Realized return volatility, asset pricing, and risk management.

• Author: Andersen, Torben G.

It is now widely accepted that expected returns, volatility, and broader financial risk measures all vary over time. In particular, there is a pronounced clustering in return volatility; occasional extreme return outliers--especially on the negative for equities; and an increase in return correlations during market downturns. This makes it more complicated for academics, regulators, and practitioners seeking to understand, monitor, act, and react to financial market dynamics to assess market conditions in real time. Textbook prescriptions for portfolio choice, asset pricing, and risk management typically are based on a static setting with known and invariant return distributions. These approaches are ill-suited for practical decision making: market agents know neither the parameters nor the parametric family of the return distribution, and the shape of the distribution is likely to change over time. Depending on the horizon, the challenges differ, with the notable exception that accurate assessment of the current volatility level remains pivotal. At daily or shorter intervals, it is critical also to understand the likely reaction of markets to impending news releases and to control for the intraday pattern in the market activity and return dynamics. For weekly and monthly frequencies, the persistence of volatility and the extent of asymmetry between return and volatility innovations both figure importantly in determining return distributions. For even longer quarterly and annual horizons, the main issues again relate to the temporal persistence of volatility, but good estimates of the non-negligible longer-run expected returns now also become critical.

The increased availability of tick-by-tick financial trade records and real-time news reports, coupled with our enhanced capacity to store and process vast amounts of data, have led to important new insights in regards to the issues discussed above. Specifically, over the last few years a very active research agenda into the direct (model-free) measurement of the realized return variation and covariation of financial assets at daily or even higher intraday frequencies has developed.

The intuition behind the realized volatility measure has been recognized for a while, albeit within a simplified setting. In a frictionless market with an unlimited set of price observations available over any interval, it is, quite generally, feasible to perfectly estimate instantaneous volatility if the process is not subject to jumps. However, given the discreteness of the price grid and other market microstructure effects, as well as the limited number of price observations available over short time intervals, even for liquid securities, instantaneous volatility cannot be measured with reasonable precision without (excessively) strong identifying assumptions. In the face of these practical limitations, we have focused a large part of our recent work on developing robust, yet accurate, volatility measures over nontrivial daily, or longer, time intervals that exploit the information available from intraday data.

In so doing, it is important to recognize the main qualitative features that affect the intraday return process but are absent at daily and lower frequency levels. Most importantly, the intraday volatility pattern and the presence of outliers (jumps) render standard ARCH-type volatility models inadequate unless they are explicitly extended to accommodate such features. We show that the original studies applying standard modeling and inference techniques to the newly available intraday data were seriously mis-specified; they produced badly downward biased estimates of the degree of volatility persistence. (1) Meanwhile, by controlling for specific intraday features, we got much closer to the type of volatility dynamics obtained from daily data, although our model specification is still not entirely adequate. In short, direct estimation of the high-frequency volatility process is difficult and very sensitive to market microstructure effects and news. (2)

We instead advocate daily (or longer-horizon) volatility and covariability measures obtained by aggregating intraday squared returns and absolute return cross-products. Focusing on a non-negligible time interval enables us to exploit many return observations, ensuring that the estimated measure is reasonably precise. Moreover, by restricting the measurement to (a multiple of) a trading day and relying on equally-spaced returns sampled, say, every five or ten minutes, we can largely eliminate the intraday volatility...