Financial Asset Returns, Direction-of-Change Forecasting, and Volatility Dynamics

Abstract

We consider three sets of phenomena that feature prominently -and separately -in the financial economics literature: conditional mean dependence (or lack thereof) in asset returns, dependence (and hence forecastability) in asset return signs, and dependence (and hence forecastability) in asset return volatilities. We show that they are very much interrelated, and we explore the relationships in detail. Among other things, we show that: (a) Volatility dependence produces sign dependence, so long as expected returns are nonzero, so that one should expect sign dependence, given the overwhelming evidence of volatility dependence; (b) The standard finding of little or no conditional mean dependence is entirely consistent with a significant degree of sign dependence and volatility dependence; (c) Sign dependence is not likely to be found via analysis of sign autocorrelations, runs tests, or traditional market timing tests, because of the special nonlinear nature of sign dependence; (d) Sign dependence is not likely to be found in very high-frequency (e.g., daily) or very lowfrequency (e.g., annual) returns; instead, it is more likely to be found at intermediate return horizons; (e) Sign dependence is very much present in actual U.S. equity returns, and its properties match closely our theoretical predictions; (f) The link between volatility forecastability and sign forecastability remains intact in conditionally non-Gaussian environments, as for example with timevarying conditional skewness and/or kurtosis.

Pessimistic Portfolio Allocation and Choquet Expected Utility

“…Our results complement recent work in the financial econometrics literature on estimation and inference in conditional quantile models, as e.g. in Engle and Manganelli (2001), Bouyé and Salmon (2002), Christoffersen and Diebold (2003), and Linton and Whang (2003).…”

Day-of-the-Month Effects in the Performance of Momentum Trading Strategies in the Foreign Exchange Market

“…The Appendix gives more details of this result. Christoffersen and Diebold (2006) note a number of interesting consequences of this result. Firstly, the sensitivity of sign predictability to changes in the variance is always negative, i.e.…”

“…The absolute sensitivity is maximised when the information ratio is about 1.4. As noted by Christoffersen and Diebold (2006), this is rather high for an information ratio, and is unlikely to be obtained systematically in practice. However, the frequency with which this information ratio is achieved depends on the volatility of volatility.…”

“…In this paper, we investigate the drivers of momentum strategies excess returns employing the directional predictability framework of Christoffersen and Diebold (2006). We first document a very pronounced calendar effect in both the Sharpe ratio and maximum drawdown of a simple moving average rule applied to an equally weighted portfolio of G10 currencies over the period 1997 to 2007.…”

“…We include the carry interest earned on the domestic or foreign currency while it is held, but ignore trading costs, which are negligible for monthly trading in the foreign exchange market. The Importance of Volatility Dynamics Christoffersen and Diebold (2006) have shown that directional predictability is inextricably linked to the dynamics of conditional volatility. In particular, they show that even if the conditional mean return is constant (i.e.…”