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
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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)