Emerging Markets Bond Index Plus (EMBI+) JPMorgan

Emerging Markets Research Bond Index J.P. Morgan Securities Inc. December 2004

Emerging Markets Bond Index Plus (EMBI+) Rules and Methodology • The EM EMBI+ was created in response to investor demand for a liquid emerging markets debt benchmark • The EMBI+ is a traditional, market-capitalization weighted index comprised of USD-denominated Brady bonds, Eurobonds, and traded loans issued by sovereign entities • Daily historical historical levels levels are available available from from December December 31, 1993

Overview The JPMorgan Emerging Markets Bond Index Plus (EMBI+) is our most liquid US-dollar emerging markets debt benchmark, and tracks total returns for actively traded external debt instruments in emerging markets. Included in the EMBI + are US-dollar denominated Brady bonds, Eurobonds, and traded loans issued by sovereign entities. The EMBI+ provides investors with a definition of the market for liquid emerging markets sovereign sovereign debt and its traded instruments. It segments further the universe of emerging markets as defined by the more comprehensive EMBI Global and EMBI Global Diversified, by placing a strict liquidity requirement rule for for inclusion. Other differences differences in inclusion rules apply. apply. (Please refer to the methodology piece EMBI Global and EMBI Global Diversified: Rules and Methodology for more information on the EMBI Global/Diversified). To be deemed an emerging market by the EMBI +, a country must be rated Baa1/BBB+ or below by Moody’s/S&P rating agencies. agencies. This criterion, along with the liquidity ranking rule, carves out a basket of liquid bonds, each capable of being bought and sold at short notice, and quoted daily by several market makers makers at relatively low bid/offer spreads. The EMBI+ is transparent and timely, representing opportunities available to investors in this market. It is geared toward managers of index funds who strictly adhere to the performance and portfolio changes of the index.

Gloria M. Kim (1-212) 834-4153 [email protected]

The certifying analyst(s) is indicated by the notation “AC.” See last page of the report for analyst certification and important legal and regulatory disclosures.

www.morganmarkets.com

Emerging Markets Research Emerging Markets Bond Index Plus Gloria M. Kim (1-212) 834-4153 [email protected]

Jennie Byun (1-212) 834-4029 [email protected]

Alvin Ying (1-212) 834-7139 [email protected]

Table 1: EMBI indices at a glance Inclusion criteria

EMBI+

EMBI Global

EMBIG Diversified

Rated Baa1/BBB+ or under by Moody’s/S&P

Low/Mid dle income for two consecutiv e years as per World Bank

Low/Mid dle income for two consecutive y ears as per World Bank

Minimum issue size

$500 million

$500 million

$500 million

Maturity requirement for initial entry

At least 2.5 years until maturity



Maturity requirement to maintain inclusion

At least 1 year until maturity



Must pass a series of liquidity tests (a minimum bid/ask price and specific number of interdealer broker quotes)

Dail y available pricing from an interdealer broker or JPMorgan

Dail y available pricing from an interdealer broker or JPMorgan

Face amt. constrained

No

No

Yes

Includes quasi-sovereigns

No

Yes

Yes

Country requirements

Instrument requirements

Liquidity criteria

Table 2: Other JPMorgan indices Index

Includes

Latin Eurobond Index (LEI)

Latin American USD-denominated sovereign and corporate bonds

Russia Corporate Bond Index (RUBI)

Russian corporate bonds denominated in USD

JPMorgan Asia Credit Index (JACI)

Asian USD-denominated sovereign and corporate bonds

EURO EMBIG/Diversified

EURO-denominated sovereign and quasi-sovereign bonds

Emerging Local Markets Index Plus (ELMI+)

Money market instruments within emerging markets denominated in local currency

Dow Jones CDX.EM

Credit default swaps: a liquid, diversified basket of emerging market sovereign CDS

Index inclusion selection process We adhere to a strict set of rules for selecting countries and instruments for inclusion in the EMBI+. To be included in the EMBI+, bonds must meet both eligibility and liquidity requirements. When a bond meets both requirements, it is added to our indices; when it does not, it is dropped. Instruments that satisfy all the following defined criteria will be eligible for inclusion in the EMBI+: 1. Instrument type 2. Issuer type classification; 3. Currency denomination; 4. Credit rating criteria; 5. Current face amount outstanding; 6. Remaining time until maturity; 7. Legal jurisdiction; 8. Settlement method; 9. Quantifiable source of cash flow return; and 10. Liquidity Ranking.

