No1 Rock-Bottom Spreads

Rock-Bottom Spreads

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Investment Strategies www.morganmarkets.com

New YorkOctober 25, 2001

J.P. Morgan Securities Inc.Portfolio ResearchPeter Rappoport (1-212) [email protected]

Overview:

Fixed income investors have at their disposal an array of analytical tools for valuingtheir interest rate exposure. However, most bonds present significant additionalexposures, notably credit and liquidity, for which valuation tools are scarce or non-existent. This volume describes the rock-bottom spread framework we have devel-oped as a first step to filling this void. Our aim is to make it possible to value thecredit exposure of fixed income instruments, much as their interest rate exposurecan be valued.

A bonds rock-bottom spread is what you, as an investor, need to be paid to bear itscredit exposure. At any lower spread, you will simply not earn enough to compen-sate for the credit risk the bond exposes you to, hence the term, rock-bottom. Itreflects four distinct components:

The cashflow pattern, maturity and seniority of the bond; Its credit quality as determined by a rating; Your views on broad credit trends over the bonds life; and The rate of return you require in general for taking risk.

So, the bonds rock-bottom spread translates its promised cashflows, viewed fromyour perspective on credit conditions, into the spread that will deliver you sufficientreturn for bearing its credit risk. If its market spread falls short of rock-bottom,you have a clear signal that holding the bond is not a good idea. It does not evenpay you enough for its credit exposure, never mind the liquidity you will forgo inholding it. If the market spread exceeds rock-bottom, then the bond will be a goodbuy if the excess spread is enough to compensate for its illiquidity. Figure 1 illus-trates this basic valuation recipe.

Figure 1Rock-Bottom Valuation: the basic recipe

Credit Views

Risk/return target Market Spreadabove Rock-Bottom

Rock-BottomSpread

Buy if surplus spreadpays for illiquidity

Do not buy thebond

Bond Characteristics,Credit Rating

Market Spreadbelow Rock-Bottom


Investment Strategies: No. 1page 2

J.P. Morgan Securities Inc.Portfolio ResearchPeter Rappoport (1-212) 834-7046

So, rock-bottom spreads allow you to remove creditfrom the valuation equation, much as duration and con-vexity allow you to remove interest rate exposure. Com-paring the excess of market spreads over rock-bottomacross bonds or bond classes is frequently sufficient toreveal significant valuation anomalies in market pricing.For example

B-rated corporates have rarely paid in excess of theirrock-bottom spreads, throughout the bull and bearmarkets of recent years. In contrast, over the sameperiod, BB-rated corporate market spreads have con-sistently exceeded rock-bottom by upwards of 100basis points. Figure 2, taken from the article Rock-Bottom Spread Mechanics in this volume, illustrates thispoint with data from June 2001.

High Yield Corporate and Emerging Markets Sovereignbonds have very different mixes of credit exposure,making comparison of their raw market spreads atreacherous indicator of relative value. However, therock-bottom spread framework allows us to price eachof these differences separately. This provides a frame-work for identifying and taking views on the keydifferences between the two markets. For example, thedecomposition of the two markets rock-bottomspreads in Figure 3, versions of which are used in theEmerging Markets versus High Yield articles, points todifferences in (assumed) recovery rates as the singlelargest contributor to the rock-bottom spread differen-tial.

Over the last few years, a strategy that sold bonds withhigher rock-bottom than market spreads, and bought

Figure 2Rock-Bottom versus Market Spreads for US Corporate Bonds

100

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AA A BBB BB B

Rock-bottom exceeds market spread

{Positive liquidity spread

Market spread

Rock-bottom spread

{Rock-bottom

less than market spread

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Rock-bottom exceeds market spread

{Positive liquidity spread

Market spread

Rock-bottom spread

{Rock-bottom

less than market spread

Figure 3Anatomy of rock-bottom spread differences

+26bp

-198bp

+218bp

-200bp

+60bp

+97bp

+157bp

EMBI Global withcurrent rating

outlooks488bp

with stablerating outlooks

514bp

and with HYcredit composition

671bp

and with historicalHY recovery rate

473bp

and with historicalHY credit migration

691bp

and with HYdiversity

491bp

and with current HYrecovery rate view

551bp

and with current HYcredit migration view

648bp

HY with currentdefault view

648bp

those with lower rock-bottom spreads than market,outperformed the High Grade market by about 1.1%annually, and outperformed the Speculative Grademarket by about 6% annually. Figures 4 and 5 docu-ment that this outperformance has occurred consist-ently, and with low downside.

This collection of articles is designed to enable you touse the rock-bottom spread framework in your creditinvestment decisions, whether strategic or tactical. Itdraws together articles JPMorgan has written andresources it has developed to calculate rock-bottomspreads, understand what drives the calculations, andexplore where they can add value. Our review is organ-ised in three sections.




1. Understanding Rock-Bottom Spreads

The first paper in this volume, Valuing Credit Funda-mentals: Rock-Bottom Spreads, develops the motiva-tion for rock-bottom spreads in detail. As with anyanalytical tool, it is necessary to feel comfortable withhow rock-bottom spreads work, and to understand whythe calculations deliver the results they do. To this end,we have included Rock-Bottom Spread Mechanicswhich shows how rock-bottom spreads follow logicallyonce you have set yourself a target risk-adjusted return,or information ratio. It then shows how to calculaterock-bottom spreads, starting from the simplest exam-ple of a one-year bond, and moving on to longer-maturity bonds. For each input to the rock-bottomspread calculation, such as a bonds coupon, maturityand assumed recovery rate, it shows how the resultingrock-bottom spread changes as the input changes. Thisgives an idea of the sensitivity of rock-bottom spreadsto changes in bond characteristics and assumptions, aswell as a sense of which drivers of the rock-bottomspread are important. All of the examples can be repli-cated using the rock-bottom spread calculator on ourMorganMarkets website, by following the recipes in thepaper.

One of the principal drivers of rock-bottom spreads isthe pattern of credit migration, that is, the frequencieswith which upgrades, downgrades and defaults occur.The most complete information is available for USissuers, but there is a widespread view that differentcredit migration assumptions are relevant for Europeanissuers. In Valuing European Credit Fundamentals,we assess the implications for credit spreads of thedifferent credit rating experience of European issuers.

Another resource for understanding rock-bottomspreads, Rock-Bottom SpreadSheet, is available onMorganMarkets. This interactive presentation builds upa complete calculator step-by-step, making it possible toexplain the source of each number in each step. Thisallows you to concentrate on particular steps of thecalculation, in a way that would not be possible in aresearch paper.

2. The Rock-Bottom Spread Web Calculator

Calculating rock-bottom spreads is a purely mechanicalmatter, once you have assembled the appropriateinputs bond characteristics, market views, etc. Theprincipal problem is to manage and manipulate the large

TABLE OF CONTENTS:

1. Understanding Rock-Bottom Spreads

Valuing Credit Fundamentals: Rock-Bottom Spreads 5

Rock-Bottom Spread Mechanics 17

Valuing European Credit Fundamentals 29

2. The Rock-Bottom Spread Web Calculator

An Annotated Introduction to the Rock-bottom Calculator 35

Introducing the Rock-Bottom Roundup 43

Rock-Bottom Roundup 45

3. Rock-Bottom Investment Strategies

Picking High Yield Bonds 49

Picking Investment Grade Bonds 57

Valuing Rating-triggered Step-up Bonds 67

Comparing Credit Fundamentals:Emerging Markets versus High Yield 69

Emerging Markets versus High Yield:Credit Fundamentals Revisited 77

US Credits Look Attractive for Japanese Investors 89

Figure 4US Investment Grade Rock-Bottom Bondpicking StrategyAnnualized return relative to Index

Figure 5US High Yield Rock-Bottom Bondpicking StrategyAnnualized return relative to Index

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amount of data involved. This problem is solved by therock-bottom spread calculator, which makes it simple totake views on credit trends, calculate the resulting rock-bottom spreads on any portfolio of bonds, and examinethe sensitivity of these spreads to changes in your views.The calculator is to be found on our MorganMarketswebsite [www.morganmarkets.com], and is described inUsing the JPMorgan Rock-Bottom Spread Calcula-tors.

The calculator makes it possible to trawl through literallythousands of bonds, and value them all in a commonframework. You can either upload your own portfoliodetails, or examine the results for groups of bonds thatare permanently accessible to the calculator, such as ourHigh-Yield Corporate and Emerging Markets sovereignindices, and High-Grade Corporates.

Since many investors may find it useful to have informa-tion on these broad asset classes, a periodic publicationwill summarize their rock-bottom and market spreadsunder a basic credit view. A sample of this Rock-Bottom Roundup is included in this volume, along withan explanation of how to read it. The Rock-BottomRoundup compares market and rock-bottom spreadsacross the three asset classes, as well as breaking themdown by rating category and seniority.

