Standard asset pricing theory, e.g., the capital asset pricing model (CAPM), predicts that investors demand an ex ante risk premium for bearing the systematic risk that they cannot diversify away. The market portfolio in the equity market is the most diversified portfolio; as such, its conditional variance represents one of the most commonly used measures of market systematic risk. A positive relation between the expected return and variance of the market portfolio is intuitively appealing and Ghysels, Santa Clara, and Valkanov (2005) argue that it is the “first fundamental law of finance.”
The empirical evidence on this relation, however, has been mixed. Some authors, including Pindyck (1984), French, Schwert, and Stambaugh (1987), and Ghysels, Santa-Clara, and Valkanov (2005), find that, consistent with CAPM, the conditional excess stock market return is positively related to the conditional stock market variance. Many others, including Campbell (1987), Glosten, Jagannathan, and Runkle (1993), Whitelaw (1994), Lettau and Ludvigson (2003), and Brandt and Kang (2004), document a significantly negative risk-return tradeoff in the data.
One important reason for the conflicting results could be that the expected return is unobservable. The early studies had to use either realized stock returns or instrumental variables as proxies for it. Such practice, albeit usually out of necessity, has its limitations. For example, as pointed out by Elton (1999), realized returns are a poor measure of expected returns. Similarly, Campbell (1987), among others, finds that the results are sensitive to the choice of instrumental variables.