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Instrument Type The EMBI+ includes both fixed and floating-rate instruments, as well as capitalizing/amortizing bonds or loans. Bonds or loans with embedded options and warrants are eligible for inclusion if a) the options/warrants are attached to instruments that would otherwise be included in the index and b) the quotation convention (as recommended by the Emerging Markets Traders Association) is for instrument prices to be quoted cum options or warrants. Convertible bonds are not eligible for inclusion into the index. Issuer type classification The EMBI+ contains only bonds or loans issued by sovereign entities from index-eligible countries. Quasi-sovereigns are not eligible for the EMBI+ even if the entity is 100% owned by the government. Instruments issued by municipalities or provinces are also not eligible for inclusion.

Instruments will not be eligible for inclusion in the index if their credit has been improved by a) giving security over commercial receivables or b) giving a guarantee from a guarantor which is not a subsidiary of the eventual obligor or the parent company/beneficiary of the issuer of the instrument. For the purposes of clarification, bonds that are secured in part by US Treasuries (e.g. Brady bonds) are eligible for inclusion. Where financing vehicles are used, bonds or loans may be included in the EMBI+ if either 1) the financing vehicle or bond is guaranteed by an index eligible issuer or 2) the transaction is structured as a pass-through where the creditor of the financing vehicle has full recourse to the underlying loan or bond between the financing vehicle and the final obligor, which itself must be an index eligible issuer. In order to avoid double counting of index instruments, a bond or loan that is issued by a financing vehicle is only eligible for inclusion into the EMBI+ if the underlying loan or bond is not itself included in the index. Currency denomination Only those instruments denominated in US dollars are considered for inclusion. Instruments denominated in US dollars where the amount of coupon or redemption payment is linked to an exchange rate are not eligible for inclusion. Prior to 1998, external-currency denominated instruments other than US-dollar, as well as corporates, were allowed in the EMBI+, but have since then been removed. Credit rating criteria Eligible instruments are determined by the rating assigned by Moody’s and S&P to the bond’s originating country. Since the EMBI+ covers external-currency debt, we have defined emerging markets countries according to the ability to repay external-denominated debt. A country must be rated Baa1/BBB+ or below in its long-term foreign currency rating for its instruments to enter and remain in the index. When a country receives a rating of A-/A3 or higher from both Moody’s and S&P, it is dropped from the EMBI+ at the next month-end rebalancing. Current face amount outstanding Only issues with current face amount outstanding of $500 million or more will be considered for inclusion.

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If an issue’s current face outstanding falls below this requirement (due to either a debt retirement by the sovereign or the amortization of principal), the issue will be removed from the index at the next month-end rebalancing date. The reverse also holds true. Existing issues that, through reopenings, increase in size to satisfy our minimum current face outstanding requirement are then considered for inclusion in the index at the next month-end rebalancing date. Time until maturity A bond can only be added to the EMBI+ as long as its remaining life is greater than 2 1/2 years at the time at which it satisfies our inclusion criteria. Once an issue is added to the EMBI+, it may remain there up until 12 months prior to maturity, assuming it continues to meet our inclusion criteria.

An instrument that has been dropped from the EMBI + is not eligible to re-enter the EMBI+ for 12 months. Such a step further ensures that the composition of each index is not subject to temporary liquidity trends. Legal Jurisdiction Effective May 31, 2002, inclusion into the EMBI + is limited to issues with legal jurisdiction that is domestic to a G7 country. Local law instruments or bonds that do not fall under G7 jurisdiction are not eligible for the index. Settlement Criteria Instruments in the EMBI+ must be able to settle internationally (either through Euroclear or another institution domiciled outside the issuing country). Quantifiable source of cash flow return JPMorgan reserves the right to exclude from the composition of the EMBI + any debt instrument that it considers to have a cash flow structure from which verifiable daily returns or other statistics (i.e. yield, spreads) cannot be calculated. Liquidity Ranking Once the eligibility requirements are met, liquidity criteria are applied to the remaining universe of instruments. We look at three attributes to determine liquidity ratings: (1) size of the issue, (2) average monthly bid/ask spread, and (3) number of designated brokers providing daily quotes. The following table summarizes our liquidity ratings: Rating