3. Rock-Bottom Investment Strategies

A bond whose market spread exceeds its rock-bottomspread is cheap, in the sense that its expected futurereturns are high relative to the anticipated credit risk.Picking High Yield Bonds and Picking InvestmentGrade Bonds develop this idea, and show that bondselection rules based on it have substantially outper-formed the High Yield and Investment Grade corporatemarkets since 1997. In each case, we examine in depththe source of the rules outperformance, and its limita-tions. In both cases, it is quite clear that the rock-bottomrule identifies a systematic source of value that is notpicked up by other, more traditional approaches to bondselection. In particular, using the rock-bottom frame-work is the obvious way to apply the same yardstick toall bonds a highly desirable feature for any relativevalue discipline.

One of the virtues of the rock-bottom framework is thatit enables you to place a value on highly complexstreams of contingent cashflows, as shown in ValuingRating-triggered Step-up Bonds, which focuses onrecently issued telecom paper. One of the features towhich it draws attention is the different value of alterna-tive step-up schedules.

We also include two earlier pieces of research, Com-paring Credit Fundamentals: Emerging Markets versusHigh Yield, and Emerging Markets versus HighYield: Credit Fundamentals Revisited. These papersdetail in particular the relative diversity of EmergingMarkets Sovereigns and High Yield Corporates, and thecredit migration assumptions we use for EmergingMarkets in the Rock-Bottom Spread Calculator.

Last, US Credits Look Attractive for Japanese Inves-tors evaluates opportunities for Japanese investors inthe US corporates, by calculating the surplus spreadthey offer over rock-bottom in Yen terms, and compar-ing it with the surplus offered by Japanese issuers.

Since the articles in this collection were originally issuedas standalone pieces we do not recommend readingfrom cover to cover. Rather, this volume is best used asa reference.

Each article contains a description of how the Rock-Bottom Spread valuation framework operates, and so,we hope, will be understandable to anyone not versed inRock-Bottom Spreads as an application of the concept.For a detailed understanding of Rock-Bottom Spreads,we recommend that you read the first article, ValuingCredit Fundamentals, to provide an overview, butconcentrate on the examples in Rock-Bottom SpreadMechanics to gain a thorough grounding in what drivesrock-bottom spreads. The examples in this article aredesigned to be easily replicable on our web calculator,and we recommend that the two be used together.




Originally published onNovember 17, 1999

Valuing Credit Fundamentals:Rock-Bottom Spreads

Rock-bottom spreads measure the lowest acceptable rewardfor bearing exposure to default and downgrades

Comparing rock-bottom spreads to market spreads iscentral to assessing the value of credit instruments

High-grade market spreads greatly exceed rock-bottomspreads, while speculative grade spreads often fall short ofrock bottom.

- this means that market spreads pay the lowest liquiditypremium for the least liquid bonds

This years deterioration in credit fundamentals

- is priced into high-grade spreads

- is overcompensated by BB new issue spreads

- is not reflected by other high-yield spreads

Do BB-rated spreads currently offer better or worse value thaninvestment grade spreads? Is the rise in A-rated spreads thisyear sufficient to compensate for growing worries about credit?Any informed view on these questions needs to take account ofcredits many moving parts: default rate trends, recovery rates,changes in credit quality. Not making these credit fundamentalsexplicit runs the risk of losing them in the shuffle.

This note shows how to value a bonds credit fundamentalsexposure, which we translate into its rock-bottom credit spread.This is the lowest spread at which an investor should bewilling to bear its credit fundamentals exposure.

The difference between market spreads and rock-bottomspreads is, accordingly, the maximum available to compensatefor corporates lower liquidity than governments. We refer tothis as the illiquidity spread. Decomposing spreads into creditfundamentals and liquidity components provides a new andsurprising perspective on the sources of value in credit markets.

Investment and speculative grades offer very differentpackages of payment for illiquidity and credit fundamentals(Figure 1). Investment grade rock bottom spreads are very lowrelative to market spreads. AA-rock-bottom spreads of 18bpcompare to market AA spreads of 90bp. This leaves 72bp ascompensation for AAs greater illiquidity than governments.

Moving down the credit spectrum, rock-bottom spreadsincrease, as we would expect. In fact, they grow faster than

market spreads. Speculative grade market spreads aredominated by rock-bottom spreads, with B-rated spreadseven falling short of rock-bottom by 203bp. High-gradeilliquidity spreads exceed high yield (Figure 1), eventhough speculative grades are much less liquid. Thismeans that the market is not pricing credit fundamentalsand liquidity exposures consistently across the creditquality spectrum.

Not only are investment grade rock-bottom spreads lowrelative to market spreads, they also move little when creditfundamentals change. Figure 2 compares rock-bottomspreads arising from two credit fundamentals scenarios,one conforming to historical average default rates, theother a credit downturn scenario, in which adverse creditconditions are expected over the next two years. AA rockbottom spreads differ by just 2bp. High-grade investorswho focus on managing their credit fundamentalsexposure at the expense of their liquidity exposure, wouldseem to be misallocating their efforts.

In contrast, as credit fundamentals change, significantmovements in speculative grade rock-bottom spreadsoccur (Figure 2). Assessing whether changes in creditfundamentals are matched by market spreads is essential

SpreadsMarket 72 90 124 165 300 510Rock-Bottom 6 18 34 99 296 713Illiquidity 66 72 90 66 4 -203

-200

-1000

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600700

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AAA AA A BBB BB B

Rock-BottomSpread

Market Spread

IlliquiditySpread

Rock-bottom spreads calculated from the credit downswing scenariodescribed in Section 5, below

Figure 1Rock-Bottom Spreads vs. Market Spreads,October 1999 (10-year maturity)Basis points

Portfolio Research www.morganmarkets.com




for high-yield investors, and is made easier by tracking rock-bottom spreads.

The body of this paper is organized into these sections:

1. Credit Fundamentals .....................................................p.3

We describe how historical default rates, recovery rates, andchanges in credit quality affect rock-bottom spreads.

2. Credit Returns ..............................................................p.4

We describe the precise features of corporate bonds pricedby rock-bottom spreads.

3. Risk Tolerance ..............................................................p.4

We describe risk tolerance in terms of a target information ratiothat credit returns need to attain, in order to be competitivewith other alternatives to investment in government bonds.

4. Rock-Bottom Spreads ....................................................p.5

We describe how we calculate rock-bottom spreads fromcredit fundamentals information and the investors risktolerance, measured by a target information ratio. Thissection may be cheerfully skipped by anyone not interestedin the mechanics of the calculations.

5. Forecasting Credit Fundamentals .................................p.6

Rock-bottom spreads are essentially forward-looking, and thecredit fundamentals on which they depend amount to aforecast of the future course of credit conditions. Creditfundamentals have many moving parts, and forecasting eachis simply not practical. We show how to boil creditfundamentals down to a very small number of features onwhich a view needs to be held.

6. Interpreting Market Spreads ....................................... p.8

We use the credit fundamentals views contrasted in Figure 2above to cast light on how the market has responded to thedeterioration in credit conditions this year.

A rock-bottom spread calculator is available on the Creditpage of our website, Morgan Markets, and is explained in aseparate document, available on the website.

Roc k-Bottom SpreadsCredit Down turn Sce nar io 6 18 34 99 296 713Historic al Average Sce nar io 6 16 29 84 259 613Dif ferenc e 0 2 5 15 37 100

0

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AAA AA A BBB BB B

Figure 2Adverse Credit Outlook: Change in Rock-Bottom SpreadsBasis points




1. Credit Fundamentals

Ultimately, credit fundamentals concern the potential forlosses from default (Figure 3). Thus, a bonds short-termlikelihood of a default and how much will be recovered indefault both figure. Similarly, the bonds credit quality maychange, altering its subsequent default probability. Losseswill also be easier to bear, the greater the diversity of theportfolio in which the bond is held.

To arrive at rock-bottom spreads, we need to quantify eachof these credit fundamentals elements. As a baselinescenario, we use historical averages for the default profile.We use the transition probabilities tabulated by Moodysto measure the likelihood of each possible change in creditquality*. The achievable diversity is measured from recentestimates of the size of the corporate bond market (Figure 4).

A few concrete examples best illustrate how these numbersdrive a bonds credit fundamentals exposure. The top rightnumber in the transition matrix in Figure 4 indicates thatAAAs have zero probability of default over one year.Consequently, a one-year AAA has zero credit fundamentalsexposure, and its rock-bottom spread will also be zero. Thebonds 10.3% chance of being downgraded to AA, 1% chanceof a downgrade to A, and so on, are irrelevant for a one-yearbond, because it will still pay in full even if it is downgraded.

However, if the bond has more than a year to go, thesepositive probabilities of downgrade during its first year openthe possibility that it can default in its second year. Forexample, if the bond is downgraded to A after one year, it thenhas a 0.01% chance of default in its second year. Of course,both the probabilities involved in this 2-year AAA exampleare minute (1% and .01%), and so contribute little to creditfundamentals exposure. This, in turn, will translate into a verysmall rock-bottom spread. Similarly, we would expect thecredit fundamentals exposure and spread of a B-rated bond tobe much higher, because with a one-year probability of 7.1%,the event of default is far less remote.

