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

Abstract

W e consider three sets of phenomena that feature prominently in the financial economics literature: (1) conditional mean dependence (or lack thereof) in asset returns, (2) dependence (and hence forecastability) in asset return signs, and (3) dependence (and hence forecastability) in asset return volatilities. We show that they are very much interrelated and explore the relationships in detail. Among other things, we show that (1) 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; (2) it is statistically possible to have sign dependence without conditional mean dependence; (3) 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, so that traditional market timing tests are best viewed as tests for sign dependence arising from variation in expected returns rather than from variation in volatility or higher moments; (4) sign dependence is not likely to be found in very high-frequency (e.g., daily) or very low-frequency (e.g., annual) returns; instead, it is more likely to be found at intermediate return horizons; and (5) the link between volatility dependence and sign dependence remains intact in conditionally non-Gaussian environments, for example, with time-varying conditional skewness and/or kurtosis.

Irrational fads, short‐term memory emulation, and asset predictability

“…The results in this work are also in accordance with the conclusions reached by Christoffersen and Diebold (2006). The profitability of the trading rules as well as the sign rate indicator improves substantially over the bear market period against a B&H strategy, as implied by the aforementioned paper for a higher volatility period that characterize the post‐bubble time interval in our test.…”

“…In this study, the trading implications of conditional volatility are examined within a broader framework as concerns the nonlinear functional form of the forecast generating mechanism as well as the presence of past returns that might have forecasting power. Christoffersen and Diebold (2006) in their paper show that volatility dependence produces sign dependence and therefore forecasting ability, as long as expected returns are nonzero. The intuition behind this relationship is that volatility changes will alter the probability of observing negative or positive returns.…”

“…The profitability of the trading rules as well as the sign rate indicator improves substantially over the bear market period against a B&H strategy, as implied by the aforementioned paper for a higher volatility period that characterize the post‐bubble time interval in our test. Moreover, for bear markets this improvement may not be depicted strongly into the results of the HM and PT tests since they have no power to detect sign dependence in the face of no zero expected returns (Christoffersen & Diebold, 2006).…”

Efficient estimation for time series following generalized linear models

“…Empirical evidence suggests out‐of‐sample predictability of excess stock market returns based on macroeconomic variables ranges from weak to non‐predictable. Christoffersen & Diebold () and Christoffersen et al. () argued that the sign of stock returns may be predictable even when the returns are not themselves predictable.…”

Day-of-the-Month Effects in the Performance ofMomentum Trading Strategies in the ForeignExchange Market

“…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.…”