2002-32

October 25, 2002

Stock Market Volatility

John Krainer

Western Banking Quarterly is a review of banking developments in the Twelfth Federal Reserve District, and includes FRBSF’s Regional Banking Tables. It is normally published in the Economic Letter on the fourth Friday of January, April, July, and October.

In recent months, it has not been unusual to see the value of major stock indexes, such as the S&P 500, change by as much as 3% in a single day. Unfortunately for many investors, the general direction of those changes has been downward. For some researchers in financial economics, the interesting question is: what drives the volatility itself? The evidence they have uncovered over the last few decades sheds light on the efficiency of the stock market and points to some important implications for economic forecasters and investors. In particular, it suggests that the degree of stock market volatility can help forecasters predict the path of the economy’s growth; furthermore, changes in the structure of volatility imply that investors now need to hold more stocks in their portfolios to achieve diversification. In this Economic Letter I survey the academic literature on the properties and causes of stock market volatility, focusing on the debate on whether the stock market varies excessively, how volatility changes over time, and some of the underlying components of volatility.

Excess stock market volatility and dividends

Stock market performance is usually measured by the percentage change in the stock price or index value, that is, the returns, over a set period of time. One commonly used measure of volatility is the standard deviation of returns, which measures the dispersion of returns from an average. Since the beginning of 1997, the standard deviation of daily returns is 1.3% for the S&P 500 Index, 2.2% for the NASDAQ, and 1.3% for the Dow Jones Industrial Average (see Figure 1).

If the stock market is efficient, then the volatility of stock returns should be related to the volatility of the variables that affect asset prices. One candidate variable is dividends. But research conducted in the early 1980s suggests that variation in dividends alone cannot fully account for the variation in prices (see LeRoy and Porter 1981 and Shiller 1981). Prices are much more variable than are the changes in future dividends that should be capitalized into prices. Asset prices apparently tend to make long-lived swings away from their fundamental values. This fact turned out to be equivalent to the finding that, at long horizons, stock returns displayed predictability. Thus, the literature on excess volatility broached the possibility that the stock market may not be efficient.

In the excess volatility literature, the researchers understood that the dividends that are capitalized in the stock price arrive in the future and need to be “discounted” back to the present using a discount rate. In the early research it was assumed that this discount rate was constant. However, discount rates depend on investors’ preferences for risk, which could very well change over time. Therefore, stock market volatility may not be excessive if discount rates are variable enough. Thus, the real contribution of the excess volatility literature was to call attention to the fact that corporate dividends are simply too smooth a series to account for the high volatility in prices. Subsequent research necessarily focused away from the payout policy of firms and toward the characteristics of investors and of actual stock market trading.

Persistence of stock market volatility

Stock market volatility tends to be persistent; that is, periods of high volatility as well as low volatility tend to last for months. In particular, periods of high volatility tend to occur when stock prices are falling and during recessions. Stock market volatility also is positively related to volatility in economic variables, such as inflation, industrial production, and debt levels in the corporate sector (see Schwert 1989).

The persistence in volatility is not surprising: stock market volatility should depend on the overall health of the economy, and real economic variables themselves tend to display persistence. The persistence of stock market return volatility has two interesting implications. First, volatility is a proxy for investment risk. Persistence in volatility implies that the risk and return tradeoff changes in a predictable way over the business cycle. Second, the persistence in volatility can be used to predict future economic variables. For example, Campbell, et al. (2001) show that stock market volatility helps to predict GDP growth.

Components of stock market volatility

Researchers have sought to analyze the relative importance of economy-wide factors, industry-specific factors, and firm-specific factors on a stock’s volatility. This approach borrows from modern asset pricing theory and its emphasis on so-called factor models, or models that assume a firm’s stock return is governed by factors such as the overall market return, the return on a portfolio of firms sampled from the same industry, or even changes in economic factors such as inflation, changes in oil prices, or growth in industrial production. If returns have a factor structure, then the return volatility will depend on the volatilities of those factors. Campbell, et al. (2001) assume the factors are the overall market return, an industry return (e.g., financial, industrial, etc.), and an idiosyncratic noise term that captures firm-specific information. They document the important empirical fact that while volatility moves considerably over time, there is not a distinct trend upwards or downwards. More interestingly, however, since 1962, there has been a steady decline in stock market volatility attributed to the overall market factor; that is, the common volatility shared across returns on different stocks has diminished over that period. The variation ascribed to firm-specific sources, by contrast, has risen. The implication for investors, then, is that they need to hold more stocks in their portfolios in order to achieve diversification.

Conclusion

Economists have long been interested in the patterns of stock market volatility. Their research on excess volatility relative to dividends found that volatility tends to ebb and flow; subsequent research found that periods of high volatility are persistent and occur during periods of stock market declines, and that the stock market volatility associated with systematic factors has been declining over time. These academic findings may offer little consolation to today’s investor for whom volatility means portfolio losses, but the research has yielded important insights into how stock market information can help forecast economic variables, and how investors can construct portfolios that can minimize volatility.

John Krainer
Economist


References
Campbell, J., M. Lettau, B. Malkiel, and Y. Xu. 2001. “Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk.” Journal of Finance 56, pp. 1-43.

LeRoy, S., and R. Porter. 1981. “The Present Value Relation: Tests Based on Variance Bounds.” Econometrica 49, pp. 555-574.

Schwert, W. 1989. “Why Does Stock Market Volatility Change Over Time?” Journal of Finance 44, pp. 1,115-1,153.

Shiller, R. 1981. “Do Stock Prices Move Too Much to Be Justified by Subsequent Changes in Dividends?” American Economic Review 71, pp. 421-436.

Opinions expressed in FRBSF Economic Letter do not necessarily reflect the views of the management of the Federal Reserve Bank of San Francisco or of the Board of Governors of the Federal Reserve System. This publication is edited by Sam Zuckerman and Anita Todd. Permission to reprint must be obtained in writing.

Please send editorial comments and requests for reprint permission to

Research Library
Attn: Research publications, MS 1140
Federal Reserve Bank of San Francisco
P.O. Box 7702
San Francisco, CA 94120