Measuring and Modeling Variation in the Risk-Return Trade-off

This chapter reviews what is known about the time-series evolution of the risk-return trade-off for stock market investment and presents some new empirical evidence. Financial markets are often hard to understand. Stock prices are highly volatile and difficult to predict, requiring that market participants and researchers devote significant resources to understanding the behavior of expected returns relative to the risk of stock market investment. Understanding the time-series properties of the Sharpe ratio is crucial to the development of theoretical models capable of explaining observed patterns of stock market predictability and volatility. The behavior of the Sharpe ratio over time is fundamental for assessing whether stocks are safer in the long run than they are in the short run, as increasingly advocated by popular guides to investment strategy. Only if the Sharpe ratio grows more quickly than the square root of the horizon-so that the standard deviation of the return grows more slowly than its mean-stocks are safer investments in the long run than they are in the short run. Such a dynamic pattern is not possible if stock returns are unpredictable, i.i.d. random variables. Thus, understanding the time series, behavior of the Sharpe ratio not only provides a benchmark for theoretical progress but also has profound implications for investment professionals concerned with strategic asset allocation.