The distribution of terminal wealth under dynamic mean-variance optimal investment strategies

In this talk, we compare the distributions of terminal wealth obtained from implementing the optimal investment strategies associated with the different approaches to dynamic mean-variance (MV) optimization available in the literature. This includes the pre-commitment MV (PCMV) approach, the dynamically optimal MV (DOMV) approach, as well as the time-consistent MV approach with a constant risk aversion parameter (cTCMV) and wealth-dependent risk aversion parameter (dTCMV), respectively. For benchmarking purposes, a constant proportion (CP) investment strategy is also considered. To ensure terminal wealth distributions are compared on a like-for-like basis, we assume that an investor, otherwise agnostic about the philosophical differences of the underlying approaches to dynamic MV optimization, requires that the same expected value of terminal wealth should be obtained regardless of the approach. We present first-order stochastic dominance results proving that for wealth outcomes below the chosen expected value target, the cTCMV strategy always outperforms the DOMV strategy, and an appropriately chosen CP strategy always outperforms the dTCMV strategy. We also show that the PCMV strategy results in a terminal wealth distribution with fundamentally different characteristics than any of the other strategies.

Short Bio: Pieter van Staden is a PhD student at UQ studying Mathematical and Computational Finance with Dr Duy-Minh Dang as supervisor. Pieter’s PhD is concerned with the numerical solution of portfolio optimisation problems arising from mean-risk objectives (risk being measured by for example variance, quadratic variation, or conditional Value-at-Risk), under realistic modelling assumptions and investment constraints. Prior to his PhD studies, Pieter completed a BEng (Industrial Engineering) and a BSc (Hons) Financial Engineering at the University of Pretoria (South Africa), as well as a MSc (Mathematics of Finance) at the University of Oxford. In addition, he has held financial risk management positions in both retail and investment banking. For the last 4 years prior to the commencement of PhD studies, Pieter managed the team of actuarial and quantitative analysts responsible for the methodology and maintenance of all Credit Risk and Credit Pricing models used within Nedbank Corporate and Investment Bank (Nedbank CIB) in South Africa.