Historically, recoveries from default have borne no relation tothe rating of the bond prior to default. Consequently, weassume that any defaulting issue will enter a recovery processwhich produces the historical average of $47 per $100 ofprincipal, albeit after 2.1 years on average. There is someuncertainty about the actual recovery amount, captured bythe $26 volatility of recoveries.

In all cases, an investor will be more prepared to take exposureto credit fundamentals at a given spread, the more it ispossible to diversify the default risks. The extent ofdiversification is captured by the diversity score in Figure 4.Introduced by Moodys, this translates a portfolio ofcorrelated exposures into a smaller number of uncorrelatedexposures. (Diversity scores are further discussed inAppendix 1). We calculate diversity scores as if theinvestors portfolio were the entire U.S. corporate market.Any less diversified portfolio would occasion a higher rock-bottom spread than we calculate.

Probability of Default

PortfolioDiversity

Credit FundamentalsExposure

Recovery Rate

Probability ofCredit Quality

Change

Figure 3Components of Credit Fundamentals

Figure 4Credit Fundamentals: Historical Average Scenario

Probability of Credit Quality Change and Default (% per year):

AAA AA A BBB BB B CCC DefaultAAA 88.7 10.3 1.0 0.00 0.03 0.00 0.00 0.00AA 1.1 88.7 9.6 0.3 0.15 0.15 0.00 0.01A 0.06 2.9 90.2 5.9 0.7 0.18 0.01 0.01BBB 0.05 0.3 7.1 85.2 6.1 1.0 0.08 0.16BB 0.03 0.08 0.6 5.7 83.6 8.1 0.5 1.5B 0.01 0.04 0.2 0.7 6.6 82.7 2.8 7.1CCC 0.00 0.00 0.7 1.1 3.1 6.1 63.0 26.2R

atin

g at

st

art

o

f yea

r

Rating at year-end

Source: Moodys. The figures are long run annual averages of thefrequency of rating changes and defaults among rated issuers, 1980-98

Portfolio Diversity:Diversity Scores

AAA AA A BBB BB B CCC30 53 66 63 59 54 19

The diversity score is the number of uncorrelated exposures to which eachsector is equivalent. See Appendix 1.

Recovery Rate:Average Recovery Rate: $47 per $100 of principalVolatility:

$26 per $100 of principalAverage time to recovery:

2.1 yearsSource: H.S. Wagner The Pricing of Bonds in Bankruptcy and FinancialRestructuring, Journal of Fixed Income, June 1996

* Standard and Poor provide similar tables. Note that we are equating the ratingcategories of the two agencies (for example, Baa and BBB), and using Standard andPoors nomenclature. These historical transition probabilities record thefrequency with which the agencies change ratings. We are thus assuming thatthese frequencies are a reliable representation of how actual credit qualitychanges. This does not require that the rating agencies anticipate changes incredit quality, just that, ex post, the frequency of rating changes matches thefrequency of credit quality movements.




2. Credit Returns

The essence of credit risk is that promises to pay cashflowsmay not be kept. Accordingly, it makes sense to comparebonds exposed to credit risk to government bonds, which, forour purposes, are those whose cashflow promises are not indoubt.

This motivates examining a bonds credit return, which is theexcess of its return over that of an identical bond whosecashflows are promised by the government. To make ourexposition of rock-bottom spreads clearer, it is simplest to thinkof the corporate bond and the government bond as trading atpar, and promising different coupons on the same date. Thecorporate bond promises more, in the form of a spread overgovernment coupons, to compensate for the uncertainty of itspromises.*

Figure 5 illustrates for the case of a one-year bond.There are only two possible scenarios default and nodefault (because the investment time horizon and maturity ofthe bond coincide). The two bonds promised cashflows,which are realized in the absence of default, differ only by thespread paid on the coupon date. Their actual cashflows willalso differ when the credit risky bond defaults.

This simple example illustrates how credit fundamentalsexposures -- the possibility of a default, and the dimensions ofwhat is recovered in the event of a default, give rise to a creditspread. The obvious question is, how much spread? For this,we need to stipulate the risk tolerance of the investor.

3. Risk Tolerance

Rock-bottom spreads are the result of combining creditfundamentals with the investors risk appetite (Figure 6).

The information ratioWe think of the investors neutral position as being investment ingovernment bonds that match liabilities cashflow-for-cashflow.This is not only relevant to fund managers who are mandated tooutperform a government bond index. It is also a sensible baselinefor assets invested to meet defined benefit pension liabilities or lifeinsurance annuity contracts. If the liabilities are cashflow-matchedwith government paper, there is no chance of failing to meetliabilities. Credit exposure creates the possibility that liabilities willnot be met due to defaults, so an excess return over governmentswill be demanded.

We want to establish the spread at which it is worth holding a bondinvolving credit fundamentals in preference to a government bondwith identical cashflows. To do so, we work backwards from thegeneral conditions that should induce an investor to hold any assetin preference to government bonds, namely that the extra returnearned on average is sufficient compensation for the extra risks.Here, the extra return that concerns us is the credit return.

We quantify this condition by requiring that the credit bond mustbe priced to offer an excess average return per unit of excess returnvolatility or information ratio commensurate with otheropportunities for outperforming governments. A rule-of-thumbused by plan sponsors is that candidate new asset classes need todemonstrate an information ratio of one-half. The historicalperformance of active managers of global government bondportfolios a competing use of the funds that might otherwise beinvested in credit is also one-half (see Maintaining returns in alow-yield world, J.P. Morgan, January 7, 1999). Accordingly, werequire credit bonds to produce an information ratio of one-half. Anasset class with an information ratio of 0.5 will underperform itsbenchmark (here governments) one year in every three.

The actual information ratio offered by a bond portfolio dependsonly on:

the credit fundamentals features depicted in Figure 3, the spread of the bonds.

We can use this relationship to back out the spread that, incombination with the bonds credit fundamentals, generates thetarget information ratio of one-half. This will be the rock-bottomspread.

Figure 5Cashflow Patterns

CreditReturn

CorporateReturn

GovernmentReturn=

Corporate Bond

Recovery $100 + $5+Spread

Default No default

Now pay...

At maturityreceive ...

1 year

$100

$100 + $5

5% Government Bond

-

$100

* An alternative is to assign the government and corporate bonds the same coupon.In this case, they do make identical promises, and the government bond will costmore than the corporate as a consequence. The two perspectives lead topractically identical rock-bottom spread figures.

Figure 6Rock-Bottom Spreads

Credit FundamentalsExposure

RiskTolerance

Rock BottomSpreads




4. Rock-Bottom Spreads

We need to flesh out the relationship between spreads and creditreturns. We start with the one-year bond described in Figure 5,whose current cost is $100, and whose annual coupon we think ofas equal to the government rate plus a spread. With aninvestment horizon that is also one year, what is the minimumspread over the one-year government rate at which you wouldhold this bond, that is, the spread that causes the bondsinformation ratio to be one-half?

The information ratio is the ratio of average credit returns to thevolatility of credit returns. We now trace the relationship of eachto the bonds promised spread.

Average credit returnsThe average credit return combines the returns in the twoscenarios, according to their probability of occurrence. Weillustrate with a BB-rated bond, so the relevant default rate is 1.5%per year. Figure 7(a) shows that the average credit returnincreases with the promised spread. The position of thisrelationship is driven principally by the default probability. Theline shifts to the right as the default probability rises, so the B-rated line would lie to the right of the BB line, while the A-ratedline would lie to the left.

If we were only concerned with breaking even with governments,Figure 7(a) would be as far as we need go, since we could read offthe required spread level as the intersection of the average creditreturn line with the horizontal axis. However, this 97bp does notcompensate at all for the risk of credit fundamentals.

Volatility of credit returnsFigure 7(b) charts the volatility of the credit returns of BB bondsagainst promised spreads. It is important to keep in mind that thevolatility of credit returns is not the same as the volatility ofexcess returns of spread instruments that we observe in themarket, since this contains the volatility of the liquiditycomponent as well. Instead, the volatility of credit returns iseffectively the range of variation between the $100 of principalreceived in the absence of default, and the average of $47,discounted back 2.1 years, that is paid out in default.Consequently, volatility varies very little as the level of promisedspreads moves over a range of a few hundred basis points. (Theline in Figure 7(b) is very flat). However, the volatility line isshifted upwards as the probability of default increases, and asportfolio diversification declines.

Finding the rock-bottom spreadIt now remains to divide the average credit return at each spreadby the corresponding volatility, to arrive at the actual informationratio corresponding to that spread (Figure 7(c)). From this, wecan read off the rock bottom spread of 152bp, at which aninformation ratio of one-half results. Comparing this figure withthe breakeven spread of 97bp reveals that our assumed riskappetite demands a risk premium of 55bp for holding BB-ratedpaper for one year.