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Definition

L1

$2 billio n face amount outstanding minimum, average bid/ask spread <= 3/8 point, and quoted by 100% of all designated brokers

L2

$1 billio n face amount outstandin g minimum, average bid/ask spread < = 3/4 point, and quoted by at least 1/2 of the designated brokers

L3

$500 million face amount outstanding minimum, average bid/ask spread <= 1 1/2 points, and quoted by at least 1/4 of the designated brokers

L4

$500 million face amount outstanding minimum, average bid/ask spread <= 3 points, and quoted by at least 1 designated broker

L5

$500 million face amount outstanding minimum, average bid/ask spread => 3 points, and not quoted by any designated brokers

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For a bond to be added to the EMBI +, it must be rated: • L1 for 1 month, or • L2 or higher for 3 consecutive months, or • L3 or higher for 6 consecutive months. For a bond to be dropped from the EMBI +, it must be rated: • L4 for 6 consecutive months, or • L5 for 1 month.

Timing of the addition of new issues A new issue that meets the EMBI+ admission requirements is added to the index on the first month-end business date after its issuance, provided its issue date falls before the 15th of the month. A new issue whose issue date falls on or after the 15th of the month is added to the index on the last business day of the next month. There are two exceptions to the rule. The first exception applies to a new issue that is released as part of a debt exchange program. For example, assume a country exchanges a portion of its outstanding debt for a new issue after the 15th of the month. At the month-end rebalancing date immediately following this event, the amount of debt retired in this exchange would be removed from the EMBI+,and the new issue would be added to the index (provided official exchange results are made available in a timely manner). The second exception concerns Reg S securities. An instrument that is issued purely in reliance on Regulation S of the U.S. Securities Act of 1933 and not pursuant to Rule 144A will be ineligible for inclusion in the EMBI Indices until it is seasoned (that is, until the expiration of the relevant Regulation S restricted period). The date at which the seasoning restriction is lifted will effectively be the new “issue” date, at which point the 15th of the month rule will apply. In extreme cases, an intra-month rebalancing can occur, where the EMBI+ is rebalanced before the end of the month. An intra-month rebalancing is triggered when: • More than $6 billion of the face amount of EMBI+ bonds are exchanged, or • More than 2/3 of the face amount of any one of the most liquid (identified as bonds with an L1 rating) index bonds is exchanged Please refer to the Intra-Month Rebalancing Met hodology, dated May 31, 2001 for precise details on the mechanics behind intra-month rebalancings. If an announcement is made for a bond to be called, it is removed the monthend prior to its call date on the basis of having less than 12 months remaining until maturity. If an announcement is not made in time for the bond to be removed the prior monthend, it will be removed the first monthend following the announcement, unless the amount to be called triggers an Intra-month rebalancing (rules above).

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Index weighting methods The weight of each instrument in the EMBI+ is determined by dividing the issue’s market capitalization by the total market capitalization for all instruments in the index. The result represents the weight of the issue expressed as a percentage of the EMBI+. Country weights for the EMBI+ are easily calculated by aggregating the weights of the instruments for each country. The market capitalization of each issue is calculated by multiplying its face amount outstanding by its bidside settlement price. Face amounts outstanding for each issue are updated at each month-end in order to reflect market events—such as reopenings or buybacks—that have increased or decreased the issue’s available supply.

Daily Production of the EMBI + The EMBI+ is produced every business day of the year. Business days are based on the US bond market calendar set by the Emerging Markets Traders Association (EMTA). Pricing on regular business days The EMBI+ is priced at 3:00pm Eastern Standard Time (EST) every business day of the year as defined by the US bond market calendar. Composite instruments are priced using the best market bid (highest) and the best market ask (lowest) indicated by the following emerging market broker screens: Eurobrokers, Garban, GFI, Tullet & Tokyo, and Tradition. For instruments where there is not a valid price available at 3:00pm EST, the last available valid price is obtained from the market. As a last resort, if there are no valid market prices for an instrument, JPMorgan traders are asked to provide a market bid and ask. For those instruments where pricing is not available on a regular basis, the composition methodology ensures that such instruments are excluded from the EMBI +. Early closes When the US bond market closes early, typically before market holidays or when EMTA recommends an early close, prices of EMBI+ instruments are captured at the latest possible time to reflect an active closing market. The liquidity of the EMBI+ is somewhat determined by whether international markets are open. On certain international holidays when the capital markets of many countries are closed, the liquidity of the EMBI+ diminishes and the index is closed early to accurately reflect market prices.

