How Risky Is the Market?

Abstract

Introduction The rate of return on a common stock investment during an accounting period can be defined as the percentage appreciation in the market price plus the dividend yield during the period. The dividend yield also is expressed as a percentage per unit time based on the market price at the beginning of the period. Since the pioneering work of Markowitz,' there has been an attempt to account explicitly for risk in portfolio analysis. In current financial literature, risk is equated with variation in the rate of return. Although various quantitative measures are available for expressing the variation of rates of return on common stocks, the one that has proved to be the most useful for analytical purposes is the variance, or average of the squared deviations from the mean. This measure and its square root-the standard deviation-have significance in statistical theory. A measure of portfolio performance that takes risk into account through the use of the standard deviation in rate of return is the rewardto-variability ratio, defined as the ratio of the excess portfolio rate of return above a risk-free interest rate to the standard deviation in the portfolio rate of return. A similar measure is the reward-to-volatility ratio in which the standard deviation is replaced by the volatility, defined as the slope of the regression line of portfolio rate of return versus market rate of return. For obtaining quantitative estimates of such portfolio performance measures, some writers have used rate of return data based on annual sampling periods, while others have used monthly sampling periods. Does the variance or standard deviation of rate of return give a good indication of the risk experienced by investors when an annual sampling period is used? Using the beginning-of-the-year and end-of-the-year Dow Jones Industrial Average (DJIA) for 1970, one notes a 3.7 percent increase for the year. The index, however, declined 22 percent during the first 5 months and then recovered with the gain noted at year end.