indus industries. tries. Timber Tim ber supplies are not fixed fixed.. Technology and recycling may dimi diminish nish the demand for for timbe timber. r. The investment horizon may be long.

Most timberland is owned and traded by institutional investors. There are two ways that t hat individu i ndividuals als can invest in timberl timberland. and. •

•

Exchange-traded funds (ETFs) track the S&P Timber and Forestry Index. Exchange-traded The two ETFs ETFs that track trac k timberland timberlan d have both underperformed the index with more volatility. volatility. Real estate inves investment tment trust trustss (R (RE EIT ITs). s). There are four four REITs REITs that invest in timberland.

Farmland

Farmland generates a crop that provides a cash flow. The cash flow is more closely linked to commodity prices than to property rents. As a result, the price of farmland itself is highly correlated with commodity prices. Owners lease Agency cy farmland to local farmers, cooperatives, and agricultural corporations. Agen risk results when investors lease land to agents (e.g., farmers) who in turn do not act to maximize the economic benefits of the property for the owners. Benefits that accrue to farmland investors include: • • •

A renewable annual cash flow stream from crop income. A potential steady cash flow stream, receiv received ed on a calendar basis, if i f the land is leased. A short growth cycle. This allows for for planting plan ting and harvesting the crop within with in one year, year, allowing for valuable, multi-purpose option options. s.

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• • • • • • •

Valuable, multi-purpose option on the land, allowing the owner to Valuable, repurpose the land. An expected increase in the world s population, which will w ill increa increase se the need for food food and thus land, increasing land values. Increasing use o f crops to produce bio-fuels incre increases ases commodity com modity prices and land lan d values. Favorable governmen governmentt policies including crop subsidies. Revenues, and thus farml farmland and prices, are less dependent on local economies because of the global demand for crops. Farmland Farm land do does es not usually deteriorate over time. Farming is scalable. It takes a relatively small marginal increase in labor and machinery to farm additional land.

Disadvantages incurred by farmland investors include: • • • • • •

Agenc y risks that result from leasing the property to farmers and Agency cooperatives. Political risks that result from government decision making. Less flex flexibil ibility ity in harvest harvesting ing sched schedules ules compared to timberland. Natural forces may destroy a crop. Droughts, floods, storms, and other natural factors can destroy an entire crop. Farm-specific Farm-spe cific inefficiencies. In some cases, a farm may earn lower returns than its competitors due to operational inefficiencies. Revenues Reven ues are driven by market factors. Macro factors affect revenues but are beyond the control of o f the farmer or owner of the farmland.

Financial Financi al Analysis o f Farmland Farmland

(ROE) is calculated as net income divided by the equity Return on equity (ROE) investment in the deal. Op erating return on ass assets ets (return on assets or yield) is also known as the cap rate (i.e., the capitalization rate). One way an investor might value real estate is to divide the annual operating income from the deal by the cap rate. The equation is as follows: value of real estate estate = annu annual al operatin operatingg income / cap rate The investor can solve solve for the cap rate given the operating o perating income and the price of the asset or the value of the asset given the operating income and the cap rate. Farmland has the potential for multiple uses, creating a higher option value than if the property had only one potential use. Three factors drive the value of the option to produce alternative crops: 1.

Correla Cor relation tion (or lack of) between between the profi profitability tability of each alternative crop. crop.

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Volatilityy of the profitability of each alternative crop. 2. Volatilit

3.

Current clo closen seness ess of the profitability prof itability of each alternative cro crop. p.

Private ownership of farmland is the key way for investors to gain exposure to farmland. There are two indices that track the farmland and agribusiness industry, industr y, both of which track publicly p ublicly traded companies companies engaged in producing agricultural products. They are the DAX Global Agribusiness Index and the Thomson-Reuter Thomso n-Reuters-in-the-G s-in-the-Ground round Global Equity Equ ity Index. Smoothing and Volatility Volatility

Many real assets are illiquid and most are not traded on an exchange. As a result, real assets are often valued based on appraisals, resulting in price smoothing. Smoothing may result in: • • • •

Lower price volatili volatility. ty. Lowerr return volatility. Lowe Assets Ass ets appearing les lesss risky than they actuall actuallyy are are.. Assetss appea Asset appearing ring to improve the risk/reward characterist characteristics ics of a portfolio more than they actually do.