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Where to find the EMBI + Daily EMBI+ results can be found in the following places: • MorganMarkets (morganmarkets.com): Contains downloadable files of daily country and instrument returns, statistics, and compositions, as well as data series of historical index levels and sovereign spreads. • Dataquery on MorganMarkets: Allows clients to view, manipulate and download user-specific queries. Access Dataquery via MorganMarkets website from Tools > Business Tools. • Reuters: Page offers a directory of results for all JPMorgan emerging markets bond indices; pages and <11EMJ> display closing and real-time levels for the EMBI +, respectively. • Bloomberg: Page is the directory page for all JPMorgan EMBI indices and their closing levels; options 4 and 5 display closing index levels and statistics; page displays real-time levels for the EMBI +. • JPMorgan’s monthly Emerging Markets Bond Index Monitor contains index returns, statistics, and composition updates for all of our emerging markets indices.

Custom Index Builder JPMorgan has also made available the Custom Index Builder (via MorganMarkets > Tools). This on-line tool allows clients to create customized indices based on the following categorization: • country selection

• fixed versus floating rate-type

• maturity buckets

• performing versus non-performing status

• credit ratings

• collateralized and uncollateralized profile

Clients can choose to fix their custom portfolio weights or let it float on a market-cap weighted basis. Using the JPMorgan Custom Index Builder, investors can hone in on the specific sectors applicable to their portfolios or evaluate potential investment scenarios with ease.

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Appendix: Instrument and index total return calculations The following is a description of our methodology for calculating returns (total, price, and interest returns). Section I describes single-instrument returns. Section II describes index total returns. Section III describes yields and spread calculations for single instruments and the index as a whole. The total return calculation for a single instrument is a means of representing the economic benefit of holding the specific security. In its simplest form, it is based on the “cash in/cash out” notion—i.e., what is paid for the security at the initial purchase versus what is received at its sale. Of course, most fixed income securities pay some form of coupon along the way, and some pay amortizations. For the calculation of individual instrument total returns, this cash is reinvested in the instrument when received. However, when the instrument is part of a portfolio whose allocations are based on market capitalization (in the case of the EMBI+), the use of this market capitalization weighting scheme in effect causes this cash to be proportionately reinvested in the other instruments that make up the portfolio. The means of calculating the total return on a basket containing various instruments is an extension of the single-instrument total return framework. To hold a “passive” portfolio, one would buy the instruments in the same proportions in which they comprise the EMBI+. Each proportional amount is a function of both the amount of the instrument outstanding (based on publicly available information) and its settlement price. These two factors, when multiplied together, equal the asset’s market capitalization.

I. Single-instrument return The total return on a performing instrument is measured from one trade day to the next using the following generalized equation: 1.

tr t =

ESVs(t) + C v(t) + AM v(t) ESVs(t −1)

×

FX i, t FX i, t −1

−1

This equation captures the three main components of a fixed income asset’s value: price, cash flow (coupon and/or amortization) and currency. These components are represented by:

8

ESVs (t )

Effective settlement value; primarily a function of the effective settlement price but also of the ex-coupon and ex-amortization rules [see equation (2) below]

C v (t )

If applicable, the coupon payment to which a holder on trade date t is entitled on value date v(t); determined by the instrument structure, ex-coupon conventions, and holiday calendar

December 2004




AM v(t )

If applicable, the amortization to which a holder on trade date t is entitled on value date v(t); determined by the instrument structure, ex-amortization conventions, and holiday calendar

FX i, t

Foreign currency exchange rate for currency i measured in U.S. dollars per unit of foreign currency. Since the EMBI+ currently contain only U.S. dollar-denominated instruments, currency does not contribute to the indices’ daily returns.

t

Trade date; all index instruments trade on a New York holiday calendar

v(t)

Value date for trade date t; date used to calculate accrued interest, which usually, but not always, coincides with the settlement date

s(t)

Settlement date for trade date t; date on which cash transaction occurs

The effective settlement value can be calculated as follows: 2.

