Analysis of the Single Index Model Optimal Portfolio Using the Sharpe and Treynor Measurement Index Related to Covid-19

Abstract

The optimum portfolio is the preferred choice among investors for determining the most favorable combination of projected return and risk. This study seeks to ascertain the ideal portfolio performance of companies in the IDX30 index on the Indonesia Stock Exchange and know the value of the stock weight in each period, over three specific periods: before to the Covid-19 pandemic, at the peak of Covid-19 cases, and after a decline in Covid-19 instances. Stocks listed on IDX30 are stock companies that have high liquidity and large capitalization value on the capital market. The pre-Covid-19 era spanned from March 2019 to February 2020. The time of peak Covid-19 occurrences occurred from April 2021 to March 2022. Lastly, the period of declining Covid-19 instances extended from September 2022 to August 2023. The study employs the Single Index Model (SIM), using the Sharpe and Treynor measurement indices. The SIM will identify the relationship between the returns from each security and market returns to construct a portfolio. Meanwhile, Sharpe and Treynor Index measures the performance of portfolio. Based on the results of the analysis of optimal portfolio formation from 30 samples of IDX30 stocks, 4 stocks were obtained (ARTO, BBCA, BBRI, and BRPT) in the period before the Covid-19 pandemic, 14 stocks (ADRO, AKRA, ASII, BBCA, BBNI, BMRI, EMTK, ESSA, INCO, ITMG, MDKA, PTBA, TLKM, and UNTR) in the period when Covid-19 cases were peaking, and 7 stocks (AKRA, AMRT, BBCA, BBNI, BMRI, BRPT, and MEDC) in the period when Covid-19 cases were sloping. The Sharpe measurement index assessment had an average value in the period before the Covid-19 pandemic 1,7836; in the period when Covid-19 cases peaked it was 1,6051, and in the period when Covid-19 cases were sloping it was 0,7236. Meanwhile, the Treynor measurement index had an average value of in the period before the Covid-19 pandemic 0,8507; in the period when Covid-19 cases peaked it was 0,4095; and in the period when Covid-19 cases sloped it was 0,1317. The best period that has the highest Sharpe and Treynor index values is the period before the Covid-19 pandemic. The expected return value of the portfolio that was formed was 0,0601 in period I, 0,0509 in period II, and 0,0210 in period III. Meanwhile, the portfolio risk formed in period I was 0,1086, in period II it was 0,0150, and in period III it was 0,0089.

Keywords

• single index model
• sharpe
• treynor.