Downside Risk

1
Downside Risk

• Andrew Ang
• Columbia University and NBER
• (http//www.columbia.edu/aa610)
• Joseph Chen
• University of Southern California
• Yuhang Xing
• Rice University

2
Motivation

• A fundamental tenet of Finance
• There is a trade-off between reward and risk
• But, how does one measure risk?
• According to the CAPM, risk is measured by beta,
  or covariance with the market
• But, the CAPM assumes an equal treatment of risk
  across down markets and up markets

3
Downside vs Upside Risk

• Investors care differently about downside versus
  upside risk
• Markowitz (1959) advocates the use of
  semi-variance as a risk measure
• In loss aversion utility, investors place greater
  weight on losses relative to gains
• Investors more sensitive to downside risk require
  a premium for holding assets with large exposure
  to downside risk
• Is there a downside risk premium in the cross-
• section of stock returns?

4
Aims and Goals

• Downside risk (downside beta)
• Covariation with the market conditional on
  downside movements of the market
• Distinguish downside risk from other
  cross-sectional effects beta, size,
  book-to-market, momentum, volatility, coskewness,
  cokurtosis, liquidity
• Downside premium of 6 per annum.
• Investigate if past downside beta predicts future
  returns

5
Downside Beta

• CAPM Measure of Risk
• Beta, , is not a sufficient
  statistic
• Downside Beta
• Relative Downside Beta

6
A Risk Story

• Requirements for a risk story
• Need to observe patterns between average returns
  and betas over the SAME PERIOD
• Sort stocks on realized and investigate
  relation to realized returns over the same
  12-month period
• Focus on equal-weighted portfolios of NYSE stocks

7
Sorts by b-
b-
8
Sorts by b-
Beta
9
Sorts by (b- - b)
b-
10
Sorts by (b- - b)
Beta
11
Fama-MacBeth Regressions

• Control for other known cross-sectional effects
• Size, Book-to-Market, and Momentum
• Volatility (Ang, Hodrick, Xing, Zhang, 2004)
• Coskewness (Harvey and Siddique, 2000)
• Cokurtosis (Dittmar, 2002)
• Liquidity risk (Pástor and Stambaugh, 2003).

12
Fama-MacBeth Regressions

• b 0.18
• b- 0.05 0.06
• b -0.03 0.02
• Log-Size -0.04 -0.03
• Book-to-Mkt 0.02 0.02
• Past Return 0.02 0.01
• Std Deviation -8.43 -6.46
• Coskewness -0.24 -0.19
• Cokurtosis 0.03 0.05
• Liquidity -0.01

13
Potential Bias?

• Is there a bias induced by computing b- and
  average returns over the same period?
• Measurement Error?
• Higher SE(b-) gt Attenuation to zero
• High betas are related to high average returns
  by construction"
• By conditioning on down moves of the market, we
  pick up periods of low returns gt A priori expect
  high b- to be associated with lower, not higher,
  returns
• b- is computed using demeaned market
• returns, which takes out any potential bias.

14
Robustness Checks

• Value-weighted portfolios and value-weighted
  Fama-MacBeth regressions
• Include all stocks (add AMEX/NASDAQ)
• Exclude small stocks
• Alternative cut-off points
• Relative to the risk-free rate
• Relative to a zero rate of return
• Use non-overlapping windows
• Use weekly 24-month returns to compute
• Control for coskewness

15
Forecasting Downside Risk

• Predicting Future Downside Risk and Future
  Returns
• There exists a strong contemporaneous relation
  between downside risk and returns.
• If we can predict future downside risk exposure,
  we could form trading strategies to predict
  future expected returns.
• Which stocks have high downside risk?
• Is past downside beta persistent?

16
Determinants of Downside Risk

• Industry effects
• Utilities have lower b- loadings than other
  industries
• Stock characteristics
• Small and value stocks exhibit greater downside
  risk
• Past winner stocks have high downside risk
• Accounting measures of performance
• Stocks with high past ROE exhibit high downside
  exposure
• No leverage effect and little evidence that firms
  paying dividends have less downside risk than
  non-dividend payers
• Contemporaneous risk measures
• High volatility, negative coskewness, and high
  cokurtosis are related to high future downside
  risk

17
Predicting Returns

• Future Returns with Past Downside Risk
• Removing Very High Volatility Stocks (Using 96
  of All Stocks)

Average Excess Returns Per Month 1
Low 0.58 2 0.69 3 0.82 4 0.82 5
High 0.92 High-Low 0.34 T-stat 2.31
18
Predicting Returns
Characteristic-Adjusted Returns (per
month) Size/Bk-Mkt Include
Additional Controls for Adjusted Momentum Coske
wness Liquidity 1 Low b- -0.25 -0.21 -0.21
-0.17 2 -0.09 -0.07 -0.07 -0.02 3
0.05 0.04 0.07 0.05 4 0.07
0.10 0.04 0.10 5 High b- 0.20 0.12
0.15 0.13 High-Low 0.44 0.32 0.36
0.30 T-stat 3.36 2.71 2.69 2.15
19
Conclusion

• If investors are more risk averse to down
  markets, then assets that have high exposure to
  downside risk are unattractive and must command a
  risk premium
• The cross-section of stock returns reflects a
  premium for downside beta risk
• The downside premium is different from standard
  beta and other known cross-sectional effects
• Past downside beta can be used to forecast future
  downside exposure, and hence future returns