Evaluasi Portofolio Optimal IDX30 Berbasis Safety First Criterion Menggunakan Rasio Sharpe, Sortino, dan Treynor

Abdul Maulana; Yundari Yundari; Evy Sulistianingsih

doi:10.37905/euler.v14i2.38342

Evaluasi Portofolio Optimal IDX30 Berbasis Safety First Criterion Menggunakan Rasio Sharpe, Sortino, dan Treynor

Abdul Maulana, Yundari Yundari, Evy Sulistianingsih

Abstract

Constructing an optimal portfolio allows investors to achieve expected returns within an acceptable risk level. Unlike conventional approaches focusing on the risk--return trade--off, the Safety First Criterion (SFC) method minimizes the probability of portfolio returns falling below an investor's specified minimum threshold. This study constructs an optimal stock portfolio from the IDX30 index for the period February 5, 2024--July 28, 2025, using Roy’s, Kataoka’s, and Telser’s criteria, and evaluates performance through Sharpe, Sortino, and Treynor indices. The dataset comprises weekly closing stock prices of IDX30 constituents. The analysis calculates returns and expected returns, selects stocks with positive expected returns, constructs optimal portfolios via the Lagrange multiplier approach for each SFC criterion, and evaluates risk-adjusted performance. This study uniquely applies and compares three SFC criteria simultaneously using three distinct evaluation metrics. Results show that the Roy portfolio comprises ANTM, INDF, and PGAS; the Kataoka portfolio includes BRPT, INDF, and PGAS; and the Telser portfolio consists of ANTM, BRPT, and PGAS. The Roy portfolio generates the highest Sharpe Index (0.1453) and Treynor Index (0.00532), demonstrating superior performance against total and systematic risk compared to other portfolios. Meanwhile, the Telser portfolio achieves the highest Sortino Ratio (0.28566), showing the best capability in managing downside risk. Overall, the Roy portfolio emerges as the most optimal choice because it excels in two out of three evaluation indicators, proving that Roy's criterion produces the best risk--return balance during the study period.

Keywords

IDX30; Roy; Kataoka; Telser; Lagrange Multiplier

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DOI: https://doi.org/10.37905/euler.v14i2.38342