Figure 7Calculating One-Year BB-rated Rock-Bottom Spreads

Divided by...

equals...

(a) Average Credit Return (%)

Spread (bps)

-1.5

-1.0

-0.5

0

0.5

1.0

1.5

50 100 150 200

(c) Information Ratio

-0.5

0

0.5

1.0

50 100 150 200

Target

BreakevenSpread: 97bp

Rock-BottomSpread: 152bp

(b) Credit Return Volatility (%)0.6

0.8

1.0

1.2

0 50 100 150 200

Explaining Figure 7

First, some abbreviations: p denotes the probability of defaultduring the year, d denotes the excess return over governments inthe event of a default (recovery-100-coupon) and s denotes thespread, n denotes the diversity score, or equivalent num ber ofindependent credit exposures in the portfolio (See Appendix 1).

The average credit return is the average of the excess returnover governments in F igure 6, weighted by their probabilities:

Hence, average credit returns increase as spreads increase. Asthe probability of default increases, the line flattens and shiftsdownwards.

p*d + (1-p)*s

The volatility of returns is:

So volatility increases with spread (although notsignificantly, s ince(s-d) is on the order of $68, and an extra100bp of spread raises this by only $1). As divers itydeclines or the probability of default increases (up to onehalf), the volatility line shifts up.

)(*)1(* dsn

pp-

-




These calculations can be carried out for any ratingcategory, as shown in Table 1. For lower credit qualities,the probability of default rises, the average credit returnassociated with any given spread level falls, and thevolatility rises. Thus, the spread necessary to deliver thetarget information ratio also rises. Spreads for AAA-ratedbonds are zero, because there is zero probability of defaultover one year, according to historical experience.

Rock-bottom spreads for longer maturitiesThis analysis is simple to extend to bonds with longer thanone year until maturity. What we needed to know tocalculate the one-year spread was the value of our bond atmaturity (par or default). To arrive at two-year rock-bottomspreads, we need to know the value of the bond in eachcredit fundamentals scenario (i.e., each rating category) atthe end of one year. But we have this information from theone-year spreads in Table 1 (which readily translate intoone-year prices). This inductive calculation can be repeatedfor each credit quality at each maturity, tracing out the entirestructure of rock bottom credit spreads by term to maturityand credit quality (see Appendix 2). Selected maturities areshown in Table 2. The 10-year spreads are those that appearin Figure 2*, under the historical average scenario.

Some perspectiveIt is worthwhile at this point to take stock. First, theframework we have used to arrive at rock-bottom spreadsmay seem similar to that used to price options or otherderivatives. There are indeed great similarities. In particular,we are using the tree type of structure to capture all thepossible scenarios. Here, the branches in the tree arise fromchanges in ratings. However, the use to which we put thisframework is entirely different from the derivatives case. Toprice an option, one takes the value of the underlyingsecurity or securities as given, and ensures that the option ispriced so that no profitable arbitrage trade involving theunderlying security and the option is possible. In the caseof rock-bottom spreads, we are valuing not a derivative, butthe underlying security itself. There is therefore no risklessportfolio (composed of the derivative and the underlying)that we can set up that enables us to ignore both the riskpreferences of the investor, and the average return of thesecurities. Instead, the risk preferences are described by theinvestors target information ratio, and the average (credit)return is the one that results from satisfying these riskpreferences in the context of the bonds credit fundamentals.We thus do not price credit risk in a way that is consistentwith market prices (i.e., arbitrage-free), but rather provide avaluation that is independent of the markets.

Second, rock-bottom spreads essentially reflect theinvestors reservation spread for credit exposure. Ineconomics terminology, we have identified a point on theinvestors demand curve. This is somewhat different fromother approaches to valuation of securities, for example, thatused in our Global Markets Outlook and Strategy (GMOS)publication. The GMOS valuation framework makesstatements about where market yields are likely to move,based on historical estimates of risk premia, and theobserved rate of mean reversion of yields to their equilibriumvalues. Thus, both supply and demand sides of the market,as well as adjustment to equilibrium, are brought under thevaluation umbrella. In the case of rock-bottom spreads, thesupply side of the corporate market is not addressed, andthere is no presumption that spreads will revert to aequilibrium fair-value levels indicated by rock-bottomspreads. In short, using rock-bottom spreads to value doesnot require any belief that the market is also using them.Instead, they reflect what the investor needs to be paid tobear the credit fundamentals risks involved, which will bedictated in part by the particular situation of the investor.Here, we have chosen the situation of a quite representativeinvestor, one whose investment problem is to, or reduces toattempting to, outperform a government benchmark. Thistype of investor has the assurance that, if his/her creditfundamentals views are correct, bond portfolios that yield inexcess of rock-bottom will produce a superior risk-returnperformance than their target information ratio.

* Our spread calculations omit compensation for individuals extra state income taxliability on corporate bonds, compared to US Treasuries. While rates vary fromzero to 12%, we have no estimates of the tax rate of the marginal investor, which isthe relevant rate. Consequently, we think of the residual illiquidity spread asincluding compensation for differential taxation. While this complicates usingthe illiquidity spread to measure total compensation for liquidity factor, it doesnot affect comparisons of spreads between rating categories, since all are taxed thesame.

Table 2Rock-Bottom Spread Term StructuresBasis points

1 3 5 10AAA 0 1 2 6AA 4 6 8 16A 5 9 15 29BBB 28 42 56 84BB 152 191 220 259B 632 645 642 613CCC 2959 2558 2239 1759

Maturity

Table 1One-year credit bonds

Rock-Annual Default Breakeven bottom Riskprobability (%) spread (bp) spread (bp) premium (bp)

AAA 0.000 0 0 0AA 0.005 0 4 3A 0.010 1 5 4BBB 0.16 10 28 18BB 1.46 97 152 55B 7.06 489 632 143CCC 26.16 2282 2959 677




5. Forecasting credit fundamentals

Rock-bottom spreads are essentially forward-looking. Thus,Figure 4s historical average credit fundamentals scenario,which we have used to illustrate how to calculate rock-bottom spreads, are relevant only if one believes that thehistorical average scenario will describe each year in thefuture. However, in general, the credit quality environmentchanges over time, and rock-bottom spreads should reflectanticipated changes in credit fundamentals. Interpretedliterally, this means taking a view on each element of thetransition matrix (including default rates) for each year in thefuture, which is obviously not practical. It is thereforeimportant to boil the necessary information down to a smallnumber of indicators, about which views can be formed.

The rating agencies regularly publish statistics on ratingsdrift (number of upgrades minus downgrades), activity(sum of upgrades and downgrades), and speculative gradedefault rates. Figure 8 shows that these have indeedfluctuated substantially around their long-term averages.They seem to be sensible measures about which to formviews about future credit fundamentals. Rating drift isanalogous to an average change of credit quality, while ratingactivity is analogous to volatility. Speculative grade defaultstrack an important source of credit returns. It is a lot moreeasy and intuitive to extend the lines in Figure 8 along anexpected future path, than it is to fill numbers in a transitionmatrix. The challenge is to propagate these pathsappropriately into anticipated transition matrices.Fortunately, a few simple rules appear to do the trick. Theseare described in Appendix 3.

To illustrate the process, assume we forecast the creditdownswing shown in Table 3:

The changes implied by the resulting transition matrix areshown in Figure 9. There is a tilt from upgrades todowngrades, and from live credit ratings to default, as

would be expected. This transition matrix is used to generatethe rock-bottom spreads for the credit downturn scenariodiscussed in the Introduction. We assume that it persists forthe next two years, after which credit fundamentals revert tothe historical average transition matrix shown in Figure 4.

Figure 9Credit Downswing Scenario: Changes in TransitionProbabilities from Historical Average

AAAAAABBBBBBCCC

AA+0.6-0.9+0.0-0.1-0.0-0.0+0.0

A+0.1+1.3-1.8-2.5-0.3-0.1-0.3

BBB+0.0+0.0+1.5+1.0-3.1-0.3-0.5

BB+0.0+0.0+0.2+1.3+0.1-3.4-1.4

B+0.0+0.0+0.0+0.2+2.5-0.7-2.8

CCC+0.0+0.0+0.0+0.0+0.2+2.0-2.0

D+0.0+0.0+0.0+0.1+0.7+2.5+7.0

Rating at year-end

Ratin

g a

t sta

rt o

f yea

r

AAA

-0.7-0.4+0.0-0.0-0.0-0.0+0.0

Source: Moodys

Figure 8Aggregate Measures of Credit QualityAnnual percentage rates

-25

-20

-15

-10

-5

0

5

10

Rating drift

Average -8.5%

0

2

4

6

8

10Speculative Grade Defaults

Average 4.1%

Dec 82 Dec 86 Dec 90 Dec 94 Dec 98

0

10

20

30

40Rating activity

Average 20%

Dec 82 Dec 86 Dec 90 Dec 94 Dec 98

Table 3Credit Fundamentals Summaries

Historical Credit

Average DownswingSpeculative GradeDefaults 4.10% 6%Activity 20% 20%Drift -8.50% -12%Which implies Upgrades 5.75% 4% Downgrades 14.25% 16%

Credit Fundamentals Scenario




6. Interpreting Market Spreads

The object of calculating rock-bottom spreads is to provideperspective on market spreads.

