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
1I20 The Journal of finance 3 8591869187918891899190919191929193919491959196919791989 anuary 1859-Decambar 19e Stock Returns Figure 2. Predictions of the monthly standard deviations of stoek returns (--- and of g-term corporate bond returns(-)for 1859-1987 A 12th tion with different monthly intercepts is used to model returns, and then the absolute residuals are used to estimate volatility in month t. To model conditional volatility, autoregressive model with different monthly intercepts is used to predict the standard month t based on lagged standard deviation estimates. This plot contains fitted values from the cients and autocorrelations of the estimates of stock return volatility based on monthly and daily data, lEsl and or. It also contains summary statistics for estimates of the volatility of short and long-term bond returns, lErstl and lerhtl nflation, IentI, money growth, Eml, and industrial production, IE Table II summarizes the autoregressions used to predict volatility. The sum of the autoregressive coefficients measures the persistence of the volatility series where a value of unity implies nonstationarity. See Engle and bollerslev(1986) for a discussion of integrated conditional heteroskedasticity. ) The F-test. meas ures whether there is significant deterministic seasonal variation in the average volatility estimates. The coefficient of determination R and the Box-Pierce (1970) statistic Q(24)measure the adequacy of the fit of the model As suggested by the analysis in footnote 1, the estimates of volatility ily data have much less error than the estimates from monthly dat m sample standard deviation of IEsel is about sixty percent larger than that of dt from 1885 to 1987, though the average values are similar. Moreover, the autocor See Table Al in the appendix for a brief description of the variables used in this paper
Why Does Stock Marhet Volatility Change Ouer Time? .018 a,2 0.016 0014 12 c00 0002 8591869187918891899190919191929193919491959196919791989 Figure 3. Predictions of the monthly standard deviations of stock returns(---) and of short-term interest rates for 1859-1987. A 12th-order autoregression with different monthly intercepts is used to model returns or interest rates, and then the absolute values of the residuals are used to estimate volatility in month t. To model conditional volatility a 12th-order autoregressive model with different monthly intercepts is used to predict the standard deviation in month t based on lagged standard deviation estimates. This plot contains fitted values from the volatility regression models relations of G, are much larger than those of |eatl, though they decay slowly for both series. This slow decay shows that stock volatility is highly persistent perhaps nonstationary. ( See Poterba and Summers(1986)and Schwert (1987 for further discussion. )The correlation between Esl and ot is 0.56 from 1885 to 1987, and the correlation between the volatility predictions lest and or is 0.78 from 1886 to 1987. The two methods of predicting volatility have similar time The autocorrelations in Table i and the summary statistics for the estimated models in Table Ii are similar for all the volatility series. The autocorrelations are small (between 0.2 and 0.4), but they decay very slowly. This is consistent with conditional volatility being an integrated moving average process, so shocks to volatility have both permanent and transitory parts. The unit root tests in Table Ii show that most of the sums of the autoregressive coefficients are reliably different from unity using the tables in Fuller(1976). However, Schwert(1987 1989a)shows that the Fuller critical values are misleading in situations such as this. The estimation error in the monthly volatility estimates biases the unit root
lI The Journal of finance 9兰 ees寸seso aeee寸e eotg 器R s→8o ∞≌et∞ss 图 ea H@的 岩 H secoso 859a2 v8
