Abstract
For the most recent years, risk has become one of the essential parameters in portfolio optimization problems. Today most practitioners and researchers in portfolio optimization have used variance as a standard risk measure. This approach has been found subjective. The Markowitz (1952) mean-variance model considered variance as an adequate portfolio risk measure, and asset returns are multivariate normally distributed and that investors have a quadratic utility function which is subjective too. Other risk measures have been suggested to overcome the limitations of the mean-variance model. This paper analyzes which portfolio optimization models can better explain the optimal portfolio performance (high return, low risk) for the Uganda Security Exchange (USE). We compare Mean-Variance (MV), Mean Absolute Deviation (MAD), Robust Portfolios and Covariance Estimation Models (The Shrinked Mean-Variance (SMV) Models & Alternative Covariance Estimator (ACE) Models) and Mean-Conditional Value-at-Risk (Mean-CVaR) models in terms of the risk and performance. For the computed monthly returns and price data (February 2010 to January 2021) for USE selected stocks, we considered the results to show that Mean-CVaR and ACE portfolios have the highest performance ratio compared to other models. We find that VaR is the best risk measure for portfolio optimization for the USE since it has lower values across all models than other risk measures. It is vital to consider all the available risk measures for a regulator or practitioner to make a good decision since using one can be subjective; as seen in our results, different risk measures yield different results.
Highlights
Covariance, Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) as risk measures to find out which model is efficient for Uganda Security Exchange (USE)
The values of the Covariance, Variance, VaR were lower for Mean Absolute Deviation (MAD) (6), MV (1) and Shrinked Mean Variance (SMV) (2.4.1) models while CVaR has higher values across all portfolios or models except in Mean-CVaR (7) model, this is because the primary objective of Mean-CVaR model is to minimize the CVaR as a risk measure
When we considered all the assets (9) for the Mean-CVaR portfolio to make sure all assets are represented, there was a reduction in the risk, that is when we reduced assets from 9 to 7 assets on the Mean-CVaR portfolio the values for risk measures Covariance, VaR and the CVaR increased
Summary
Modern Portfolio Theory (MPT) Markowitz (1959) laid the groundwork for MPT defining an investor’s portfolio selection problem regarding expected return and variance of return. He postulates that an investor should maximize expected portfolio return while minimizing portfolio variance of return. Since the introduction of Markowitz (1952) Mean-Variance (MV) model, variance has become the most common risk measure in portfolio optimization. This model relies strictly on the assumption that the returns of assets are multivariate normally distributed or the investor’s utility function is quadratic (Hoe et al, 2010). It is observed that in postwar US data, the slope of the mean-standard deviation frontier is much higher than reasonable risk aversion and consumption volatility estimates suggest. Brooks and Kat (2002) show that hedge funds returns are not normally distributed
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