Serious concern over adverse credit conditions has onlyemerged during the middle of the year, as speculativedefaults rose, and downgrades accumulated and once againoutstripped upgrades. Earlier in the year, creditfundamentals were actually hovering around their historicalaverage (Figure 8). We characterize the view prevalent in themarket at that time as one that historical average creditfundamentals would persist into the future. Figure 10compares the resulting rock-bottom spreads with marketspreads in May 1999. The same pattern emerges as weexhibited in Figure 1 for October (repeated here). Inparticular, a minimal or negative liquidity premium is presentin speculative grade market spreads.

Since May, spreads have backed up as the credit picture hasworsened. The question that thus arises is whether the newlevels of spreads represent good or bad value. Figure 11compares the May-to-October rise in market spreads to thedifference in rock-bottom spreads between the historicalaverage and downswing credit fundamentals scenarios.

The change in investment-grade rock-bottom spreads hasbeen 4-7 points less than the move in market spreads.Interestingly, 10-year swap rates, which are one measure ofthe markets pricing of liquidity (see Valuing MarketLiquidity, J.P. Morgan, August 1999), are now higher byabout 10bp. Consequently, our revaluation of creditfundamentals, plus the swap markets revaluation of theliquidity premium, add up to approximately the backup inmarket spreads.

In contrast, speculative grade market spreads have risen lessthan rock-bottom spreads. As such, there is now only 4bpof liquidity premium in BB spreads, compared to 16bp inMay, and the B-rated illiquidity premium has declinedfurther, from -153bp to -203bp. Evidently, while havingaccounted for changes in credit fundamentals, the markethas done so in a way very different from our baselineforecasts.

One novel development in the high yield market currently isthe stark departure between new issue and secondary marketspreads (Table 4 provides some examples). For BB-ratedissues, secondary market spreads are around 300bp at 10years, while new-issue spreads have averaged 400bp. Onthe assumption that both new and seasoned issues have thesame credit fundamentals profile, this implies an illiquidityspread in BB-rated new issues of 104bp, which is the largestacross all rating categories. There is a similar effect in B-rated issues, the difference between new-issue andsecondary market spreads standing at about 130bp.

Figure 11Market Spread Changes: Oct 99 versus May 99Rock-Bottom Spread Changes: Credit Downswing vs. HistoricalBasis points

Spread ChangesMarket 6 5 12 22 25 50Rock-Bottom 0 2 5 15 37 100

0

20

40

60

80

100

AAA AA A BBB BB B

Market Spread Change

Rock-Bottom Spread Change

Figure 1Rock-Bottom Spreads vs. Market Spreads, October 1999Basis points


-200

-100

0

100

200

300

400

500

600700

800

AAA AA A BBB BB B

Rock-BottomSpread

Market Spread

IlliquiditySpread

Rock-bottom spreads calculated from the credit downswing scenario

Rock-bottom spreads calculated from the historical average scenario

Figure 10Rock-Bottom Spreads vs. Market Spreads May 1999Basis points

-200

-100

0

100

200

300

400

500

600

700

AAA AA A BBB BB B

Rock-BottomSpread

MarketSpread (10 yr)

IlliquiditySpread





Figure 12Illiquidity SpreadsBasis points, March 1997

-200

-150

-100

-50

0

50

100

AAA AA A BBB BB B

{ forever2 yearsEarly 97 conditions persist

Consequently, the B-rated illiquidity spread on new issues is-73bp: a great improvement on the secondary markets -203bp(Figure 10), but still not in the same risk-adjusted league asdouble-Bs.

Just as we can calculate the spread implications of particularpatterns of expected future credit fundamentals, we can alsoreverse the reasoning, and calculate the credit fundamentalsimplied by the level of market spreads. Credit conditions wereextremely benign in early 1997 (Figure 8), as speculativedefault rates fell to one-third of their long-term average, andMoodys ratings upgrades exceeded downgrades in numberfor the first time. Spreads hit an all-time low in March of 1997.What view of the future would have justified these spreads?

Had the favorable credit conditions been expected to persistindefinitely, the resulting rock-bottom spreads wereconsistent with the typical pattern of illiquidity spreads:about 30-50bp in high grade, small but positive for BB-ratedpaper, and negligible for B-rated (see Figure 12). However, ifthese favorable conditions were to last for only two years,high-yield spreads were much lower than rock-bottom: therewas a negative payment for liquidity in the order of 40bpimplied by BB-spreads, and of about 150bp implied by B-rated spreads. Evidently, spreads in 1997 priced in a

substantially optimistic view of the future. Marketparticipants expressed concerns informally at the time. Thesefigures provide an explicit measure of the degree of optimism.

Table 4Indicative High Yield Spreads:Recent New issues versus Comparable Secondary Market Issues

Source: J.P. Morgan

Spread Rating Spread RatingLTV 09 586 Ba3/BB- LTV 07 490 Ba3/BB-

IASIS Healthcare 09 689 B3/B- Triad 09 509 B3/B-Lifepoint 09 487 B3/B-

Sbarro 09 625 Ba3/BB- Dominos Pizza 09 500 B3/B-

Unilab 09 725 B3/B- Dynacare 06 585 B2/B+

New Issue Secondary Issue




Conclusion

Our valuation framework for credit fundamentals providesinformation that is basic to any decision concerning value incredit markets: the spread level the investor needs tocompensate for the risk of credit fundamentals.

Rock-bottom spreads are essentially a reservation price(spread) for credit risky bonds. This kind of valuation drawsonly on credit fundamentals data that are essentially externalto the market, such as default rates and recovery rates, andon the investors risk tolerance. Thus market spreads do notfigure anywhere in the calculation of rock-bottom spreads.The independence of rock-bottom spreads from marketspreads is what makes them useful as a valuation tool.Comparing rock-bottom spreads with market spreads is theway to decide whether market spreads offer good or badvalue.

Of course, if rock-bottom spreads differ from market spreadsfor credit fundamentals, the implication is that the market isusing different rules to value. For example, other marketparticipants (in aggregate) may be employing a differentinformation ratio, or a different view on the future course ofdefaults. We can back out such assumptions from marketspreads, as we have illustrated above.

This difference of opinion does not mean that the investorsassumptions should be brought into line with the marketassumptions. Nor does it entail that market spreads willmean-revert to the investors valuation in the short term.Instead, it highlights a difference of opinion or investorcircumstances, which can be expressed by taking thedifferent sides of a trade. As bonds near maturity, theinvestor will realize a profit if his/her credit fundamentalsviews were closer to reality than the markets.

We emphasize that it is the framework that is the mainmessage, not the baseline scenarios we have used toillustrate the calculations and reasoning involved. Thus, ourcredit downturn scenario may be thought too draconian, ornot severe enough. Either way, the framework still applies.All that is warranted is a change in credit fundamentalsassumptions. The consequences for rock-bottom spreadscan be examined using the calculator on our MorganMarkets website.

However, we are struck by themes that persist in the face oflarge changes in credit fundamentals. For example,significant movements in credit fundamentals produce littlemovement in investment grade rock-bottom spreads,suggesting that high-grade investors should be focusingtheir efforts on the drivers of liquidity. Speculative gradestypically pay nothing, or worse, for liquidity. This mayreflect a segmented market, where greater pursuit of total

return occurs among high-yield investors. Or it may reflectthat quantitative evaluation of credit fundamentals has notbeen part of the picture to date.




Appendix 2:Rock Bottom Spreads for long maturities

Here, we look at credit-risky bonds that pay the samecoupon, irrespective of rating or maturity, and trade atdifferent prices to reflect their credit exposure, rather thanpaying different spreads and trading at par. It is simple torepeat our one-year-maturity calculation in this form.

To fix ideas, think in terms of valuing a two-year BB-ratedbond. Whereas a one-year bond could finish the year in oneof two possible credit states (default and non-default), weconceive eight possible credit states for a longer-maturitybond at the end of its first year: the seven live ratingcategories, and default. We know the prices of the bond inthe event that it ends up in any one of these states. Usingthe probabilities of these outcomes in Figure 4, we have allwe need to calculate average credit returns and theirvolatility (and thus the spread that generates an informationratio of one-half) over the first year of the two-year bondslife.

