THE JOURNAL OF FINANCE VOL. XLIV. NO. 5. DECEMBER 1989 Why Does Stock Market Volatility Change Over ime? G. WILLIAM SCHWERT ABSTRACT his paper analyzes the relation of stock volatility with real and nominal macroecond ata from 1857 to 1987. An important fact, previously noted by Officer(1973), is that tock return variability was unusually high during the 1929-1939 Great Depression hile aggregate leverage is significar related with volatility, it explains a relatively mall part of the movements in stock volatility. The amplitude of the fluctuations ggregate stock volatility is difficult to explain using simple models of stock valuation, especially during the Great Depression ESTIMATES OF THE STANdARd deviation of monthly stock returns vary from two to twenty percent per month during the 1857-1987 period. Tests for whether differences this large could be attributable to estimation error strongly reject the hypothesis of constant variance. Large changes in the ex ante volatility of market returns have important negative effects on risk-averse investors. Moreover, hanges in the level of market volatility can have important effects on capital investment, consumption, and other business cycle variables. This raises the question of why stock volatility changes so much over time. Many researchers have studied movements in aggregate stock market volatility Officer(1973) relates these changes to the volatility of macroeconomic variables. Black (1976) and Christie(1982)argue that financial leverage partly explains this phenomenon. Recently, there have been many attempts to relate changes in stock market volatility to changes in expected returns to stocks, including Merton (1980), Pindyck (1984), Poterba and Summers(1986), French, Schwert, and Stambaugh(1987), Bollerslev, Engle, and Wooldridge(1988), and Abel(1988) Mascaro and Meltzer(1983)and Lauterbach (1989) find that macroeconomic volatility is related to interest rates Shiller (1981a, b)argues that the level of stock market volatility is too high relative to the ex post variability of dividends. In present value models such Shiller's a change in the volatility of either future cash flows or discount rates William E. Simon Graduate School of Business Administration, University of Rochester, and National Bureau of Economic Research. I received helpful comments from David Backus, Fischer Black, Marie Davidian, Harry DeAngelo, Beni Lauterbach, Ron Masulis, Grant McQueen, Robert Merton, Dan Nelson, Charles Plasser, Paul Seguin, Robert Stambaugh, Jerold Zimmeri participants at Yale University and at the Universities of Chicago, Michigan, Rochester, and Washington, and three anonymous referees. Ken French and Rene Stulz deserve special credit for their help. The Bradley Policy Research Center at the University of Rochester provided support for his research 1115
1116 The Journal of finance causes a change in the volatility of stock returns. There have been many of Shiller's work, notably Kleidon(1986). Nevertheless, the literature volatility"has not addressed the question of why stock return volatility at some times than at others This paper characterizes the changes in stock market volatility through time In particular, it relates stock market volatility to the time-varying volatility of a variety of economic variables. Relative to the 1857-1987 period, volatility was unusually high from 1929 to 1939 for many economic series, including inflation money growth, industrial production, and other measures of economic activity Stock market volatility increases with financial leverage, as predicted by Black and Christie, although this factor explains only a small part of the variation in stock volatility. In addition, interest rate and corporate bond return volatility are correlated with stock return volatility. Finally, stock market volatility in creases during recessions. None of these factors, however, plays a dominant role explaining the behavior of stock volatility over time It is useful to think of the stock price, Pr as the discounted present value expected future cash flows to stockholders E-1P=E-1∑ (1 where Do+h is the capital gain plus dividends paid to stockholders in period t +k and 1/[1 R+hl is the discount rate for period t k based on information available at time t-1(Er-1 denotes the conditional expectation. )The conditional variance of the stock price at time t-1, var,-1(P), depends on the conditional variances of expected future cash flows and of future discount rates, and on the conditional covariances between these series. 1 At the aggregate level, the value of corporate equity clearly depends on the health of the economy. If discount rates are constant over time in(1),the conditional variance of security prices is proportional to the conditional variance of the expected future cash flows. Thus, it is plausible that a change in the level of uncertainty about future macroeconomic conditions would cause a proportional change in stock return volatility. If macroeconomic data provide information about the volatility of either future expected cash flows or future discount rates they can help explain why stock return volatility changes over time. "Fads"or bubbles"in stock prices would introduce additional sources of volatili Section I describes the time series properties of the data and the strategy for modeling time-varying volatility Section II analyzes the relations of stock and bond return volatility with the volatility of inflation, money growth, and indus trial production. Section III studies the relation between stock market volatility The variance of the sum of a sequence of ratios of random variables is not a simple function of the variances and covariances of the variables in the ratios, but standard asymptotic approximations depend on these parar " For a positively autocorrelated variable, such as the volatility series in Table Il, an unexpected ncrease in the variable implies an increase in expected future values of the series for many steps ahead. Given the discounting in(1), the volatility series will move almost proportionally. See Poterba and Summers(1986)for a simple model that posits a particular arima process for the behavior of the time-varying parameters in a related context
