Application of a Robust Maximum Diversified Portfolio to a Small Economy’s Stock Market: An Application to Fiji’s South Pacific Stock Exchange

In this study, we apply a novel approach of portfolio diversification—the robust maximum diversified (RMD)—to a small and developing economy’s stock market. Using monthly returns data from August 2019 to May 2024 of 18/19 stocks listed on Fiji’s South Pacific Stock Exchange (SPX), we construct the RMD portfolio and simulate with additional constraints. To implement the RMD portfolio, we replace the covariance matrix with a matrix comprising unexplained variations. The RMD procedure diversifies weights, and not risks, hence we need to run a pairwise regression between two assets (stocks) and extract the R-square to create a P-matrix. We compute each asset’s beta using the market-weighted price index, and the CAPM to calculate market-adjusted returns. Next, together with other benchmark portfolios (1/N, minimum variance, market portfolio, semi-variance, maximum skewness, and the most diversified portfolio), we examine the expected returns against the risk-free (RF) rate. From the simulations, in terms of expected return, we note that eight portfolios perform up to the RF rate. Specifically, for returns between 4 and 5%, we find that max. RMD with positive Sharpe and Sortino (as constraints) and the most diversified portfolio offer comparable returns, although the latter has slightly lower standard deviation and downside volatility and contains 94% of all the stocks. Portfolios with returns between 5% and the RF rate are the minimum-variance, the semi-variance, and the max. RMD with positive Sharpe; the latter coincides with the RF rate and contains the most (94%) stocks compared to the other two. An investor with a diversification objective, some risk tolerance and return preference up to the RF rate can consider the max. RMD with positive Sharpe. However, depending on the level of risk-averseness, the minimum-variance or the semi-variance portfolio can be considered, with the latter having lower downside volatility. Two portfolios offer returns above the RF rate—the market portfolio (max. Sharpe) and the maximum Sortino. Although the latter has the highest return, this portfolio is the least diversified and has the largest standard deviation and downside volatility. To achieve diversification and returns above the RF rate, the market portfolio should be considered.