Credit term structures do not necessarily slope upwards: forB- and CCC-rated credit qualities, 10-year spreads are lowerthan 5-year. Here is an intuitive, if not entirely rigorousexplanation. Think of a bond as either defaulting or beingalive (irrespective of rating) at the end of one year. If itdefaults, it pays off a standard amount, irrespective ofmaturity or rating. So, performance in the default scenariodoes not drive the difference in spread of 10-and 9-yearbonds of the same rating category. Instead, it is what goeson in the live scenario, which is that high grade bondstend to decline in credit quality over time (AAAs are anextreme case), whereas low-grade bonds tend to improve(from Figure 4, B-rated bonds have a 7.1% chance ofupgrade, against a 2.8% chance of downgrade). Thus, a low-grade bond will be a better credit risk after a year if it doesnot default, i.e., it will experience a capital appreciation in thelive scenario (over and above pull-to-par), and so it cancommand a lower spread. Similarly, a high-grade bond willbe a worse credit on average in the live scenario, and so itrequires an increasing spread as maturity increases.

Throughout these calculations, we assume that thegovernment curve is flat and does not change over time,which is, of course, wildly unrealistic but greatly simplifiesand shortens calculations. However, we are looking atcredits outperformance of governments, which is analogousto hedging away government exposure. As a result, theactual dynamics of the government market do not greatlyaffect rock-bottom spreads. Pricing credit risk is the contextof a mean-reverting government curve, exhibiting thevolatility of the last 10 years, lowers 10-year BB rock-bottomspreads by 3bp.

Appendix 1:Diversity Scores

We need to measure the correlation of movements inissuers credit quality. To do so we adopt a variant of thediversity score approach developed by Moodys toanalyze collateralized debt obligations. This converts aportfolio of correlated exposures to a smaller number ofindependent exposures. Moodys assume that issuers in thesame industry are highly correlated, and so diversity scoresfor individual industries do not move much beyond sixequivalent independent exposures. They assume that thereis zero correlation across industries, and so add the diversityscores of the bonds in each industry group, to arrive at aportfolio diversity score.

We use S&Ps issuer counts by (12) industries for the entirerated U.S. corporate market, for which we have tabulateddata (see Table A1), to arrive at our diversity scoreestimates. Since Moodys partition the issuer populationinto over thirty industries, their diversity score estimateswould be larger. The largest diversity score Moodysassigned to J.P. Morgans BISTRO deals was 91 (for an A-rated pool): compared to the 66 we arrive at using S&Ps 12-industry classification. Adjusting our diversity scores inthis range has little impact of meaning on rock-bottomspreads. A 50% increase in all our diversity scores, (so theA-rated figure rises from 66 to 99), results in 10-year rock-bottom spreads falling by less than four percent of theirTable 2 values.

Moodys describe their diversity score framework in theirpublication Rating Cash Flow Transactions Backed byCorporate Debt 1995 Update, by Alan Backman and GeraldOConnor, April 7, 1995.

Table A1Standard and Poors Rated Issuers, 1996

AAA AA A BBB BB B CCCAerospace 4 18 89 74 75 76 4HiTech 3 16 31 25 28 27 1

Service 4 47 96 89 85 109 5Leisure 0 9 29 34 81 84 3Health 5 18 55 41 43 33 3Building 0 4 33 39 41 28 0Energy 10 24 34 43 30 27 1Utility 1 50 133 107 18 2 0Telecom 9 32 27 8 8 16 5Transport 3 5 27 47 29 24 3Finance 43 136 376 133 34 11 3Insurance 43 77 83 40 23 8 1

Total Issuers 125 436 1013 680 495 445 29

Diversity Score 30 53 66 63 59 54 19




Appendix 3:Translating default, drift and activity forecasts

Rating categories have differed in the volatility of their actualtransitions, and their sensitivity to the overall incidence ofrating changes. We account for this by inferring a forecast ofeach rating categories downgrades from a historicalregression on aggregate downgrades, and we repeat thisprocess for upgrades and speculative defaults. The slopes ofthese regressions (shown in Table A3) increase as credit

quality declines, testifying to the different sensitivities ofrating categories to the overall environment. The table alsoshows the changes in downgrade rates that result from ourcredit downturn scenario, which pushes aggregatedowngrades from 14.25% to 16% yearly (Table 3). Forexample, the implied forecast of AA downgrades is anincrease of 1.4 percentage points. This results from theforecast aggregate downgrade figure exceeding the 14.25%historical average figure by 1.75%, multiplied AA-bondssensitivity of 0.79 (1.75*0.79=1.4).

Our last step is to propagate these changes amongdowngrades by one, two, or more notches. We distribute theincrease in downgrades according to the shares of differentnotches in Moodys historical transition matrix (see Figure 4).For example, downgrades of AAs to A have historicallyaccounted for 94% of all downgrades (9.6/(9.6+0.3+0.15+0.15),from the second row of the transition matrix). Accordingly, theAA-to-A downgrade rate in our forecast transition matrix willbe 9.92% (9.6%+0.94*1.4%).

Table A3Transition Matrix Adjustments

Downgrades Upgrades Speculative DefaultsSlope Change Slope Change Slope Change

AAA 0.38 0.7 0.00 0.00AA 0.79 1.4 0.25 -0.4 0.00 0.00A 1.00 1.7 -0.01 0.0 0.01 0.01BBB 0.89 1.6 1.51 -2.6 0.07 0.12BB 1.52 2.7 1.96 -3.4 0.36 0.69B 1.13 2.0 2.18 -3.8 1.31 2.50CCC 2.89 -5.1 3.71 7.05




Rock-bottom spread mechanics

A bonds rock-bottom spread prices its credit exposure

We explain with examples what goes intocalculating rock-bottom spreads, emphasizing:

o how credit risk is accounted for

o the key role of views on default andrecovery rates, and how to formulate them

o the minor effects of interest rates andrecovery rate uncertainty

A new rock-bottom spread calculator onMorganmarkets lets you replicate and further

dissect the examples

Corporate bonds have two principal drawbacks relative toswaps or government bonds: greater credit exposure, and

lower liquidity. Investors need to assess whether marketspreads pay enough for these drawbacks. This task is moremanageable if the exposures can be translated into spread

terms. JP Morgans rock-bottom spread framework doesjust this for credit exposure.

Rock-bottom spreads are built around the idea of areservation price: the highest price at which you can buy anasset and remain consistent with your investment

performance goals. A bonds rock-bottom spread is theamount you need to be paid for bearing its potential fordowngrade or default, and expected recovery rate, taking

into account your ability to diversify these risks. If thebonds market spread is below its rock-bottom spread, onaverage it will not deliver sufficient return for the credit risk

it entails. Similarly, the difference between its marketspread and rock-bottom measures how much you are gettingcompensated, if at all, for its lower liquidity. Figure 1

illustrates.

In several other research pieces, we have used the rock-

bottom spread framework as a common yardstick fordisparate asset classes such as high yield and investmentgrade corporate bonds and emerging markets sovereigns.

Similarly, the approach makes it simple to place a value oncredit-driven features of individual securities, such as callprovisions in high yield bonds, and coupon step-up clauses

triggered by rating changes.

The mechanical steps involved in calculating rock-bottom

spreads are explicitly laid out in this note. We first show

how the combination of your investment performance goals

and a bonds credit fundamentals determine its rock-bottomspread. Then we explain how the rock-bottom spread isaffected by each element of credit fundamentals: coupons,

maturity, recovery rates, default rates, and so on. We alsodescribe a simple framework for translating your own viewsof future credit fundamentals trends into rock-bottom spread

numbers that you can compare with market spreads.

Figure 1

Rock-bottom spreads versus market spreads (bp)

100

200

300

400

500

600

700

800

900

AA A BBB BB B

Rock-bottomexceeds

market spread

{Positiveliquidity

spread

Marketspread

Rock-bottomspread

{Rock-bottom

less thanmarket spread

Spreads over US Treasuries curve for (duration-weighted) averages of 5-

10yr senior, unsecured bonds in the JP Morgan High-Yield index (BB andB-rated), and liquid investment grade bonds. Market spreads are as ofJune 1, 2001. Rock-bottom spreads incorporate the negative credit viewfor the next 12 months that is described in the last section of the paper.

Recovery rates on defaulted bonds are assumed to be $35 per $100 ofprincipal, in line with current traded prices of defaulted debt.

Of course, this is scarcely vacation reading. Rather, it isintended as a reference that will make it possible to takeapart the rock-bottom spread calculations in our

publications, and that can now be carried out painlesslyusing our new web calculators. All but a few of thecalculations in this research note used these calculators. In

the text, we provide the recipe that will enable you toreplicate each calculation. An accompanying spreadsheet,available from our website [10]1, demonstrates how to build

a simple rock-bottom spread calculator. Thus armed, youwill be able to take apart and rationalise any rock-bottomspread valuation.

1 Numbers is square brackets refer to the publications listed on p.12

Portfolio Research www.morganmarkets.com

Originally published onAugust 1, 2001




ValuationValuing an asset means determining a reservation price atwhich you are prepared to buy it. The reservation price isthe highest price consistent with achieving your investment

objectives, given your views of how the asset will perform.Thus, implicit in any valuation of a financial asset are:

the prices at which you believe the asset can be sold ineach possible future scenario;

your view of the relative likelihood of each scenario; a performance target, typically relating to the assets

risk and return

We will now explain the role of each of these components in

the rock-bottom spread valuation framework.

