“The Empirical Relationship Between Average Asset Correlation, Firm Probability of Default, and Asset Size” by Jose A. L

1. “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

2. 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.

3. II. Discussion of Main Results • Cross-countrydifferences in average firm factor correlations • Country PortfolioAverage 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 PortfolioAverage 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

4. Firm asset sizedifferences in average firm factor correlations • Firm Asset SizeWorld 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.

5. 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.

6. 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?

7. 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.

8. 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.

9. 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.