ESVs(t) = ESPs(t) + xc v(t) + xam v(t)

where: ESPs(t )

Effective settlement price, which is the price paid for a bond that is traded on trade date t and settled on settlement day s(t). The settlement date is determined by the settlement convention of the bond and holiday calendar for the settlement convention; in short, the amount of money, including accrued interest, etc., owed at the settlement date.

xc v ( t )

Ex-coupon placeholder; in some markets, market convention designates a date that begins an “ex-period,” ending on the coupon payment date, during which a seller of the bond is entitled to keep the upcoming coupon. This ex-period is usually 30 days. In effect, the coupon is stripped from the bond, such that the current buyer is no longer buying the rights to the coupon, and therefore the ESP paid by the buyer should be reduced by the amount of the foregone coupon. For the total return, however, it is imperative to maintain the continuity of the traded asset – i.e., the bond should be “reconstituted” to its cum-payment before the ex-structure. To do this, we account for the value this coupon represents to the seller via an ex-coupon placeholder. Intuitively, the placeholder is an amount representing the value of the next coupon discounted to the settlement date of the transaction and is calculated as: xc v(t)

=

C ds, t

(1 + L t ) 360

December 2004

C

Coupon amount to be paid at the end of the ex-period

Lt

One-month Libor, used as the cash rate for the discounting

ds,t

Number of days from settlement to the next coupon

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xamv(t)


Ex-amortization placeholder; this concept is completely analogous to the ex-coupon placeholder and is calculated in the same way: xam v(t)

=

AM ds, t

(1 + L t ) 360

The ex-coupon and ex-amortization placeholders are carried in both the numerator and the denominator of the total return formula and effectively cease to exist when the ex-period elapses. Although this equation is sufficient for the generalized concept of total return, complexities stem from the determination of the effective settlement price and the treatment of interim cash flows. Therefore, below we describe the differences between instrument types, then show how these differences are incorporated into the generalized equation. Effective settlement prices, ESPs(t) Effective settlement price is the instrument’s settlement “price”—i.e., the amount of money owed at settlement. ESP calculations translate the quoted price into this settlement price, taking into account appropriate quotation conventions and settlement practices.

The quotation and settlement of USD-denominated bonds in the emerging markets currently follow guidelines set by two different groups. Brady bonds and Eurobonds follow standard international settlement, set by the International Securities Markets Association (ISMA). Price quoting conventions are overseen, but not set by, the Emerging Markets Traders Association (EMTA); EMTA members also agree upon trading and settlement practices for loans. There currently are two settlement practices used for instruments in the EMBI +: standard international settlement and loan settlement. The standard international settlement period was seven calendar days through June 1, 1995, and became three business days on June 7, 1995. Loan settlement follows an EMTA prescribed “batch settlement” process, whereby trades executed during specified time periods all settle on single pre-determined settlement dates. Two types of price-quoting distinctions apply: the clean versus dirty pricing convention and the current versus original face pricing convention. Clean versus dirty quote conventions The clean-dirty distinction refers to whether an instrument’s quoted price is inclusive of accrued interest or not. Since the effective settlement price refers to all money paid at settlement, if a bond is quoted clean, the accrued interest through the value date owed at settlement must be added to the instrument’s price.

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Current face versus original face value quote conventions The current face-original face value distinction applies to amortizing and capitalizing bonds; it refers to whether a bond’s quoted price is for a current face amount of 100 or for the original face value of the bond, which may reflect the fact that the instrument has amortized to an amount less than 100 or has capitalized to an amount greater than 100. Since effective settlement price refers to the money actually paid at settlement, which is based on the current outstanding face value of the bond, an adjustment is made to the bond’s quoted price on a current-face basis to adjust it to an original-face basis. Table 3 shows the pricing conventions of instruments in the EMBI +. Table 3: Price quoting conventions for EMBI + instruments Clean (without accrued interest) Dirty (with accrued interest)