Credit scenariosFor bonds that pay cash, the future scenarios are quite simpleto lay out, because we have an anchor at the maturity date.

For example a one-year (annual-paying) 8% bullet promises$108. Of course, the key word here is promises, becausethe bond can also default. The payout in the event of default

is uncertain, and will be the result of a complicatedliquidation or restructuring process. For concreteness, weshall assume that the bond is worth an average of $45 per$100 of principal, in line with the historical average prices of

bonds that have just defaulted2. So, at maturity, two creditscenarios are possible (see Figure 2).

Figure 2

Credit scenarios for a 1-year 8% bond

Default

$45

No default

$108

Today In 1 year

The value you place on the bond will depend on how likely

you view each scenario to be. For example, your viewcould be in line with the frequency of default that has beenobserved historically (see Table 1). We shall use these

figures to illustrate how to calculate rock-bottom spreads,but it is worth stressing that there is nothing sacred aboutthem. They simply describe past experience, and have no

automatic claim to represent your view of future creditconditions. They are just one possible set of input valuesthat really only should be used if you have no strong

feelings about credit trends.

2 Of course, this is a simplification; recovery rates are anything but certain once abond has gone into default. The full rock-bottom spread calculation prices in

uncertainty about recovery rates.

Table 1

Moody's 1-year default ratesAverages, 1983-2000

AAA 0.00%

AA 0.03%

A 0.00%

BBB 0.18%

BB 1.52%

B 7.46%

CCC 29.21%

Performance criterionThe performance criterion behind rock-bottom spreads is

based on the information ratio . In general, an assetsinformation ratio measures its return relative to abenchmark, adjusted for risk. It is just the difference

between the expected returns of the asset and benchmark,divided by the assets return volatility around thebenchmark, or tracking error. The higher the information

ratio, the better the asset is expected to perform.

Requiring your investments to attain a target level of the

information ratio is a sensible performance criterion. Itcorresponds to setting a target rate of return on capital.Taking risk around your benchmark costs capital in one

form or another, and a low information ratio implies thatyou are getting a low return on capital. Here, we set thetarget annual information ratio at 0.5, which has become

something of a standard in the investment managementindustry. In particular, we can point to investmentstrategies, such as active management of global government

bond funds, which have achieved this target in the past.Why pursue a strategy that produces a lower informationratio than the available alternatives?

From target information ratio to rock bottomHow does setting a target level for the information ratioenable you to put a value on credit exposure? Via itsdependence on returns, an assets information ratio also

depends on its current price: the higher the price, the lowerthe information ratio. So there is some price at which theinformation ratio will just equal 0.5. This price is precisely

the value you place on the asset. It is the highest you canafford to pay and still satisfy your performance criterion. Inthe context of valuing credit exposure, this defines the rock-

bottom price, from which the rock-bottom spread followsvia a conventional price-to-yield calculation.

To calculate rock-bottom spreads, we thus need to assemblethe components of the information ratio provided by creditexposure. In our case, the relevant benchmark is an

investment on which there is no chance of default, which weshall call a government bond. Our 8% bonds credit return




in a scenario (default or no default) is the excess of its return

over the government bond:

-

-

=

return

govt

pricecurrent

price

current

scenario

inprice

scenarioin

returncredit

So, the information ratio we are interested in is:

volatilityreturncredit

returncreditaverage

ratio

ormationinf=

The numerator of the information ratio averages across the

credit return scenarios, while the volatility in thedenominator is the standard deviation of credit returnsacross the scenarios.

The information ratio depends on the price you pay for thebond today, because credit returns depend on the price

today. Since we know the prices in each future scenario(see Figure 2), and the probabilities of each scenario, theonly unknown quantities in this equation are the information

ratio and the current price. Once we set the informationratio at its target level, there is only one unknown, thecurrent price. The value of the current price that satisfies theequation is the rock-bottom price: it is the price consistent

with the target information ratio, under the assumed creditconditions

As a practical matter the rock-bottom price could be solvedfrom the information ratio equation by trial and error.However, it is easier and more revealing to reexpress this

equation as a definition of the rock-bottom price.

First, we deal with the average credit return across

scenarios. To calculate this, you multiply the credit returnin each scenario by its probability, and sum acrossscenarios. We assume for the moment that the government

return does not change across scenarios. So, the price inscenario term is the only element of the credit return thatchanges from one scenario to another. The average of the

government return across scenarios is just the governmentreturn, and the same goes for the current price.Consequently, the average credit return is:

+-

=

return

govt

pricecurrent

scenariosacross

priceaverage

return

credit

average

1

A similar rule holds for the volatility of credit returns, whichis just

pricecurrent

scenariosacross

volatilityprice

volatility

return

credit

=

Why is the (1+govt return) term absent from volatility?

Since it has the same effect in each scenario, its level doesnot affect the range of variation across scenarios, whichvolatility measures. Why is the current price present in the

denominator? It would not be there if we were just lookingat the volatility of profit and loss (future price minus currentprice). But returns are scaled P&Ls: the more you pay

currently, the smaller the proportionate return (in absoluteterms) resulting from any price movement, so, the smaller istheir range of variation, and volatility needs to be scaled

accordingly.

Now we can put together these two pieces of the

information ratio, and a little bit of algebra expresses thecurrent price in terms of average future prices and theirvolatility, the information ratio, and the government return:

( )returngovt1scenariosacross

volatilityprice*

ratio

ninformatio

scenariosacross

priceaverage

price

current

+

-

=

The rock-bottom price is simply the price that delivers theinvestors target information ratio. If we now set the

information ratio at the target level of 0.5, we have a rule forthe price that will deliver that target, given expected creditreturns and their volatility, and given government returns:

( ) ( )returngovt1

scenariosacross

volatilityprice*

ratio

ninformatio

target

returngovt1

scenariosacross

priceaverage

price

Bottom

Rock

+

-

+

=

Notice that the current market price of the bond is absentfrom this definition. This is exactly as it should be if rock-

bottom prices are to offer an independent measure of valueagainst which market prices can be compared.

The final step is to translate the rock-bottom price into a

rock-bottom spread. First, we calculate the yield to maturityon the bond that is implied by its rock-bottom price andcashflows. Then we calculate the yield of the identical set

of cashflows, using the government curve. The differencebetween these two yields is the rock-bottom spread overgovernment rates.

Calculating Rock-Bottom SpreadsWe now proceed to use the rock-bottom price equation tovalue generic bullet bonds. We distinguish bonds by theircoupon, maturity, seniority, and senior credit rating of their

issuers. To keep the volume of numbers manageable, westick to the broad or 8-state rating categories listed inTable 1, instead of the more detailed 18-state

classification (BBB+, Baa1, etc) now used by the ratingagencies. Most of the calculations that follow can be




replicated on the 8-state version of our web calculator3, by

entering the appropriate input values. Each calculation is asmall variation on a basic set of inputs:

Baseline inputs for rock-bottom spread calculations

Default/Downgrade View Historical

Recovery rate average 0.45

Recovery rate volatility 0

Information ratio 0.5

Diversity score 70

Government curve Flat 6%

Coupon 8%

The terms Diversity score and Default/Downgrade View will beclarified below.

Rock bottom: a single 1-year bondTable 2 assembles the elements of the rock-bottomcalculation for the 8% one-year bond, on the assumptionthat it is rated BB. The average future price is $107.04, and

the volatility of future prices is $7.71. Assuming agovernment return or annual yield of 6%, this translates intoa rock-bottom price of $97.35, equivalent to a spread of

494bp. By historical standards, this is quite high for a BB-rated bond. It is correct for an investor whose entireportfolio is invested in a single issuer: for this type of

investor, a spread of less than 494bp will result in aninformation ratio of less than 0.5. However, investorstypically hold more diversified portfolios, the result ofwhich is to lower the volatility of the credit returns they

face. As a consequence, a lower spread will suffice for theirtarget information ratio.

Table 2

Average Price and Price Volatility for a 1-yr BB-rated

Bond

Scenario

Price in

Scenario Probability

Price

*Probability

Deviation

from

Average

Price

Squared

Deviations

*Probability

No Default 108 98.48% 106.36 0.96 0.90

Default 45 1.52% 0.68 -62.04 58.51

Average 107.04Volatility 7.71

35970601

7175004107.

.

.*..

price

BottomRock

=

+

-

=

To produce these figures with the 8-state rock-bottom spread calculator,use the Baseline Inputs, but set the diversity score equal to 1.

