Stocks that are highly correlated with the market when the market declines have higher expected returns than stocks that are not highly correlated with the market during its downturns. The difference between portfolios with the most downside risk and the least downside risk is very large, more than 6.5 percent per year.
In Downside Risk and the Momentum Effect (NBER Working Paper No. 8643), authors Andrew Ang, Joseph Chen, and Yuhang Xing show that there is a premium for holding stocks with a higher downside risk. They find that stocks that are highly correlated with the market when the market declines have higher expected returns than stocks that are not highly correlated with the market during its downturns. The difference between portfolios with the most downside risk and the least downside risk is very large, more than 6.5 percent per year. The researchers find that some of the profitability of the recently observed momentum effect (that stocks with high past returns continue to have high future expected returns) can be explained as compensation for bearing exposure to downside risk.
The concept of downside risk, according to Ang, Chen, and Xing, is highly intuitive. Stocks that are more likely to decline when the market return is below its mean are less attractive. In order for investors to hold these assets, the average return on these stocks must be higher (to compensate for their increased downside risk). The premium compensates investors for extreme periods when the market crashes, times when these high-downside-risk stocks crash along with the market. By meticulously analyzing portfolios, the authors show that the high expected returns commanded by stocks with high downside risk cannot be explained by market risk, the size effect, or the book-to-market effect, and cannot be attributed to liquidity.
Since the traditional risk factors cannot price the high returns on high-downside-correlation stocks, the authors construct a "mimicking factor" that captures the high downside risk premium. This downside risk factor shorts stocks with low downside risk (these stocks have low expected returns) and goes long on stocks with high downside risk (these stocks have high expected returns). The authors find that their downside risk factor forecasts future macroeconomic conditions and prices (by construction) the downside correlation effect.
Conventional explanations of the momentum effect use behavioral models with imperfect information and investor behavior and rely on the fact that arbitrage is limited, so that arbitrageurs cannot eliminate the apparent profitability of momentum strategies. In this paper, the authors show that momentum strategies have high exposures to the systematic downside risk factor, and this exposure to downside risk cannot be arbitraged away. In particular, stocks with high past returns have greater exposure to the downside risk factor than stocks with low past returns. That is, past "winner stocks" do well because, during periods of extreme market distress, these stocks are much more likely to crash with the market than stocks that are past losers. Therefore, some portion of the profitability of momentum strategies can be explained as compensation for bearing downside risk.
The researchers note that because downside risk is priced and stocks' sensitivities to downside risk play a role in asset pricing, theoretical models are needed to explain the underlying economic mechanisms that bring about the downside correlation effect. It remains to be determined, the authors conclude, whether risk aversion, loss aversion, or other factors best explain the mechanism driving cross-sectional variations in downside risk.