Volatil Vo latility ity Impact o f Managed Manage d Returns

Some managers have discretion with respect to reporting asset values. This results in managed returns. Asset values and returns may m ay be managed man aged in four ways: 1.

Market manipulation manipulation.. The prices of thin ly traded tra ded ass assets ets may be manipulated through trading activity.

2.

Model manipulation. Assumptions in valuation valua tion models may m ay be altered to get the desired price and return results.

3.

Selective appraisals. A manager can manipul ma nipulate ate the timing tim ing of the appraisal.

4.

Favorable mark. A manager may request a valuation valuat ion of a thinly thin ly traded asset from a source that has an incentive to bias the value in favor of the manager.

It is impossible to conclude whether market prices are better than appraised values. Mark Market et prices for stocks stocks seem undu u nduly ly influenced i nfluenced by the market market’’s mood and emotions (e.g., contagion). Conversely, appraised values may not reflect true values in a timely fashion and result in smoothed price and return data.

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This results in the false perception that t hat the underly un derlying ing appraised ass assets ets are superior investments compared to identical market-priced assets. Historical Performance of Timber and Farmland

Average Sharpe ratios for both timberland Average timb erland and farmland fa rmland were strong str ong during du ring the period January 2000 to December 2014. The Sharpe ratio of 1.45 for NCREIF Farmland is the highest of the reported indices. In addition, both asset classes have low correlation with other asset classes and low maximum drawdowns (-6.5% (-6 .5% fo forr timber and 0% for farmland). Even Even if returns returns and volatility ar aree somewhat artificially smoothed due to appraisals, farmland and timberland offer diversification potential to an investment portfolio. i c 3.2: C o m m o d i t y F o r w a r d P r i c i n g T o p ic

Forward and Futures Contracts

Gaining economic exposure to commodities can be accomplished simply by purchasing some quantity of a physical commodity. The problem, however, is that once the commodity is purchased, the investor must store it. As an alternative, investors may gain exposure to commodities through forward or futures contracts. A forward contract contract is a bilateral contract that obligates one party to buy and one party to sell a specific quantity of an asset, at a set price, on a specific date futures contract contract is a forward contract that is standardized and in the future. A futures exchange-traded. The main differences with forwards are that futures are traded in an active secondary market, are regulated, are backed by the clearinghouse, and require daily settlement of gains and losses.

Futures exchanges require traders to post margin and settle their accounts on a daily basis through a process known as marking-to-market. This adjusts the futures contract price to the spot, resulting in a zero contract value. Initial margin is the collateral that must be deposited in a futures account before any trading takes place (less than 10% of contract price). Maintenance margin is the amount of margin that must be maintained in a futures account (usually 75% to 80% of initial margin). variation tion Increases or decreases in the trader’s margin account are called varia margin. If the value of a futures position increases (decreases), the trader will

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accrue gains (losses), and the value of the traders margin account will increase (decrease). If the margin balance in the account falls below the maintenance margin level, a margin call occurs and additional funds must be deposited to bring the margin balance back to the initial margin level. Rolling Contracts

Using futures contracts presents a challenge for an investor who wants to maintain long-term exposure exposure to commodities commodities without taking delivery of the the underlying commodity. In order to maintain commodity exposure, the investor willl have to repeatedly close out the existing wil exi sting futures position and establish a new position in a new futures contract (i.e., roll the contract forward). This process is called rolling contracts and can be costly depending on the structure of the market for the particular commodity. Futures investors that roll contracts have two key choices to make when rolling: • •

Whe n wil When willl the roll be initi initiated ated (e.g., contract expiration or or sometime bef before ore)? )? Which Wh ich deferred deferred contract wil willl be be used in the the roll roll (e.g., the next nearest contract or longer maturity contract)?

Term Struc S tructure ture o f Forward Forwar d Prices

The term structure of forward prices refers to the relationship between forward prices (or forward rates in the case of interest rate contracts) and time. Futures prices and, therefore, the term structure of futures prices are determined using arbitrage-free pricing models. The forward pricing prici ng relationship r elationship for physical and a nd non-physical no n-physical ass assets ets (where applicable) is as follows: F( T) =S xe (r +c- d-y)xT Arbitrage is more complicated com plicated for commodity commod ity forwards for two reasons. reasons. 1.

Difficulty Difficul ty creating short positions.

2.

Differing convenience yields and storage cos costs. ts.

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CAIA level 1 Secret Book 2018

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