Determining the optimal trading strategy of a second tier fund manager under different covariance structures

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June, 2016
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The 2nd-tier fund managers have limited investment capital, making it impossible to invest in all securities on the stock market. However investing in fewer stocks may not present the needed financial base that could withstand the possible financial shocks and guarantee high returns. On the other hand, actuaries can employ actuarial tools such as covariance structure to forecast the prospects of a selected stocks which could complement each other to reduce the probable risk and improve investment output. Fund managers are therefore required to make an informed investment decisions adopting reliable actuarial tools that could minimize the risk that can be associated with investing in fewer stocks. The decision they make on their investments affect returns, and that of their clientèle eventually. The study looked at three different covariance structures: Toeplitz, Autoregressive(1) and Unstructured and the amount to optimally invest in each security under these structures. Correlated and uncorrelated stocks under the different covariance structures on simulation study were studied. Monthly data was taken from companies that deal in AAPL, TNET and BAX from 1st January, 2008 to 31st December, 2012. Kolmogorov - Smirnov and Anderson Darling tests were used to check the distributions of the market data. After a hypothesis testing,the observation was that AAPL, BAX and TNET were from the Normal, Weibull and Weibull distributions respectively with a negative correlation between BAX and TNET. Inferring from the results obtained in this study, investing more than half of the investment capital in the TNET security was considered optimal. In conclusion, this study has demonstrated that fund managers can rake in high returns if more than half of the amount available for investment was put in the TNET security. Additionally, the Toeplitz covariance structure proved efficient in predicting the suitable stocks to invest the 2 tier fund.
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fufillment of the requirement for the degree of M.Phil Actuarial Science,