Volatility forecasting is central to financial decision making. To assess the tradeoffs between risk and return, investors need forecasts of average return and volatility of different assets. Similarly, for the pricing of options and other derivative securities with non-linear payoffs, investors not only need to estimate current volatility, but also need to forecast it up to the maturity of the options. Forecasts of covariances across assets are as invaluable for basic needs in finance, such as the efficient diversification of risks, or the valuation of convertible securities that can either become into stocks or bonds in the future. Motivated by recent economic models of time varying volatilities, in this paper we show that empirical measures of economic uncertainty predict future volatility above and beyond traditional lagged-based forecasts.
Most financial economists today believe that asset price volatilities and cross covariances change over time, and that the movements are persistent. Starting with the seminal work on auto regressive conditional heteroskedasticity in asset prices (Engle 1982), a family of models emerged in the time series literature that generalized this important finding, tested alternative specifications, and added information in economic variables (see, e.g., Bollerslev, Chou and Kroner 1992 for a survey). Despite its success in fitting volatility processes, the ARCH family of models has had only limited success in forecasting (Figlewski 1997). While Anderson and Bollerslev (1998) show that GARCH models do provide accurate one-week-ahead forecasts, Diebold and Christoffersen (2000) show that the forecasting power of these models declines quite rapidly with the time horizon. In this paper we augment these lag-based forecasts of variances and covariances with empirical measures of uncertainty that investors have over future inflation and earnings growth, and find quite remarkably that for forecast horizons of one and two years, the proportion of explained future variation increases from about a fourth to a half.
A natural question that arises in constructing forecasts of volatility is, What causes volatility to fluctuate? From a purely theoretical standpoint, a number of explanations have been put forward, including (i) stochastic volatility of fundamentals, such as dividends, consumption or inflation (see, e.g., Gennotte and Marsh 1993); (ii) leverage effects (Black 1976); (iii) changing risk aversion or discount rates (Campbell and Cochrane 1999, Mehra and Sah 1998), (iv) investors’ fluctuating uncertainty on the future values of fundamentals (David 1997 and Veronesi (1999, 2000)). From an empirical standpoint, Schwert (1989) shows that recession dummies are able to proxy for all these effects, rendering each of them insignificant in simple regressions. Other empirical studies that relate the conditional heteroskedasticity of asset returns to macroeconomic events include Bit-tlingmayer (1998), who finds that political uncertainty affects stock volatility, Jones, Lamont and Lumsdaine (1998), who find that macroeconomic announcements affect the volatility of bond returns but show no persistence at all and, David and Veronesi (2002), who find that an uncertainty measure obtained from a regime switching model of real earnings growth is related to options’ implied volatility. Roll (1984) finds compelling evidence that volatility is higher during trading days, implying that the logistics of the trading process can exacerbate price movements from fundamental news and cause volatility to fluctuate.
These authors however do not explain why volatility movements are forecastable, a void that we fill in this paper. Suppose the average growth rate of fundamentals is time varying, but variations in these growth rates are not observable by investors. Instead, they must learn about these shifts from observations of fundamental growth and other signals. Due to the noise in fundamental processes, investors take time to learn about these shifts, and during this learning period, they give more weight to news and update their beliefs more rapidly. Asset prices, as a discounted value of fundamentals, will thus also become more volatile. If an econometrician is able to estimate the frequency of shifts in average growth rates and the level of noise in fundamentals, then she can predict how long the episode of increased uncertainty (volatility) will persist. Similarly, in periods of low uncertainty, she can estimate the time for the next shift and episode of high volatility. In our empirical estimation, we find that shifts of fundamental average growth rates occur at the business cycle frequency, causing forecastability of volatility at the one and two year horizons.
We similarly provide intuition for the forecastability of covariances across assets. Periods of high uncertainty (over both inflation and earnings growth) are characterized by a higher covariance between bond and stock returns. The finding is economically sensible: In an equilibrium model, during periods of high uncertainty, investors’ discount factors will respond more swiftly to news. This generates a common factor across stock and bond prices, which pushes up their covariance. As uncertainty is partly forecastable, so will be the covariances.
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