Loss aversion and expected returns

Posted by TEBI on June 19, 2020

Loss aversion and expected returns




It has been well documented that, due to behavioral biases, investors/markets make persistent mistakes in pricing securities. As a result, there are many anomalies in the literature. An example of a persistent mistake is that investors under-react to news — both good and bad news are only slowly incorporated into prices, resulting in the momentum anomaly. My book Investment Mistakes Even Smart Investors Make and How to Avoid Them covers 77 mistakes, most of which are related to behavioural errors (others are simply due to lack of knowledge). 

Ji Cao, Marc Oliver Rieger and Lei Zhao contribute to the literature on how investor biases impact prices with their May 2019 study Safety First, Loss Probability, and the Cross Section of Expected Stock Returns They began by noting that investors are loss averse, seeking to minimise the risk of bad outcomes. In general, they take a “safety first” approach to buying stocks and constructing portfolios.

With those concepts in mind, they hypothesised that investors would view loss probability (LP) as an important determinant of risk — when buying stocks, investors care about more than just volatility. Thus, LP should impact prices. Their measure of a stock’s LP in a given month is the fraction of the total trading days in the month with a return below the risk-free rate.

To test their theory, they sorted stocks by their LP during the previous month and investigated the monthly returns of the resulting portfolios over the period July 1963 through December 2016. Following is a summary of their findings:


– Stocks with a high (low) LP have high (low) subsequent returns because of investors’ desire to avoid high LP stocks.

– The difference between monthly returns on the equal-weighted (value-weighted) decile portfolios with the highest and lowest LPs is 0.88 percent (0.66 percent). The t-values are highly significant (t = 6.27 for the equal-weighted portfolio, and t = 4.88 for the value-weighted portfolio). On an equal-weighted basis, excess returns increase monotonically. On a value-weighted basis, the increase is nearly monotonic.

– Carhart’s four-factor (beta, size, value and momentum) monthly alpha of a zero-cost portfolio that is long high-LP stocks and short low-LP stocks (high-low LP portfolio) is 0.91 percent (t = 7.43) if equal-weighted and 0.75 percent (t = 5.48) if value-weighted.

– Though the alphas of a low LP portfolio are negative, the LP effect is greater among high LP stocks.

– The positive return and alpha differences remain highly significant after controlling for size, illiquidity, momentum and short-term reversal.

– While high-LP stocks tend to be small, illiquid securities with low returns over the prior 11 months, the findings are robust to the exclusion of micro-cap stocks.

 The findings were also robust to various definitions of LP, to sub-period performance, to using a zero return instead of the risk-free rate to determine a loss, and to using the prior two or three months’ returns to determine LP. However, the magnitude of alpha decreases as the LP estimation window increases from one month to three months, and it disappears beyond three months —suggesting that average investors might only look at recent stock returns to have a sense of loss probability).

– The predictive power of LP for subsequent stock returns is stronger among stocks that are less subject to arbitrage activities (e.g., small stocks, illiquid stocks and stocks with high idiosyncratic volatility) and among stocks better known to investors (e.g., stocks with high analyst coverage).

– Institutional ownership does not mitigate the “mis-pricing” caused by LP-averse investors.


The authors noted that their findings are consistent with the literature on momentum, which has found a strong effect of short-term reversal characterised by the observation that previous stock return performance over short periods, such as a month, tends to be negatively related to future performance. This is why most momentum strategies exclude the most recent month’s returns.

They concluded: “Investors are less (more) willing to hold stocks that exhibit a high (low) LP during the previous month, and thus these stocks are undervalued (overvalued) and earn higher (lower) subsequent returns.”   


LARRY SWEDROE is Chief Research Officer at Buckingham Strategic Wealth and the author of  numerous books on investing.
Want to read more of his work? Here are his most recent articles published on TEBI:

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