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Computations in determining a financial proxy which optimizes de-trended stochastic asset prices under fixed-mix portfolio strategies

The performance of portfolios of a fixed-rate asset and a risky asset of major companies in a South African market index the FTSE/JSE with strategies which rebalances fixed proportions of wealth in every rebalancing period is analysed in a long term. Recent findings in portfolio management theory by Dempster, Evstigneev and Schenk-Hoppé (2010, 2008, 2007, 2003) and by Browne (1988) note optimality of fixed-mix portfolios which assert fast exponential growth in stationary markets. A quantitative analysis is performed to analyse quantifiable measures in order to optimize the application of self-financing constant rebalanced portfolio strategies that contribute to the financial engineered prospects suggested by Dempster et al. (2010) for fixed-mix portfolios. The comparative performance of fixed-mix portfolios with a proxy strategy and without proxy strategy relative to a buy and hold strategy shows the superiority of fixed-mix portfolios in generic market conditions. The research extends the utilization of constant rebalanced self-financing portfolio investment strategies by assessing the market price of risk under the mean-variance model of Markowitz (1952). Effective implementation tactics of the strategy are examined by focusing on the market risk and the financial risk. The frequent reversals and trending of stochastic asset prices in the financial market are analysed to adjust the market price of risk by considering tradable financial securities to determine the financial proxy of de-trending. The proxy hypothesis which evaluates the stationary financial condition in a fixed-mix portfolio is validated by an option-based myopic strategy using a lookback straddle option. A myopic strategy is a strategy which considers a single period ahead, Fabozzi, Forcardi and Kolm (2006). The realised growth under a financial proxy is found to have a linear strategic asset allocation with a low degree of concavity relative to a buy and hold performance in the market risk of self-financing portfolio strategies.