“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
I. Contribution of the Paper
• The BCBS’s 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 paper’s procedure for estimating a credit’s factor correlation is
1) Compute an appropriate capital charge for a portfolio based on
each credit’s correlation derived from KMV’s 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.
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
• 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.
• 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 credit’s correlation
should depend on its EDF at the time the credit is issued, not its
current EDF.
• These interpretations are subject to empirical tests.
(A) As a given credit’s 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?
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 riskarbitrage: 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.
• Empirical specifications
1) What is the correct underlying sample of credits?
The paper’s 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 paper’s 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.
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.