Optimal Rebalancing of Portfolio Weights under Time-varying Return Volatility

This paper considers horizon effects on portfolio weights under time varying and forecastable return volatility. The return volatility is modelled as a GARCH-M, which is general enough to encompass both constant and time varying mean. The analysis confirms earlier results, namely that there are no horizon effects when the stochastic process, that governs asset returns, has constant mean. However, when time varying and forecastable volatility is included in the mean equation, there are horizon effects. The horizon effect arises because the ratio of mean over variance is not constant over time. We show that three features are important for the horizon effect: First, the size of the parameter on conditional volatility in the mean equation. Second, persistence in conditional volatility. Third, the asymmetry in volatility have some effect. In addition the parameter of relative risk aversion is important, the relationship between risk aversion and horizon effects is positive. Portfolio weights increase at a decreasing rate for 2-3 years and the total effect is about 10%.