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