Essays on dynamic portfolio management
Over the last three decades, there has been an increasing interest in the problem of the investor's optimal consumption and portfolio rules. Despite the substantial amount of related literature, there remain many areas for further investigation. The thesis, therefore, addresses a number of important issues relating to the theory and practice of dynamic portfolio strategies. The thesis consists of five essays. The first two essays, Chapters 3 and 4, are concerned with efficient dynamic asset allocation programs under alternative market assumptions. Chapter 3 studies a situation where the simple time-invariant portfolio strategies are efficient and provides a complete characterisation of the strategies using the efficiency arguments. The popularised constant proportion portfolio insurance (CPPI) is embedded as a special case. Chapter 4 relaxes the assumption of a constant interest rate to allow the interest rate to follow a one factor stochastic process. The factor risk premium is then determined in a way that is consistent with the underlying equilibrium. These results are then applied to solve explicitly for an investor's optimal portfolio choice problem under the special case of a Vacisek short rate model and alternative utility functions. The third essay, Chapter 5, relaxes the assumption of a constant equity risk premium to allow the risk premium to vary through time. The evolution of the market risk premium in a representative agent equilibrium (consistent with the Black-Scholes option pricing) is investigated using a unified approach. The presence of dividends and intermediate consumption proves to be the key element that enables us to obtain a stationary economy with decreasing relative risk aversion, a theoretical result that has not be established in the existing literature. The last two essays. Chapters 6 and 7. are concerned with issues of portfolio efficiency and performance measurement. Chapter 6 uses the result from Chapter 5 that, without dividends and intermediate consumption, the market risk premium must satisfy the Burgers' equation, and applies Dybvig's payoff distribution pricing model to measure the inefficiency costs incurred when this condition is violated. The numerical results show that the degree of inefficiency is not very significant, at least for the cases which we postulate, but the findings also reassure negative result predicted from the model. Finally, Chapter 7 proposes a new utility based performance measure that can be applied in the ex-post evaluation of dynamic portfolio strategies. We construct a contingent claim estimation approach to estimate the nearest efficient strategy from a single realisation and then quantify the opportunity cost resulting from the departure of the observed strategy from the nearest efficient one. The numerical examples show that the technique is remarkably robust.