Current Face

Original face

Bradys, Euros, Moroccan Tranche A

None

Argentine defaulted debt

For example, a bond that is trading at par but has just amortized 10% would trade at a price of 100 on a current-face basis, but at a price of 90 on an originalface basis. Also, a bond that is trading at par and has just capitalized 10% would trade at 100 on a current-face basis and 110 on an original-face basis. The adjustment from a current-face to an original-face basis is achieved by using a “balance” scalar, Bv(t), which keeps track of the remaining balance of a bond after capitalizations and amortizations. For bonds that have amortized from par, the balance scalar will be between 0 and 1, starting at 1 at issue and decreasing to 0 at the final amortization (maturity) of the bond. For bonds that capitalize, the number rises starting at 1, as determined by the capitalization rates of the bond. This balance scalar strictly follows the quoting conventions of a bond and is not necessarily related to the balance of outstanding bonds as tracked by an issuer. For example, in the case of bonds that trade with an ex-period for amortizations, the “ex-balance” follows the same convention. If the bond goes ex-amortization 30 days before the coupon, on that date the seller retains the right to the coupon; therefore, the effective settlement price is lowered (jumps down) by the amount of the amortization, since the buyer is no longer entitled to it. For a bond trading on a current-face basis, this adjustment at settlement is made via the Bv(t) scalar. This scalar is an important variable because it adjusts other variables affecting the effective settlement price. Accrued interest, for example, is normally computed on a cash basis (i.e., coupon rate x day count), ignoring the current balance of the bond. Here, again, the scalar is used to adjust the accrued interest for the balance on the bond. Because the balance scalar is determined independently (i.e., it is based solely on the cash flow structure and quoting conventions for the bond), it can be used to scale all other variables. The remainder of this description assumes that all non-price variables have been appropriately adjusted and, therefore, defined on an original-face basis.

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With these concepts in mind, we can generalize the equation for the effective settlement price of performing instruments as follows: 3.

ESPs(t) = bp t × { if CO = 1, B v(t) , if CO = 0, 1} Q

Q

+ CO × AC v(t) × bp t + CD × AI v(t)

where: bp Q t

Bid price of a bond according to the quoting conventions of the bond’s market; total return is calculated on the bid side so as to represent the “cash out” value of the bond on a given day

CO

Current face/original face value indicator: 1 = Bond quoted on a current-face basis (i.e., needs scaling if applicable); and 0 = Bond quoted on an original-face value basis

Bv(t)

Face balance scalar used to adjust for principal balance due, as determined by the cash-flow structure, and settlement and ex-balance conventions

ACv(t)

Accrued capitalization; for bonds that capitalize and are quoted on a current-face basis, an adjustment is made at settlement for the portion of the next capitalization that is not included in the quoted price. Since capitalization is a payment for principal (unlike accrued interest, which is a payment for interest), the accrued capitalization, AC, is multiplied by the quoted price; AC is determined analogously to accrued interest (i.e., capitalization rate x day count convention)

CD

Clean/dirty indicator: 1 = Bond quoted on a clean basis; and 0 = Bond quoted on a dirty basis

AIv(t)

Current period’s coupon rate x day count convention; this is calculated up to, but excluding, the value date, v(t). Although conventions covering accrued interest calculations can be generalized, exceptions do apply.

Settlement and interest calculations EMBI+ calculations take into account accrued interest conventions, settlement conventions, and ex-coupon/ ex-amortization conventions of each security and market. Day-count basis In general, the day-count basis will depend on whether a bond has a fixed or floating rate. For fixed-rate bonds, it is usually 30/360, and for floating-rate bonds, it is usually either actual/360 or Treasury actual/actual. Exceptions exist, which apply to certain Brady bonds.

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Coupon payment Depending upon the specific debt instrument, coupons can be scheduled monthly, quarterly, semiannually, or annually. How the coupon end-of-period and pay dates are set vary from bond to bond. Several conventions apply to situations in which the end of a coupon’s period falls on a weekend or holiday, as defined by EMTA. These conventions are detailed in Table 4. Table 4: End-of-period conventions If a scheduled end-of-period (EOP) date falls on a weekend or holiday, the end of period:

EOP/Pay 1

Remains on that date, and the actual pay date is moved to the next business day.

EOP/Pay 2

And the actual pay date are moved to the next business day.

EOP/Pay 3

And the actual pay date are moved to the next business day, unless that pushes them to the next calendar month, in which case they are moved to the preceding business day.

EOP/Pay 4

And the actual pay date are moved to the next business day, and all subsequent ends of periods are benchmarked from that day.

EOP/Pay 5

All hybrid cases of 1 through 4.

