Portfolio optimization using Single Index Model and historical Value at Risk (VaR) and Tail Value at Risk (TVaR):An empirical study on the Standard and Poor’s Sri Lanka 20 (S&P SL20)

The core of modern investment management practice involves portfolio optimization and risk measurement, particularly when markets move erratically, such as with emerging economies. The Markowitz model provides a well-established theoretical framework, but it requires extensive calculation, which can be a barrier. The Single Index Model (SIM) provides another viable alternative with fewer problems. The practical application, however, still must be extensively researched, particularly regarding to Sri Lanka and its Standard and Poor’s Sri Lanka 20 (S&P SL20) Index. In this paper, the optimization of the portfolios is carried out through the S&P SL20 Index using the Single Index Model, and the impact that the selection of returns has on the measurement of simple returns or log returns is examined. The paper also examines the evaluation of the risk associated with the portfolio through the historical estimation of Value at Risk (VaR) and its corresponding Tail Value at Risk (TVaR) The selection of time intervals is based on the performance of the stock market from February 1, 2022, to November 21, 2025, which includes the post-pandemic era, the 2022 Sri Lankan economic crisis, and the subsequent recovery. The results indicate that different return measures do not substantially affect the selection of assets, but they do affect the results in terms of how much weight each asset receives, along with differences in terms of expected return and risk calculations. There is a slightly better trade-off between risk and return in portfolios using simple returns, and a more statistically stable selection in portfolios using log returns. TVaR values are also significantly higher in all portfolios than VaR values, which shows a higher risk in these difficult financial environments. Overall, it supports using SIM in Sri Lanka and highlights the importance of specifying asset return and risk measures in dealing with emerging markets.