Why Does Stock Marhet Volatility Change Over Time? 25 16 0.15 teck Returns jonuary 1859-Oocembor 1987 Pptn升 gHion rc1 Figure 4. Predictions of the monthly standard deviations of stock returns(---)and of roducer price index inflation rates(-)for 1859-1887. A 12th-order different monthly intercepts is used to model returns or infation rate, and then the absolute values of the residuals are used to estimate volatility in month t. To model conditional volatility, a 12th in month t based on lagged standard deviation estimates. This plot contains fitted values from the volatility regression models. was a period of very high volatility. Since the early 1950's the volatility of the onetary base growth rate has been relatively low and stable. Both the PPI inflation rate and the monetary base growth rate exhibit much lower levels of volatility after World War II. In each case, the sample used to measure these variables has expanded over time, and there have been major nstitutional changes that have been intended to dampen macroeconomic fluc tuations. without detailed analysis similar to Romer's work on industrial pro duction, unemployment, and gross national product it is impossible to tell how important the changes in measurement techniques have been in reducing vola Table iii contains tests of the incremental predictive power of 12 lags of PPI inflation volatility leer in a 12th-order vector autoregressive (VAR) system for ° It is surprising pattern of volatility is so different for the money base growth rate and the ppi inflation rat rtheless, I have also analyzed the volatility of money supply (M2)growth and the Consumer ex(CPI) inflation rates since 1915, and they lead to similar conclusions The lack of relatiol monetary volatility and price volatility is an interesting question for future research
1126 The ournal of Finance 0,c5 0.03x .01 认M 18591869 918s91899190919191929193919491959196919791989 January t880-Dacambar 1987 Figure 5. Predictions of the monthly standard deviations of stock returns(---)and of money base growth rates ()for 1880-1987. A 12th-order autoregression with different ate, and then the absolute values of the residuals are used to estimate valatility in iel conditional volatility, a 12th-order autoregressive model with different monthly 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 stock volatility, high-grade bond return volatility lernel, and short-term interest volatility that allows for different monthly intercepts. The VAR model uses both the monthly measure of stock return volatility IEsl and the daily measure a 0 These VAR models are generalizations of the autoregressive model in(3b), but they include lagged values of other variables to help predict volatility. The F-tests in Table iii measure the significance of the lagged values of the column variable in predicting the row variable, given the other variables in the model. F tatistics that are larger than the 0.01 critical value 2.28 are indicated with asterisks The largest F-statistics are on the main diagonal of these matrices, and the size of the statistics decreases away from the diagonal. For example, lagged stock 1e Models using the volatility of medium-grade(Baa-rated)bond return volatility, lerma, instead of high-grade bond return volatility, yielded similar results for the post- 1920 periods. Medium-grade bond valatility is more strongly related to the stock volatility and more weakly related to the short term interest rate volatility but the relations with the macroeconomic valatility series are generally similar. Because these data are only available from 1920 to 1987 and the results are similar, they are not reported
Why Does Stock Market Volatility Change Ouer Time? 1127 volatility is the most important variable in predicting current stock volatility Lagged bond return volatility also helps in most sample periods, and lagged short-term interest volatility contributes less. Likewise, stock volatility helps predict bond return volatility in most periods, but it rarely improves predictions of interest rate volatility. In most sample periods, short-term interest volatility helps predict bond return volatility and vice versa. Except for monthly stock volatility from 1953 to 1987, there is little evidence that inflation volatility helps to predict future asset return volatility The present value relation in(1)is forward-looking. In an efficient market speculative prices will react in anticipation of future events. Thus, it is also interesting to see whether asset return volatility helps to forecast later volatility of macroeconomic variables. Except for long-terrm bond returns from 1859 to 1987, there is no evidence that either stock or bond return volatility helps to predict inflation volatility. Perhaps this is because the major changes in inflation volatility occur during wars, and there seems to be little effect of wars on stock or bond return volatility Table IV contains tests of the incremental predictive power of 12 lags of monetary base growth volatility lEmel in a 12th-order VAR system similar to Table IiI. The relations among the measures of financial return volatility are similar to Table IlL. There is evidence that money growth volatility helps to predict the volatility of long-term bond returns from 1885 to 1919. Also, from 1885 to 1987, 1885 to 1919, and 1920 to 1952, there is evidence that money growth volatility helps to predict the volatility of stock returns measured using daily data On the other hand, from 1920 to 1952(and the sample periods that include this subperiod), both measures of stock return volatility help to predict the volatility of the base growth rate The relations between inflation or money growth volatility and the volatility of asset returns are not strong. It is surprising that. these macroeconomic measures of nominal volatility are not more closely linked with the volatility of short- and long-term bond returns B Real Macroeconomic volatility Since common stocks reflect claims on future profits of corporations, it is lausible that the volatility of real economic activity is a major determinant of stock return volatility. In the present value model (1), the volatility of future expected cash flows, as well as discount rates, changes if the volatility of real activity changes Figure 6 contains a plot of the predicted volatility of the growth rates of industrial production leil. Note that the right-hand industrial production volatility scale is about 3 smaller than the left-hand stock volatility scale. Summary statistics for these estimates are in Tables I and II. Industrial produc tion volatility was high during the mid-1930,'s, during World War I, and especially data from Macaulay(1938)and the volatility af the liabilities of business failures nd Bradstreet(Citibase (1978)). Neither of these "real activity"variables was stro