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Visible and Hidden Risk Factors for Banks

Til Schuermann, Kevin J. Stiroh*Research, Federal Reserve Bank of New York

FDIC-JFSR Bank Research ConferenceArlington, VA 13-15 September, 2006

* Any views expressed represent those of the authors only and not necessarily those of the Federal Reserve Bank of New York or the Federal Reserve System.

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Banks and Systemic Risk

Are banks closely tied to the “observable risk factors”?

Are those residuals highly correlated?

Are banks more similar to each other than other sectors?

If “yes,” banks susceptible to systemic risk– DeBandt and Hartmann (2002): 2 channels

• Narrow contagion• Broad simultaneous shock

– Rajan (2005): compensation-induced herding

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Overview

Estimate a range of standard market models and compare

– Explanatory power– Residual correlations– Factor loadings

Principal component analysis (PCA) of residuals– Explanatory power of 1st PC – Diffusion of hidden factors– Homogeneity of PC loadings

To provide context– Large vs. small banks– Large banks vs. large firms in other sectors

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Market Models

, , , ,i t i m i m t i tr r

CAPM

, , , , , ,i t i m i m t HML i t SMB i t i tr r HML SMB Fama-French

, , , , , , ,

, , , , , ,

i t i m i m t HML i t SMB i t VOL i t Y i t

TM i t Aa i t Baa i t Y i CP i t i t

r r HML SMB VOL YIELD

TERM Aa Baa CP

Nine-Factor

, , , , , , ,i t i m i m t Y i t TM i t Baa i t i tr r YIELD TERM Baa Bank-Factor

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Data

Weekly bank equity returns, 1997 – 2005, year-by-year– On avg. 488 banks/year– CRSP– Conditioning variables from various data sources

Define “large” as inclusion in S&P 500– About 34 large banks per year– About 454 small banks per year

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Comparing Market Models

Need a way to compactly analyze 16,340 regressions (about 45494 bank/year/model estimates)

Data is a panel, so one may think of each year as a random coefficient model (Swamy 1970)

– Use mean group estimator (MGE) interpretation due to Pesaran and Smith (1995)

– Firms may on average have = 1, but with variation around that mean ()

Use cross-sectional distribution of estimated parameters to make inference on “betas” in a given year t

, , ,ˆ ˆ ˆ, ,m t m t m tSE t

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Comparing Market Models: Results

Market factor dominates, followed by Fama-French factors

– Rise in explanatory power from 1999-2002, but no obvious trend

Bank factors have relatively little impact– Change from empirical literature in the 1980’s

(Flannery & James 1984)– Risk management / hedging

Other factors show considerable heterogeneity– Reflects differences in banks’ strategies and

exposures

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Comparing Market Models: Results

CAPM Bank-Factor Fama-French Nine-Factor

Panel A: Large Banks Market 1.0546 (9/9; 0%) 1.0804 (9/9; 0%) 1.2206 (9/9; 0%) 1.2520 (9/9; 0%) Yield -0.0222 (5/9; 60%) -0.0242 (2/9; 59%) Term -0.0721 (5/9; 65%) -0.0120 (3/9; 60%) Baa spread 0.0238 (5/9; 39%) -0.0024 (4/9; 54%) Aa spread 0.0104 (5/9; 47%) CP spread -0.0077 (3/9; 49%) HML 0.2742 (6/9; 30%) 0.2989 (7/9; 30%) SMB -0.3308 (7/9; 78%) -0.2534 (4/9; 69%) Mkt. volatility 0.4351 (3/9; 37%)

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Adjusted R2: large banksLarge Banks

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1997 1998 1999 2000 2001 2002 2003 2004 2005

CAPM

Bank-Factor

Fama-French

Nine-Factor

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Adjusted R2: other banksOther Banks

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1997 1998 1999 2000 2001 2002 2003 2004 2005

CAPM

Bank-Factor

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Nine-Factor

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Relative to Large Banks, Small Banks Show…

Lower correlated returns– Mean pair-wise correlation of 11% vs. 57% (large)

Smaller link to systematic risk factors– Lower adj. R2 of 13% vs. 46%

Stronger evidence of conditional independence– Mean pair-wise correlation of residuals of 3% vs. 25%

Less systematic market risk m of 0.5 vs. 1.2

Tighter link to interest rate and credit spread factors– Less intensive users of interest rate/credit derivatives

Stronger loadings on Fama-French factors

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Average correlation of returns/residuals

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1997 1998 1999 2000 2001 2002 2003 2004 2005

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1997 1998 1999 2000 2001 2002 2003 2004 2005

Returns CAPM residsBank Factor resids Nine-Factors residsFama-French resids

Large Banks

Small Banks

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Finding those Hidden Factors

Considerable residual variation remains for large banks– Mean pair-wise correlation of residuals 25%

Are hidden factors important?– Remaining variation is diffuse with 1st PC accounting

for only 27% of residual variance– But, 93% of loadings on 1st PC have the same sign

Systemic implication– Given a shock to hidden factor, virtually all (big)

banks will move the same way

Recent interest in credit risk– Frailty models of Das, Duffie, Kapadia & Saita (2006)

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Are Banks Different?

Compare large banks to other large firms– 10 other sectors comprised of S&P 500 firms

Return correlation is highest– 57% vs. 36% (sector median)

Returns are relatively easy to explain– adj. R2, Nine-Factor model: 46% vs. 28%

Residuals are typically diffuse– 1st PC: 27% vs. 21%

Residuals are relatively homogeneous and correlated– Factor loading on 1st PC: 93% vs. 84%– Mean pair-wise correlation of resids: 24% vs. 12%

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Average Adj. R2 across Sectors, 1997-2005

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Conclusions

Positive: no “special” risk factor for banks– Returns can be modeled conventionally– Residuals typically diffuse

Negative: residuals are relatively correlated and homogeneous

– “Broad” systemic concern?

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Thank You!http://nyfedeconomists.org/schuermann/