Coupon accrual Generally, interest accrues from the previous coupon date (inclusive) to the settlement date (exclusive). If a bond trades ex-coupon, negative accrued interest will accrue from the ex-date to the coupon date. Cash reinvestment Since coupon income and amortization payments on performing instruments are reasonably certain, reinvestment is done on the date on which the value date for the trade captures the next cash payment. This allows the investor to affect the reinvestment trade such that, when the trade settles, the cash payment is available. Price and interest return Price return is the component of total return that follows just the price movement. Intuitively speaking, it is the original-face, clean-priced bond’s return, Pt(o,c). This bond’s return is calculated using variables already defined:

4.

{ if CO = 1, Bv(t) , if CO = 0,1}+ CO × ACv(t) × bpQt + xamv(t) − { if CD = 0, AIV(t) , if CD = 1,0} O,C

Pt

Q

bpt

=

×

Price return, adjusted for currency, then is: 5.

Pr t

=

PtO,C

+

AM v(t)

C PtO, -1

×

FX i, t FX i, t -1

−

1

Finally, interest return is simply a residual of total return and price return: 6.

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1 + ir t

=

tr t

+

1

Pr t

+

1

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Treatment of non-performing instruments In the event of an unexpected delay of or default on a payment, the specific cash flow would not be recognized until the payment is actually received. The calculation of an individual non-performing instrument’s return and the resulting index return would follow the settlement-cash flow entitlement convention set by either EMTA or a similar market trade group.

A default will not force the removal of the affected instrument from the EMBI +. As long as the affected instrument continues to satisfy our inclusion criteria, it will not be removed from the index.

II. Index total return To compute a daily index value, we need to know the following: 1. The list of instruments to be included and their amounts outstanding; 2. The daily total return of each instrument; and 3. The weight of each instrument as of the prior business day’s close. The first factor, the list of instruments and amounts outstanding, comprises parameters that are exogenous to the other factors and, therefore, changes to it should not result in changes in value of the index. These “rebalancing” events are done to the index on the last business day of each month, such that the index’s next month’s composition reflects the new instrument balance. When a rebalancing event occurs, it is as if the investor sells the entire portfolio at the day’s closing bid-side prices, and then immediately reinvests the proceeds in the new portfolio in proportion to the new market values based on the same closing bid-side prices. This results in a shift in the relative weights but not a change in the overall portfolio value. It is worth noting what is meant by the amount outstanding of an instrument. Recall that amortizations and capitalizations, where applicable, result in changes to the amount outstanding. These changes are “passive,” however, and are already captured in the effective settlement price via the balance scalar. Therefore, the figure used in determining market value is the original amount outstanding, plus or minus any “active” changes to the amount outstanding resulting from reopenings or buybacks (which we will refer to as N, the “number of bonds”). Since this is an original-face-value concept, it is consistent with all our other variables, also defined in terms of original face value.

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The total return on day t, TR t, is the arithmetically weighted average of each instrument’s return from the period t-1 to t. The weights are marketcapitalization weights from the prior business day, t-1: 7.

TR t =

∑ m i,t',t 1 × tr i, t −

i∈L (t' )

In this equation, the “ith” bond’s dirty market-capitalization weight on day t-1 is defined by: m i, t', t −1 =

N i, t' × ESVi, s(t −1)

∑ Ni, t' × ESVi,s(t 1) −

i∈L (t' )

where:

∑ mi, t', t 1 = 1 −

i∈L (t' )

and: L(t’) t’ Ni,t’

Instrument list on day t’ Last rebalancing day Number of bonds (see above); usually equal to the amount outstanding, except for capitalizing or amortizing bonds

Each term in the summation in Equation 7 measures the percentage contribution of an instrument to the change in the index portfolio’s value between day t-1 and day t. Since each instrument’s weight is updated daily, it is possible to see how cash reinvestment is done. Because the effective settlement price of an instrument drops concurrently with its cash payment (the accrued interest, balance scalar, quoted price, or cash-promised variable drops, depending on the type of instrument), the instrument’s market-capitalization weight drops, raising the relative importance of the other instruments within the portfolio. This achieves cross-index reinvestment. Since the scheduled cash flow causes the instrument’s market capitalization and weight as a percentage of the index to drop, a simultaneous increase in the weight of the other instruments in the index occurs. As a result of this shift in instrument weights, from a mathematical perspective cross-index investment of t he cash flow is achieved. Once the aggregate daily total return of the EMBI + is known, it is then applied to the index’s prior day closing level to arrive at the current day’s closing value: 8. It-1

December 2004

I t = I t -1 × (1 + TRt )

The closing cumulative total return index level for the EMBI+ as of the prior business day (where December 31, 1993 = 100)

15




Price and interest return All of the variables needed to calculate index price returns are defined above, except for one. This remaining variable represents the clean market capitalization, which is computed in an analogous way to the dirty market capitalization, but uses the clean-price concepts described earlier for bonds and loans, instead of the effective settlement price. Therefore, portfolio price return is the weighted average—in which the weights are clean—of the price returns of the constituent instruments. Interest return calculations continue to be based on the same formula.

