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The Empirical Relationship Between Average
Asset Correlation, Firm Probability of Default,
and Asset Size by Jose A. Lopez
Discussion by George Pennacchi Department of
Finance University of Illinois
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I. Contribution of the Paper

• The BCBSs Foundation approach to Internal
  Ratings Based capital
• requirements assumes that portfolio credits of
  a particular type have
• identical correlations with a single, common
  risk factor.
• The papers procedure for estimating a credits
  factor correlation is
• 1) Compute an appropriate capital charge for a
  portfolio based on
• each credits correlation derived from
  KMVs multi-factor model.
• 2) For the same portfolio, constrain the KMV
  model to a single
• factor and find the common correlation for
  all credits that gives
• the same capital charge as in 1).
• This procedure is repeated for portfolios of
  World, U.S., Japanese,
• and European credits, with the credits varying
  by firm size and EDF.

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• II. Discussion of Main Results
• Cross-country differences in average firm
  factor correlations
• Country Portfolio Average
  Correlation
• U.S. 0.16
• Europe 0.13
• Japan 0.26

• Morck, Yeung, and Yu (2000) JFE confirm these
  results computing
• average stock correlations using domestic and
  U.S. market indices.
• Country Portfolio Average Correlation
• U.S.
  0.14
• U.K. 0.25
• France 0.27
• Europe Netherlands 0.32
• Germany 0.34
• Italy 0.43
• Japan 0.48

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• Firm asset size differences in average firm
  factor correlations
• Firm Asset Size World Portfolio
  Correlation
• (0, 100m 0.1000
• 100m, 300m 0.1125
• 300m, 1,000m 0.1375
• ? 1,000m 0.2000

• Paper explains Larger firms can generally be
  viewed as a portfolio
• of smaller firms.
• But Roll (1988) JF finds that large firms are
  not just portfolios of
• randomly selected smaller firms. Large firms
  tend to specialize in
• an industry, reducing the potential for
  cross-industry diversification.
• Moreover, Roll (1992) JF finds that some
  countries specialize in
• particular industries, partially explaining
  cross-country differences.

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• Average firm correlations increase with credit
  quality (lower EDF)
• though the effect holds primarily for larger
  firms.
• (A) A time series interpretation When a given
  firm gets riskier, say
• during an industry downturn, its assets
  correlation with the common
• factor declines.
• Why should this be so? Do distressed firms
  switch to activities
• (assets) having less correlation with the
  common factor?
• (B) A cross section interpretation Firms whose
  assets have greater
• factor correlation tend to choose safer
  capital structures (lower EDFs).
• Whether (A) or (B) is true has implications for
  implementing capital
• standards. If (B), but not (A), is correct,
  then a credits correlation
• should depend on its EDF at the time the
  credit is issued, not its
• current EDF.

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• These interpretations are subject to empirical
  tests.
• (A) As a given credits EDF increases
  (decreases) over time, does
• the firm assets estimated factor
  correlation tend to fall (rise)?
• (B) When credits are originated, do borrowers
  with high (low) EDFs
• tend to have assets with low (high)
  estimated factor correlations?

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III. Other Issues

• Property rights as an explanation for assets
  factor correlations
• Morck, Yeung, and Yu (2000) JFE find stocks
  have higher factor
• correlations in developing economies with poor
  private property rights.
• Factor correlations are also greater in
  developed economies lacking
• corporate governance that protects public
  investors. Poor property
• rights leads to inter-corporate income shifting
  and inhibits risk-
• arbitrage firm values are less affected by
  firm-specific news.
• Time series variation in assets correlations
• Campbell, Lettau, Malkiel, and Xu (2001) JF
  document that average
• U.S. stock correlations have decline
  dramatically, from 0.28 in 1962
• to 0.08 in 1997. Possible reasons younger,
  smaller firms are now able
• to issue publicly-traded securities trend
  toward breaking up
• conglomerates.

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• Empirical specifications
• 1) What is the correct underlying sample of
  credits?
• The papers equally weighted sample of
  publicly-traded firms
• or a value weighted sample of rated
  credits typically held by
• banks?
• 2) What is the correct composition of the
  common factor?
• The papers U.S. and unassigned industry
  factors or a global
• value weighted average of all country and
  industry factors?
• If choice does not matter, this may
  indicate the poor fit
• of any single factor.

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EndNote Morck, Yeung, and Yu (2000) JFE and
Campbell, Lettau, Malkiel, and Xu (2001) JF
report R2s. I have converted them to
correlations by taking the square root. These
papers correlation estimates may not be
directly comparable to those of the current
paper because correlation calculations are done
using returns over different holding periods.
However, the relative differences across
countries and time are noteworthy. Though these
papers report firms equity (stock)
correlations, if firms liabilities grow
deterministically (as is assumed by the KMV
model), they also equal the firms asset
correlations.