Investigation into optimal portfolio allocation of stocks having non-normal returns

Abstract

Abstract Introduction and context description: According to the traditional asset pricing methods the returns of stocks are assumed to be normally distributed with mean and standard deviation in these cases the mean and the standard deviation in these cases, the mean and the standard deviation will completely characterize the entire distribution. However, it has been observed that some stocks returns do not follow a normal distribution. In such cases, the above method may not necessarily result in an optimal allocation. Hence we propose to probe into this area of stocks with non-normally distributed returns and investigate alternate measures to perform optimal portfolio allocation of investment. 1) Research questions: To investigate the optimal portfolio allocation in case of stocks with non-normal returns using measures of central tendency other than mean return and measures of dispersion other than return variance. To compare the results obtained from the above with those obtained using mean returns and variance as measures of return and variability respectively. 2) Methodology; We started by surveying literature in the following fields. Methods of describing skewed distributions mathematically. Methods of portfolio allocation We then identified alternate measures appropriate for characterizing the distribution of returns of the above identified stocks. Using the alternate parameters identified we tried to allocate investment between 2 stocks. We then compared the portfolios created by the proposed method and by the traditional method with using different performance measure and analyzed the findings. Findings: Based on the experiments carried out the following important things were noticed (exhibit5) In cases in which both the stocks have non normally distributed stock returns the VaR performance of the more or less stable in the new method whereas the wealth fluctuated from very low to very high in the traditional method. The new method performed far better in cases where both the stocks were poised to make significant losses. In fact, it made some profit at the end of the investment horizon whereas under similar situations the traditional method made significant losses. Limitations of the study: Did not consider correlated stocks. Was restricted to a small number of stocks Scope for further work: Explore the issue of correlated stocks in this framework . compare the performances of the two methods using other measures of performance evaluation . increase the complexity of the model to include more the three stocks . Look at other measure of risk and return. Key words: Mean various allocation leptokurtic ,median absolute deviation ,value at Risk, Learning’s from the IP process: Importance of dividing the work into objective deliverable schedules importance of regular work on the IP Importance of learning’s achieved from consulting various sources.