Mean variance optimisation, stochastic simulation modelling and passive formula strategies for equity investments
Pawley, Mark Gary
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The research is a quantitative study that formulates an approach to future portfolio asset allocations within the South African domestic equity market, and the diversification of assets across global markets, specifically the U.S.A. The research takes the view that investors are rational, have a long term investment horizon and seek investment wealth maximisation by applying a sustainable investment strategy towards the ongoing management of the portfolio. Investors experience a significant negative divergence in investment outcomes relative to the potentially achievable result. This negative divergence is a result of the lack of a strategic approach to, and an understanding of asset allocations, and the lack of a sustainable approach to the management of a portfolio. Repetitive sub-optimal investment performance, below the levels of inflation, is an investment disincentive with negative micro and macro implications. The purpose of the study is therefore to address the issue sub-optimal investment performance through the effective application of a strategy that includes the integration of the mean-variance model through the use of a mean-variance optimiser, using resampled data inputs, the mean reversion of markets, passive investment management, appropriate asset class selection and the ongoing management of a portfolio, using both calendar and contingent rebalancing techniques, and passive formula strategies. The challenge is accordingly to develop a reliable asset allocation model that accommodates past performance, and which is stable enough to produce optimised forward-looking investment portfolios, which are able to address the issue of optimal asset allocation and selection, within a global context, and which produce optimised investment outcomes, taking cognisance of the fact that the future is unknowable and dynamic. The research methodology makes a positivist assumption that something exists and can be numerically tested. In this regard various portfolios are constructed, using passive investment instruments, in accordance with mean-variance model principles, using resampled data inputs to minimise the instability of the mean-variance optimiser. This resampling process is fundamental to the research, and incorporates the use of a stochastic simulator. A unique aspect of the research was solving the issue of multiple market integration particularly when the domestic markets are comprised of multiple asset classes. Finally, the resultant resampled efficient portfolios are compared to control portfolios in order to ascertain whether the resampling process indeed offers a return premium. Due to the dynamic nature of equity markets contingent and calendar rebalancing strategies are applied to the asset allocation in order to maintain an optimal portfolio. This dynamism may necessitate the adjustment of asset allocations. The test for asset allocation optimality takes the form of measuring portfolio outcome correlations to the actual market outcome. Where the portfolio is sub-optimal the asset allocations are redetermined, otherwise the portfolio is merely rebalanced to the original asset allocations. Regarding the management of the portfolio a value averaged passive formula strategy is applied. This process acknowledges that markets may behave stochastically over the short term, therefore a predetermined value line is derived that the portfolio is to achieve. This value line is based on a long term equity premium plus inflation. Should the portfolio breach the value line on the upside a portion of the investment is liquidated, conversely when the portfolio fails to reach the value line the portfolio is elevated to the value line by means of increasing the investment. The results of the research manifest unambiguous results in favour of resampled portfolios. In this regard, therefore, data resampling does seem to produce stable portfolio results that are effective at capturing a higher proportion of future returns than a simple market portfolio. Furthermore, the rebalancing process, although not absolutely perfect, does provide a level of adjustment to the asset allocation to ensure optimality. Finally, management of the portfolio through value averaging unambiguously provides an internal rate of return in excess of a portfolio that is allowed to stochastically rise and fall. In summary, the integration of the identified processes clearly provides a performance premium in excess of alternative approaches, and within a framework that is sustainable from period to period.
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