It is now widely agreed that, although daily and monthly financial asset returns are approximately unpredictable, return volatility is highly predictable, a phenomenon with sweeping implications for financial economics and risk management (e.g., Bollerslev, Engle and Nelson, 1994). Of course, volatility is inherently unobservable, and most of what we think we know about volatility has been learned either by fitting parametric econometric models such as GARCH, by studying volatilities implied by options prices in conjunction with specific option pricing models such as Black-Scholes, or by studying direct indicators of volatility such as ex-post squared or absolute returns. But all of those approaches, valuable as they are, have distinct weaknesses.
For example, the existence of competing parametric volatility models with different properties (e.g., GARCH versus stochastic volatility models) suggests misspecification; after all, at most one of the models could be correct, and surely, none is strictly correct. Similarly, the well-known smiles and smirks in volatilities implied by Black-Scholes prices for options written at different strikes provide evidence of misspecification of the underlying model. Finally, direct indicators, such as ex-post squared returns, are contaminated by measurement error, and Andersen and Bollerslev (1998a) document that the variance of the “noise” typically is very large relative to the “signal.”
In this paper, motivated by the drawbacks of the popular approaches, we provide new and complementary measures of daily asset return volatility. The mechanics are straightforward: we estimate daily volatility by summing high-frequency intraday squared returns. With sufficiently frequently sampled underlying returns, the resulting volatility estimates are largely free of measurement error. Hence, for practical purposes we can treat volatility as observed. We do so, and proceed to examine the distributional characteristics directly. The assumed observability allows us to rely on much simpler techniques than required when volatility is latent.
Our analysis is in the spirit of, and directly extends, earlier contributions of French, Schwert and Stambaugh (1987), Hsieh (1991), and Schwert (1989, 1990), and more recently Taylor and Xu (1997). We progress, however, in a number of important ways. First, we provide rigorous theoretical underpinnings for the volatility measures for the general case of a special semimartingale. Second, much of our analysis is multivariate; we develop and examine measures not only of return variance but also of covariance.
Finally, our empirical work is based on a unique high-frequency dataset consisting of ten years of continuously-recorded 5-minute returns on two major currencies. These high-frequency returns enable us to compute and examine daily volatilities, which are of central concern in both academia and industry. In particular, the persistent volatility fluctuations of interest in risk management, asset pricing, portfolio allocation, forecasting, and analysis of market microstructure effects are very much present at the daily horizon.