Incorporating diversificationPortfolio diversification results from (the lack of)correlation of the underlying asset values of the bond

3 The calculator is accessible on the Credit Page of MorganMarkets.com, and is

described in reference [1]

issuers. As a practical matter, it is easiest to calculate the

impact of portfolio diversity when issuers fortunes areindependent of each other (and horrendously difficult if theyare correlated). Consequently, we use a variant of Moodys

diversity score measure to translate a portfolio ofcorrelated issuers paper into a (smaller) number ofindependent issuers that would provide the same degree of

diversification.[2,3] The price volatility of a diversifiedportfolio is simply the price volatility of a single bond,divided by the square root of the diversity score. As a

result, the rock-bottom price for a portfolio is

( )returngovt1

scorediversity

scenariosacross

volatilityprice

*

ratio

ninformatio

Target

scenariosacross

priceaverage

price

Bottom

Rock

+

-

=

Figure 3 traces the effect of diversification on the rock-bottom spread of a BB-rated portfolio. As diversificationincreases, rock-bottom spreads initially drop precipitously,

but at a diversity score of 20 or so, the curve has all butflattened out. This is fortunate, since calculating diversityscores is far from a precise science. The Figure shows that

it does not matter materially whether the diversity score is50 or 100: the resulting difference in BB rock-bottomspreads is 17bps.

Figure 3

Rock Bottom Spreads for BB-rated bonds held in a

diversified portfolio

100

150

200

250

300

350

400

450

500

0 10 20 30 40 50 60 70 80 90 100

Diversity score

The entire US High Yield corporate sector offers a diversityscore of about 70. This means that, although there are

approximately 1000 rated speculative-grade issuers theyonly provide the same diversity as would 70 issuers withindependent asset values. 4 A fully diversified investor

would thus face a rock-bottom spread of 141bps for a BBbond.5 Less-diversified investors would require greaterrock-bottom spreads for one-year BB bonds.

4 The Appendix to [3] contains a fuller discussion of diversity scores5 The rock-bottom price in Table 2 becomes (107.04-0.5*7.71* 70)/1.06 =100.55




Interpreting rock-bottom spreadsThe rock-bottom price has two components. The first is thebreakeven price:

( )returngovt1scenariosacross

priceaverage

price

even

Break

+

=

so called because if this is what you pay for the bond, thenyou will earn the same return on average as you would byinvesting in government bonds. Consequently, your

average credit return will be zero.

Only investors who are indifferent to risk would settle for

breaking even. If you are risk-averse, you will refuse to payas much as the breakeven price, because of the uncertaintycredit exposure presents. Via its second component, the

rock-bottom price requires a discount from the breakevenprice for this risk:

-

=

Discount

Risk

price

even

Break

price

Bottom

Rock

In its current form, the risk discount is driven by pricevolatility associated with the uncertainty of the issuers

rating one year from now, and diversification. Later, weshall also include the effects of uncertain recovery rates,without changing the basic form of the rock-bottom price.

While we have thus incorporated risk aversion in the rock-bottom price, we have not done so by stating outright how

risk-averse investors are. We have simply reasoned thatthey should demand from credit a risk discount that bringsits performance in line with what they apparently demand

from other investment strategies. This led us to a targetinformation ratio of 0.5.

Table 3

Valuing 1-yr 8% Bonds

Rock Rock

Breakeven Risk Bottom Bottom

Spread Premium Spread Price

AAA 0 0 0 101.89

AA 2 7 9 101.80

A 0 0 0 101.89

BBB 11 16 27 101.63

BB 95 46 141 100.55

B 483 107 590 96.52

CCC 2177 249 2426 82.91

To produce the rock-bottom spreads with the 8-state rock-bottom spreadcalculator, use the Baseline Inputs. Breakeven spreads result by setting the

information ratio equal to zero.

AA spreads are higher than A spreads because the historical AA-rated one-year default rate is higher (see Table 1). This derives from the fact thatone issuer rated A3 at the start of a calendar year defaulted within that year

(DFC, in 1989). It does not mean that Aas are more risky than As, asdefault frequencies over longer horizons show [4]. It is a statistical

anomaly, which we could have removed by smoothing out the defaultprobability estimates, rather than using the raw historical numbers, as we

have done for simplicity.

Table 3 shows how one-year rock-bottom spreads

decompose into a breakeven spread (corresponding to thebreakeven price) and a risk premium (corresponding to therisk discount component of the rock-bottom price). Each

rating category entails different default probabilities, andtherefore different average future prices and breakevenspreads. The risk premia rise as the probability of a default

rises, because this causes price volatility to rise.

Longer-maturity bondsTo this point, we have applied the principle that a bondsvalue today is driven by its value in the future to derive

rock-bottom prices and spreads for one-year bonds. We cannow use these one-year bond values to value two-yearbonds. One year from now, a two-year 8% BB bond can

finish up in default, as before. Alternatively, it can finishthe year as a one-year 8% bond rated AAA, AA, A, BBB,BB, B, CCC. Its value with one year to go will be different

according to its rating, as we have calculated in Table 3,because its chance of going into default in its last year willdiffer in each case. So, we need to expand the no-default

category to these possibilities, as Figure 4 shows.

Figure 4

Price scenarios for a two-year bond

1 yr to go

AAA

AA

A

BBB

BB

B

CCC

D

BB

Maturity

AAA

AA

A

BBB

BB

B

CCC

D

2 yrs to go

109.89

109.80

109.89

109.63

108.55

104.52

90.91

45.00

108

108

108

108

108

108

108

45

It remains to attach probabilities to these events , namely thatone-year from now, our two-year BB bond will be ratedAAA, or A, etc. Again, we use historical data for

illustration. Table 4 shows the frequency of changes inratings by Moody over the last two decades. If we treatthese as the probabilities of future changes in credit quality,

then we have all the ingredients to calculate rock-bottomprices and spreads for two-year bonds. The relevantprobabilities for BB bonds are in the fifth row. Table 5

details the calculation of the rock-bottom price of 100.67,which translates into a rock-bottom spread of 162bps.

As noted above, this calculation penalises bonds for theirvolatility. However, it is only credit volatility that isconsidered, by which we mean the variation in the future

value of the bond as its future credit quality varies (seeFigure 4). Market price volatility does not enter into the




picture, which is in keeping with our aim of pricing the

credit component of the bond.

Table 4

Moody's 1-yr credit migration ratesAAA AA A BBB BB B CCC D

AAA 89.20% 9.69% 1.08% 0.00% 0.03% 0.00% 0.00% 0.00%

AA 1.03% 89.31% 9.14% 0.37% 0.09% 0.02% 0.00% 0.03%

A 0.04% 2.48% 90.97% 5.57% 0.72% 0.21% 0.01% 0.00%

BBB 0.04% 0.29% 6.24% 86.96% 5.15% 1.09% 0.05% 0.18%

BB 0.03% 0.03% 0.60% 5.59% 82.94% 8.67% 0.62% 1.52%

B 0.01% 0.06% 0.25% 0.58% 6.43% 82.06% 3.14% 7.46%

CCC 0.00% 0.00% 0.00% 1.12% 2.87% 6.77% 60.03% 29.21%

Table 5

Average Price and Price Volatility for a 2-yr BB-rated

Bond

Scenario

Price in

Scenario Probability

Price

*Probability

Deviation

from

Average

Price

Squared

Deviations

*

Probability

AAA 109.89 0.03% 0.04 2.69 0.00

AA 109.80 0.03% 0.03 2.61 0.00

A 109.89 0.60% 0.65 2.69 0.04

BBB 109.63 5.59% 6.13 2.43 0.33

BB 108.55 82.94% 90.03 1.36 1.52

B 104.52 8.67% 9.06 -2.68 0.62

CCC 90.91 0.62% 0.57 -16.28 1.65

D 45.00 1.52% 0.68 -62.19 58.76

Average 107.19

Volatility 7.93

Diversified 0.95

68.10006.01

70

93.7*5.019.107

price

Bottom

Rock

=+

-

=

To produce these figures with the 8-state rock-bottom spread calculator,use the Baseline Inputs

The recipe for 3-year bonds uses the prices calculated for 2-

year bonds as input, and so on. In this way, we can trace outan entire credit- and term-structure of rock-bottom spreads,as shown in Table 6.

Table 6

Rock-bottom spreads by rating and maturityBased on 8% annual coupon bond

Maturity 1 2 3 5 7 10

AAA 0 1 1 2 3 5

AA 9 9 9 9 10 13

A 0 3 6 11 17 24

BBB 27 33 39 50 60 72

BB 141 162 179 204 219 230

B 590 590 584 563 539 506

CCC 2426 2088 1820 1452 1228 1037

To produce these figures with the 8-state rock-bottom spread calculator,use the Baseline Inputs

Spread term structuresIt may seem counterintuitive that B- and CCC-rated rock-bottom spreads fall with maturity, since a longer maturitymeans a greater chance of losing the principal. Actually, the

falling low-grade credit curve is no more surprising than therising high-grade credit curve, and both emanate from thesame source.

Figure 5

Cumulative Default Probabilities

0%

1%

2%

3%

4%

5%

6%

7%

8%

0 1 2 3 4 5 6 7 8 9 10

BBB

A

AA

AAA

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

0 1 2 3 4 5 6 7 8 9 10

CCC

B

BB

Time horizon (years)

Figure 5 shows the cumulative default probabilities,

derived from the figures in Table 4.which indicate thechance that a bond will have defaulted by a given number ofyear

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