Why Does Stock Market Volatility Change Ouer T'ime? 1117 and macroeconomic activity. Section IV analyzes the relation between financial leverage and stock return volatility. Section V analyzes the relation between stock market trading activity and volatility. Finally, Section VI synthesizes the results from the preceding sections and presents concluding remarks I. The Time Series Behavior of Stock and Bond Return Volatility A. Volatility of stock returns Following French, Schwert, and Stambaugh(1987), I estimate the monthly standard deviation of stock returns using the daily returns to the Standard and Poor's(S&P)composite portfolio from January 1928 through December 1987. The estimates from February 1885 through December 1927 use daily returns on the dow Jones composite portfolio. (See Schwert(1989d) for a more detailed description of these data. )The estimator of the variance of the monthly return is the sum of the squared daily returns(after subtracting the average daily return in the month) where there are N daily returns ru in month t. Using nonoverlapping samples of daily data to estimate the monthly variance creates estimation error that is uncorrelated through time. A Daily stock return data are not readily available before 1885. Also, macroeco nomic data are rarely measured more often than monthly. To estimate volatility from monthly data, I use the following procedure: (i)Estimate a 12th-order autoregression for the returns, including dummy variables D, to allow for different monthly mean returns, using all data available for the series R:=∑a;Dx+∑aR-+et (3a) (ii)Estimate a 12th-order autoregression for the absolute values of the errors from (3a), including dummy variables to allow for different monthly standard deviations 12 a|=∑yDn+∑n|-|+ (3b) a French, Schwert, and Stambaugh(1987)use one lagged crass covariance in(2), and th no adjustment for the mean return. Their estimator is not guaranteed to be positive. Indeed, month in the 1885-1927 period, the French, Schwert, and Stambaugh estimate of volatility is The estimates from( 2)are very similar to the french, Schwert, and Stambaugh estimates, except that they are always positive. If the data are normally distributed, the variance of the estimator as is od/2N, where o? is the true variance(Kendall and Stuart (1969, p. 243)). Thus, for N.=22 and a.=0.04, the standard error of d, is 0.006, which is small relative to the level of dg. Since this is a classic errors-in-variabl problem, the autocorrelations of the estimates G will be smaller than, but will decay at the same rate as, the autocorrelations of the true values o
The Journal of finance (iii) The regressand e is an estimate of the standard deviation of the stock market return for month t similar to a(although it uses one rather than 22 observations). The fitted values from(3b)Ie estimate the conditional standard deviation of R, given information available before month t. This method is a generalization of the 12-month rolling standard deviation imator used by Officer(1973), Fama (1976), and Merton (1980) because it lows the conditional mean return to vary over time in(3a) and allows different weights for lagged absolute unexpected returns in (3b). It is similar to the autoregressive conditional heteroskedasticity(ARCH) model of Engle(1982) Davidian and Carroll(1987) argue that standard deviation specifications such as (3b) are more robust than variance specifications based on 22. They also argue that iterated weighted least squares(WLS) estimates, iterating between(3a) and (3b), provide more efficient estimates. Following their suggestion, I iterate three times between(8a)and (3b)to compute WlS estimates Figure 1 plots the predicted standard deviations from monthly returns esc for 1859-1987, along with the predicted standard deviations from daily returns a (from a 12th-order autoregression for ar as in (3b))for 1885-1987. Volatility predictions from the daily data are much higher following the 1929 and 198 stock market crashes because there were very large daily returns in October 1929 and October 1987. Otherwise, Figure I shows that the predicted volatility series are similar. Stock return volatility is persistent over time B. Volatility of bond returns If the underlying business risk of the firm rises, the risk of both the stock and e bonds of the firm should increase. Also, if leverage increases, both the stocks and the bonds of the firm become more risky. Thus, in many instances the risk of corporate stock and long-term corporate debt should change over time in Figure 2 plots the predicted standard deviations of long-term corporate bond returns lerhtl for 1859-1987. It also shows the predicted standard deviations of stock returns lEsl for comparison. Note that the scale of the right-hand bond return axis is about three times smaller than the scale of the left-hand stock return axis, showing that the standard deviation of monthly stock returns is about three times larger than for bond returns over this period. There are many similarities between predicted volatilities of stock and bond returns. In particular volatility was very high from 1929 to 1989 compared with the rest of the 1859- 1987 period. Moreover, bond returns were unusually volatile in the periods during and immediately following the Civil War(1861-1865). In recent times, the"OPEC oil shock"(1973-1974)caused an increase in the volatility of stock and bond returns Figure 3 plots the predicted standard deviations of short-term interest lErat for 1859-1987. The volatility of Int measures time variation in the ex ra Since the expected value of the absolute error is less than the standard deviation from istribution, Elfrl a(2/=), all absolute errors are multiplied by the constant (2/=) A 1. 2533 Dan Nelson suggested this correction
Why Does Stock Market Volatility Change Oue 0.25 ,25 0.2 cox-0c9t00gc机 1591019181901111 Figure 1. Predictions of the. monthly standard deviation of stock returns based nthly data (--) for 1859-1987 and on daily data (- for 1886-1987 For month returns, a 12th-order autoregression with different monthly intercepts is used to me returns, ay then the absolute values of the residuals are used to estimate volatility in month t For daily returns, the returns in the month are used to estimate a sample deviation for each month. To model conditional olatility, a 12th-order autoregressive model with different monthly intercepts is used to predict the tandard deviation in month t based on lagged standard deviation estimates. This plot contains fitted vaiues from the volatility regression models. nominal interest rate, not risk, since these securities are essentially default free. Note that the right-hand interest rate volatility scale is over 12 times smalle than the left-hand stock volatility scale. There are periods in the 19th century when short-term interest rate volatility rose for brief periods, many of which were associated with banking panics. (See Schwert(1989b). )It is clear from Figures 2 and 3 that long-term bond return and short-term interest rate volatility increased dramatically around 1979. There is not a similar increase in stock return volatility. As noted by Huizinga and Mishkin(1986), the Federal Reserve board changed its operating procedures to focus on monetary aggregate targets at that time The plots in Figures 2 and 3 are consistent with the following Short-term interest rate and long-term bond return volatility hat rarities due to inflation and monetary policy. Stock and long-term bond re latinity have similarities due to real financial and business risk Table I contains means, standard deviations, skewness, and kurtosis coeffi 6 See Fama(1976) for an analysis of the variability of short-term nominal interest rates