The tradeoff between risk and return is one of the cornerstones of financial economics. When capital markets are in equilibrium, they determine a tradeoff between expected return and risk. The only way for investors to achieve a higher expected return is by taking on extra risk. This relationship between return and risk was first formalized by Harry Markowitz in 1952. In what later came to be known as the modern portfolio theory, he examined the tradeoff between risk and return in the context of the optimal selection problem for a portfolio of securities. In this theory investors aim to achieve the highest expected return for a certain level of risk; alternatively, they aim for the lowest level of risk for a certain expected return. An interesting graphical treatment of the risk-return tradeoff and variations in tastes for risk is given by James Tobin (1958).
Risk is measured as the standard deviation of the portfolio returns. This relationship is generally confirmed in total annual risk and return series. For example, over the period 1926 to 2002 stocks of small U.S. companies showed a mean return of 16.9 percent, stocks of large U.S. companies had a mean return of 12.2 percent, long-term government bonds had a mean return of 6.2 percent, and short-term government bonds had a mean return of 3.8 percent. The standard deviations of the returns are in line with the realized returns, as they are 33.2 percent for the small stocks, 20.5 percent for the large stocks, 9.4 percent for long-term government bonds, and 3.2 percent for short-term government bonds (Ross, Westerfield, and Jaffe 2005).
The difference in returns between stocks and short-term government securities is generally referred to as the equity premium. In their 1985 work Rajnish Mehra and Edward Prescott questioned the high level of the equity premium. Their argument is that the size of the equity premium implies an unrealistically high degree of risk aversion on the part of the investors. Stephen Ross, Randolph Westerfield, and Jeffrey Jaffe, in their 2005 study, present an average equity premium of 8.4 percent over the period from 1926 to 2002. They also show that the premium was much lower between 1802 and 1870 (2.9 percent) and between 1871 and 1925 (4.6 percent). Ross, Westerfield, and Jaffe (2005) state that, because of the low-risk premiums in the historical data from 1802 to 1925, caution is needed in making assumptions about the current equity premium.
An important lesson from the theory of Markowitz is that, on the level of individual securities, the covariance between different securities is a more important risk measure than the variance of the individual securities. Securities that have a negative covariance with each other tend to absorb each other’s risk. If the price of one of the securities goes down, the other goes up and vice versa. In the 1960s the portfolio theory of Markowitz was further developed into the capital asset pricing model (CAPM). According to this model, the contribution of a security to the risk of a large well-diversified portfolio is proportional to the covariance of the security’s return with the market’s return. The standardized contribution is the beta, which can be interpreted as the responsiveness of the security’s return to that of the market. According to this model investors divide their wealth between the market portfolio of assets and the risk-free asset. They are allowed to hold short positions in either the market portfolio or the risk-free asset. The market portfolio consists of all risky investments in the economy. Therefore it does not only include shares of common stock, but also corporate bonds, real estate and more exotic investments such as wine and stamp collections. From a theoretical point of view, the CAPM has been criticized because it assumes a market portfolio the contents of which are not observable, thus making it impossible to test this model. Empirical research by Eugene Fama and Kenneth French in 1993 has shown that the responsiveness to the market is not the only determinant of the expected return of a security. Besides the earlier mentioned beta, their three-factor model includes two additional explanatory variables for security returns. These are the ratio of the market value of stock to the book value and the size of the company.
An important disadvantage of the use of the portfolio variance as the risk measure is that the variance is symmetrical. This means that it assigns the same weight to positive and negative deviations from the expected value. In other words, variance does not capture the common notion of risk as negative and undesired. The 2006 study by Chris Veld and Yulia Veld-Merkoulova of risk preferences of individual investors found that most investors use more than one risk measure. For those investors who systematically choose one risk measure, semivariance is most popular. This is also the case for stock investors, whereas bond investors favor the probability of loss as the most important risk measure.
