Narrow Results

Consider a partially informed trader who does not observe the true drift of a financial asset. Under Gaussian price dynamics with stochastic unobserved drift, including cases of mean-reversion and momentum dynamics, we take a filtering approach to solve explicitly for trading strategies which maximize expected logarithmic, exponential and power utility. We prove that the optimal strategies depend on current price and an exponentially weighted moving average (EMA) price, and in some cases current wealth, not on any other stochastic variables. We establish optimality over all price-history-dependent strategies satisfying integrability criteria, not just EMA-type strategies. Thus the condition that the optimal trading strategy reduces to a function of EMA and current price is not an assumption but rather a consequence of our analysis. We solve explicitly for the optimal parameters of the EMA-type strategies and verify optimality rigorously.

This chapter finds that the intraday Nikkei futures returns exhibit different patterns of momentum or mean reversion when changing observation intervals. Using a Markov chains methodology, a significant return momentum was found at 1-min observation interval. However, a significant return mean reversion was found at 10-min observation interval. This switching pattern of momentum to mean reversion is robust to intraday seasonality. Further, the sources that contribute to the high-frequency momentum and mean reversion are explored and it is concluded that large limit orders and the bid-ask effect can play the role.

In this chapter, we explore how long-run mean reversion in stock returns could have significant implication on the forecast or predictability of such returns.

In this chapter, we shall study bonds and their term structures. Bonds are a major class of investment assets distinct from equities, and they have salient features that will be explained. Continuous time stochastic processes are briefly introduced in this chapter to show their usage in modelling bond prices and therefore the resulting credit spreads and yields. Multiple regression analyses involving explanation of credit spreads and of bond returns are described.