The credit spread puzzle

1
The credit spread puzzle

• Eli M Remolona
• Seminar presentation
• Singapore Management University10 October 2003

2
The issue at stake Why are credit spreads much
wider than expected losses?
3
The corporate spread puzzle

• In general, corporate spreads are many times
  wider than what expected default losses would
  imply.
• In 1998-2002, the average default probability on
  BBB corporates was 0.5 with a 50 recovery rate.
• The average spread was about 200 basis points,
  eight times the expected loss from default.
• Why are risk-neutral probabilities of default so
  much higher than physical probabilities?
• If one could fully diversify a portfolio of
  corporate bonds, there should be no difference
  between the risk-neutral and physical
  probabilities.

4
The puzzle for different ratings(1998-2002, in
basis points)
5
Structure of discussion

• A quick tour of the literature with just three
  papers
• Liquidity the preferred explanation but it
  cannot be the whole story
• An arbitrage strategy that works (hence the gap
  is real and it is not all liquidity)
• Explaining the strategy in terms of CDOs
• Limits of the strategy diversification in the
  face of a skewed distribution
• The role of default correlations and diversity
  scores
• Conclusion the puzzle is explained by the
  difficulty of diversifying credit risk

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A tour of the literature with three papers

• Elton, Gruber, Agrawal and Mann (2001) look at
  the level of the spread
• Taxes explain about 28 to 73 depending on the
  maturity and credit rating.
• Systematic risk and other explain 24 to 50.
• Collin-Dufresne, Goldstein and Martin (2001) look
  at changes in the spread but are unable to find
  any macroeconomic or financial variables to
  explain these changes.
• Huang and Huang (2002) look at the five most
  popular structural models of credit risk. None
  of them can explain the spread.
• All the above assume complete diversification of
  credit risk.

7
How EGAM decompose the spread(as a percentage of
the spread)
8
How about liquidity?

• Proxies for liquidity are among the factors
  Collin-Dufresne, Goldstein and Martin (2001) look
  at. These variables fail to explain changes in
  the spread.
• Perraudin and Taylor (2003) look at Eurobonds
  rated AAA to A,sorting prices on liquidity
  proxies -- quote frequency, age and issue size.
• They find that liquidity accounts for 10 to 28
  basis points.
• Liquidity premia exceed expected losses from
  default.
• But they also assume complete diversification of
  credit risk.
• Among benchmark bonds the most liquid
  corporates -- the wide spreads remain.

9
Benchmark bondsFinance company spreads on August
6, 2003as quoted by Deutsche Bank
10
The puzzle for different ratings(1998-2002, in
basis points)
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An arbitrage strategy

• To arbitrage the gap between credit spreads and
  expected default losses, do the following
• Create a diversified portfolio of BBB corporates
  to earn a spread of 203 basis points over
  Treasuries.
• Against every 100.25 of the portfolio as
  collateral, borrow 100. Since the expected loss
  on the portfolio is 25 basis points, you should
  be able to borrow at the AAA rate at a spread of
  78 basis points.
• This would leave 100 basis points on the table!
• This arbitrage strategy actually works, although
  not completely. And it works by turning
  relatively liquid assets into less liquid ones!
• The strategy is called a CDO.

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CDOs a brief introduction

• A collateralised debt obligation (CDO) is a
  securitisation with the following structure
• The collateral (ie, assets) tends to be risky
  debt
• Liabilities are largely highly rated securities.
• There are two basic types
• Balance sheet CDOs
• Driven by regulatory arbitrage
• Collateral tends to be loans on a banks books
• Often very large, eg, 10 billion
• Arbitrage CDOs
• Driven by market arbitrage
• Triple-B securities are the most common
  collateral
• Liabilities are often less liquid than the
  collateral

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Porter Square CDO I, Ltd 396 million
14
A typical CDO structure
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Why arbitrage CDOs do not eliminate wide credit
spreads

• If arbitrage CDOs worked completely, there would
  be no spread puzzle.
• Assume a portfolio of bonds, with say 100
  different issuer names. Assume also independent
  default times.

• For this analysis, the binomial distribution is
  very useful

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Small probabilities of heavy lossescreate
negative skewness
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Bigger portfolios do not easily makeunexpected
losses go away
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The economics of arbitrage CDOs

• The size of over-collateralisation is

• The margin
• but the zeroes become more common as n gets
  larger
• and

• Let
• Then the arbitrage gain is
• which grows with n. But in practice, n is
  less than 200.

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The limits of arbitrage CDOs

• The bigger the collateral pool ie, the greater
  the number of names the smaller the proportion
  of over-collateralisation.
• The arbitrage gain is a non-decreasing function
  of the number of names.
• Yet few CDOs typically have more than 200 names.
• In practice, it can take a manager many months to
  assemble the collateral pool.
• Beyond the benchmark bonds, the search cost for
  additional names must rise sharply. Is this a
  form of illiquidity?
• The arbitrage opportunity is greater for double-B
  collateral than for triple-Bs, but the latter are
  more commonly used in CDOs because they are
  easier to find.
• Hence, full diversification is never achieved,
  and the spread puzzle is not eliminated.

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What about default correlations?

• Correlations in default times add to the risk of
  unexpected losses. For example, a default
  probability of 0.5 on a portfolio of 1000 bonds
  could mean
• Five defaults every year with independence or
• Ten defaults every other year with correlation.
• Copula-based estimates of default correlations
  focus on lower tail dependence in asset
  returns.
• Estimates based on actual defaults are quite low
• Moodys intra-industry estimates for junk bonds
  range from 6 for banking to 1 for technology
• The highest such estimate by Das, Fong and Geng
  (2001) is 25.

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The rule of thumb for default correlations
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Correlations and diversity scores

• To rate CDOs, Moodys has developed the concept
  of a diversity score, an inverse measure of the
  correlations of a collateral pool.
• The diversity score is an idealised comparison
  portfolio
• The total face value is the same as that of the
  collateral pool.
• The bonds have equal face values and are equally
  likely to default.
• Defaults are independent.
• The score is the number of bonds such that the
  portfolio has the same risk distribution as the
  collateral pool.
• Diversity scores allow us to continue using the
  binomial formula.

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Illustrative diversity scores for names in the
same industrySource Duffie, April 2003
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Correlations in a portfolio would
typicallyreduce 1000 names to 750
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Diversity scores have a modest effect on risk
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Conclusions on the credit spread puzzle

• Skewness in the distribution of returns means a
  truly diversified credit portfolio would have to
  be very large.
• Evidence from the CDO market suggests that such
  large portfolios are not achieved in practice.
• Default correlations do not seem to be a big
  deal.
• Search costs in the market for collateral may be
  the critical limiting factor in diversification.
• Unavailability of collateral may be a form of
  illiquidity.
• Limits to the size of CDOs mean there remains a
  high degree of undiversified credit risk.
• Wide credit spreads are a compensation for such
  risk.