Investment strategies under risk measures

Abstract

Risk measure and optimal portfolio selection are both important issues in modern finance. In recent years several continuous-time optimal dynamic strategies have been developed for attaining various goals over an invest- ment horizon and in mean time various risk measures have been proposed in the literature. However, the risks associated with these continuous-time strategies are poorly understood and the issues of comparing performance of these strategies under various risk measures have not received much atten- tion. The aim of this thesis is to fill this gap. Depending on whether to guarantees the portfolio value above a lower bound at all times, strategies of portfolio management can be classified into two classes: the tamed strategy and the untamed strategy. With a focus on bankruptcy probabilities under various well-known continuous-time strate- gies, we show that long-term investment following the untamed strategies will surely lead to bankruptcy no matter how small the expected return rate is set. For the tamed strategies, each has a unique threshold value in the expected return rate. When following them in long-term investments, the bankruptcy will never occur or surely occur, depending on whether the ex- pected return rate is set below or above the threshold value. Bankruptcy probabilities under finite investment horizon are also studied. These results show that for a long-term investor, it is very important to choose a tamed strategy and set the expected return rate below the bankruptcy threshold. We also compare behaviors of these seemingly different tamed strategies in various parameter regions and reveal close connections among them. Downside risk and drawdown risk measures are two important measures which quantify the risk characteristics of a portfolio. In the latter part of this thesis, we focus on the performances of three tamed strategies with the expected return rate below the bankruptcy threshold. We examine in detail their risk characteristics in long-term investment and portfolio frontiers under various downside and drawdown risk measures. We determine that for a given downside or drawdown risk measure, which strategy among the three performs best in various parameter regions. An investigation on the correlation among different risk measures has also been carried out.

Date of Award	3 Oct 2006
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Qiang ZHANG (Supervisor) & Jonathan James WYLIE (Co-supervisor)