III. Yield and spread calculations Instrument Level Yield Blended Yield to Maturity is simply the internal rate of return of the bond instrument. Stripped Yield measures the pure issuer risk by stripping out any collateralized cashflows from the instrument. In the case for uncollateralized bonds the blended yield is equal to the stripped yield. Stripped yield is usually referred to as Sovereign Yield for the Emerging Markets sovereign bonds and the EMBI indices. Embedded options are ignored for yield to maturity calculations. Instrument Level Spread Spread measures the credit risk premium over US Treasury bonds. The Blended Spread is the regular Spread over Treasury. Spread over treasury is simply the difference between the Yield to Maturity Bond and the Yield to Maturity of the corresponding point on the US treasury spot curve. Since Yield to Maturity is simply the discount rate at which all present value of all future cashflows equals the market price of the bond, all cashflows are discounted at the same (flat) rate.

Spread Over Treasury is a poor measure of sovereign risk for Brady bonds. All cashflows are discounted using the same rate, regardless of any collateral. For collateralized debt, this rate represents the return on blended and sovereign risk. For uncollateralized debt, this rate represents the return on pure sovereign risk. Therefore comparisons between collateralized and uncollateralized bonds or bonds with different amounts of collateral are distorted. Stripped Spread is a better measure for these comparisons because it accounts for collateral. In the calculation of stripped spread the value of collateralized flows (if any) are ‘stripped’ from the bond. In the case of a bond with principal collateral, the present value of the collateral is discounted using US Treasury Strip rates and subtracted from the price of the bond. To calculate the Stripped Spread the zero curve is then parallel shifted upwards and used to discount the remaining unsecured flows until the present value of the cashflows equals the ex-collateral price of the bond. The number of basis points the curve must be shifted upwards is called the Stripped Spread.

16

December 2004




Stripped Spread is the value of Z such that market value of portfolio equals ∑ [(CFt)/ (1+ R t +Z)t]

where CFt

cashflow at time t

R t

zero-coupon rate at the t- year point of the curve

This calculation is also valid for uncollateralized bonds. For Emerging Markets sovereign bonds, the stripped spread is more commonly known as Sovereign Spread. Stripped spread is calculated using offer side prices. Note that stripped spread of the index does NOT equal to the market cap weighted average of individual bond spreads. Composite level yields and spreads The calculation methodology for index level yields and spreads are the same as at the instrument level. Cashflows from all the individual bonds in the portfolio are added up to create a single “superbond”. The yield and spread for this superbond is then calculated as described above for the single instrument. Note that the result will be different from the market capitalization weighted spread derived from individual bonds in the portfolio.

IV. Other Index Metrics Effective Interest Rate (EIR) Duration: Measure of sensitivity of dirty price with respect to the US Interest Rates parallel shift. It approximately shows the percentage change of dirty price if all US interest rates change by 100 bps. Effective Spread Duration: Measure of sensitivity of dirty price with respect to the sovereign spread movement. It approximately shows the percentage change of dirty price if stripped spread changes by 100 bps. Average Life: Weighted average time of principal repayment. For nonamortizing bonds, the average life is equal to the years to maturity of the bond.

V. Credit Quality With the launch of the EMBI Credit Subindices in April 2002, JPMorgan categorizes and calculates analytics on four distinct credit buckets: Investment Grade, BB, B and Residual (CCC+ and below) subindex. Where we publish index statistics for ratings-based subindices, we take the higher of the S&P and Moody’s ratings to determine an instrument’s ratings category.

December 2004

17

JPMorgan Emerging Markets Research Contact Information Joyce Chang, Global Head of Emerging Markets Research, Foreign Exchange, and Commodities (1-212) 834-4203 j oyce.chan g@j pmor gan.com

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Emerging Markets Bond Index Plus (EMBI+) JPMorgan

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