Why Does Stock Market Volatility Change Ouer Time? Summary Statistics for Autoregressive Predictive Models for the Volatility of Stock Returns, Bond Returns, and the growth Rates of the Producer Price Index, the Monetary Base, and industria Production, 1859-1987 A 12th-order autoregression with different monthly intercepts is used to model the growth e errors irom nthly standard deviations. The exception is the estimate of stock market volatility based tock returns within the month. The 12th-order autoregression for the volatility estimates is 12 l=∑v;Dn+Σpl-l+ table shows the sum of the autoregressive coefficients(pr+ latility. a t-test for whether the sum equals unity, indicating nonstationarity, is in parentheses ow the sum. It also shows an F-test for the equality of the 12 monthly intercepts(yu nd its p-value. Finally, it shows the coefficient of determination R and the Box-Pierce(1970)Q(24) statistic for the residual autocorrelations(which should be distributed as x?(12)in this case) Surm of ar Coefficients F-Test for Equal Volatility Series R2Q(24) Monthly stock returns 08471 0.132458 (-372 Daily stock returns 0.524602 Manthly short-term interest rates 0.7925 0.371 Monthly high-quality long-term bond returns 0.260594 Monthly medium-quality lang-term bond returns 0.7765 0280166 PpI inflation rates 027163 (-429) (0961) Monetary base growth rates (0.787) Industrial production growth rates 08336 0.219469 (-382) estimates toward stationarity The results for the estimate of stock volatility from daily data &, support this conclusion since the sum of the autoregressive coefficients is closer to unity and the test statistic is small C Measurement Problems-The Effects of diversification Even though the set of stocks contained in the"market"portfolio changes over me, the behavior of volatility is not affected. There are few stocks in the sample 6 Also see Pagan and Ullah(1988) for a discussion of the errors-in-variables problem associated
1124 The Journal of finane in 1857, and they are all railroad stocks. Nevertheless, they represent most of he actively traded equity securities at that time. Also, railroads owned a wide variety of assets at that time i have calculated tests for changes in stock volatility around the times when major changes in the composition of the portfolio occurred and, surprisingly there is no evidence of significant changes. Schwert(1989d) analyzes several alternative indices of United States stock returns for the 19th century and finds that the different portfolios have similar volatility after 1834 Though the number of securities and industries included has grown over time the plot of stock return volatility in figure l does not show a downward trend This conclusion contrasts with the analysis of unemployment, industrial pro duction, and gross national product data by romer (1986a, b, 1989 ) Also, when the Bureau of Labor Statistics has expanded the monthly sample used to calculate the CPI inflation series, there have been noticeable reductions in the volatility of measured inflation rates. Shapiro (1988) argues that the stability of stock return volatility between the 19th and 20th centuries supports Romer's conclu sions that the higher level of volatility in pre-1930 macroeconomic data is primarily due to measurement problems. Nonetheless, it is perhaps surprising that stock return volatility is not higher in the 19th century due to measurement problems IL. Relations between Stock Market Volatility and Macroeconomic Volatility A. Volatility of Inflation and Monetary Growth The stock returns analyzed above all measure nominal(dollar) payoffs. When inflation of goods' prices is uncertain, the volatility of nominal asset returns should reflect inflation volatility. I use the algorithm in equations(3a)and (3b) to estimate monthly inflation volatility from 1858 to 1987 for the PPI inflation rate. Figure 4 plots the predicted PPI inflation volatility lepe! from 1859 to 1987 Note that the right-hand PPI inflation volatility about的 smaller than the left-hand stock volatility axis. The volatility of infation was very high around the Civil War(1860-1869), reflecting changes in the value of currency relative to gold after the U.S. went off the gold standard in 1862. Since the U. K remained on the gold standard, this also represents volatility in the exchange rates between U.S. and U.K. currencies. The Spanish-American War(1898), World War I and its aftermath(1914-1921), and World War II (1941-1946)are also periods of high inflation uncertainty. Another increase in inflation volatility occurred during the 1973-1974 oPeC oil crisis. While inflation volatility increased during the 1929-1939 period, this change is minor compared with the volatility that occurred during wars Figure 5 plots the predicted volatility of the monetary base growth rates |em om 1880 to 1987. The volatility of money base growth rates rose during the bank panic and recession of 1893 and remained high until about 1900. The next sharp increase in volatility occurred during the bank panic of 1907. The period following the formation of the Federal Reserve System(1914-1923)was another period of high volatility. Finally, the period of the great Depression(1929-1939)
