An Application of Portfolio Mean-Variance and Semi-Variance Optimization Techniques: A Case of Fiji

In this paper, we apply the Markowitz portfolio optimization technique based on mean-variance and semi-variance as measures of risk on stocks listed on the South Pacific Stock Exchange, Fiji. We document key market characteristics and consider monthly returns data from SEP-2019 to FEB-2022 (T = 30) of 17/19 listed companies on the stock exchange to construct various portfolios like 1/N (naive), maximum return, and market and minimum-variance with and without short-selling constraints. Additionally, we compute each stock's beta using the market capitalization-weighted stock price index data. We note that well-diversified portfolios (market portfolio and minimum-variance portfolio) with short-selling constraints have relatively higher expected returns with lower risk. Moreover, well-diversified portfolios perform better than the naive and maximum portfolios in terms of risk. Moreover, we find that both the mean-variance and the semi-variance measures of risk yields a unique market portfolio in terms of expected returns, although the latter has a lower standard deviation and a higher Sharpe ratio. However, for the minimum-variance portfolios and market portfolios without short selling, we find relatively higher returns and risks using the mean-variance than the semi-variance approach. The low beta of individual stock indicates the low sensitivity of its price to the movement of the market index. The study is an initial attempt to provide potential investors with some practical strategies and tools in developing a diversified portfolio. Since not all the portfolios based on mean-variance and the semi-variance analyses are unique, additional methods of investment analysis and portfolio construction are recommended. Subsequently, for investment decisions, our analysis can be complemented with additional measures of risk and an in-depth financial statement/company performance analysis.