# Presentation: 174879

## Visible and Hidden Risk Factors for Banks

**Til Schuermann, Kevin J. Stiroh***
**Research, Federal Reserve Bank of New York**
- FDIC-JFSR Bank Research Conference
- Arlington, 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.

## 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

## 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

## Market Models

## 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

## Comparing Market Models

- Need a way to compactly analyze  16,340 regressions (about 45494 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*

## 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

## Comparing Market Models: Results

## Adjusted R2: large banks

## Adjusted R2: other banks

## 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

## Average correlation of returns/residuals

_**Large Banks**_

_**Small Banks**_

## 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)

## 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%

## Average Adj. R2 across Sectors, 1997-2005 

## 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?

## Thank You!

**http://nyfedeconomists.org/schuermann/ **