Portfolio Optimization Considering Behavioral Stocks with Return Scenario Generation

Research by: Michael N. Young, TJ Troy N. Chuahay, Yen-Hsien Lee, John Francis T. Diaz, Yogi Tri Prasetyo, Satria Fadil Persada, & Reny Nadilfatin

Executive Summary

This study extends the application of behavioral portfolio optimization by estimating the return of behavioral stocks (B-stocks). The cause-and-effect relationships of the respective irrational behaviors on the stock price movements and the unique information provided by B-stocks in terms of knowing with a calculated probability when (time duration) a specific effect (e.g., positive cumulative abnormal return) after a certain trigger point (cause of the irrational behavior) is spotted. To fit in the framework of behavioral portfolio optimization, the scenarios used for the optimization are generated utilizing regression analysis, based on which the safety-first scenario-based mixed-integer program is applied to obtain the optimal portfolios. This study also proposes two new types of B-stocks with corresponding operational definitions for herding and ostrich-effect, along with the previously identified over-reaction, under-reaction, and disposition-effect B-stocks. Back-test results show that the portfolios are profitable and can significantly outperform a benchmark and the market.

This research improved upon the existing research on behavioral stock portfolio optimization by providing a variation of the basic framework of portfolio selection and a more accurate way of estimating future returns of the investment pool (B-stocks) through regression analysis. Aside from the disposition effect, over-reaction, and under-reaction B-stocks, 2 other types of B-stocks are also considered. These 2 are herding and ostrich effect B-stocks. The respective operational definition (OD) of these irrational behaviors was identified using the available related literature.

The study used regression equations for a quarter and subsequently updated for the following quarter. For testing purposes, on a given trading day, the Tth day (next trading day) returns of B-stocks that were already on their T – 1st day were estimated through scenario generation using the corresponding regression equations. The top 20 MSCI stocks in the same quarter were also estimated using a single index regression model. The B-stocks and top 20 MSCI stocks were then used as the investment pool on that trading day. Assuming equally likely return scenarios, the generic scenario-based Mathematics of 20 safety-first portfolio selection model was applied to identify the optimal portfolio (MB portfolios). To check the performances of the MB portfolios, the resulting portfolios were compared with the index return of the MSCI Index, Market, exchange-traded fund (ETF), and mutual fund (MF). The MB portfolios were also compared to the M portfolios or those safety-first optimal portfolios considering only MSCI stocks.

Test results show that MB portfolios are superior to the M portfolios, MSCI Index, Market, ETF, and MF. MB portfolios have better return statistics and higher cumulative returns throughout the test period. In addition, the pair-return differences between the MB portfolios and other portfolios are mostly significant. Thus, it can be concluded that MB portfolios can be an excellent alternative investment option and possibly be a generic portfolio selection framework for individual investors.

This research has potential extensions to exploit B-stocks or behavioral stocks further. Identification of the operational definitions of other irrational behaviors can increase the types of B-stocks available to individual investors. It is also interesting to study the interconnection between the operational definition of each B-stocks. Other estimation methods can be done to have a more accurate estimation of returns. Scenario generation methods can be applied to produce reliable return scenarios. Weighting techniques can assign scenario probabilities that reflect investors’ risk attitudes. Lastly, the appropriate optimization model can be used to get the corresponding optimal portfolio for individual investors.

To cite this article:  Young, M.N., Chuahay, T.T.N., Lee, Y.-H., Diaz, J.F.T., Prasetyo, Y. T., Persada, S.F., & Nadilfatin, R. (2022). Portfolio optimization considering behavioral stocks with return scenario generation. Mathematics, 10(22), 4269. https://doi.org/10.3390/math10224269

To access this article: https://doi.org/10.3390/math10224269

About the journal

Mathematics is a peer-reviewed, open-access journal which provides an advanced forum for studies related to mathematics and is published semimonthly online by MDPI. It devotes exclusively to the publication of high-quality reviews, regular research papers, and short communications in all areas of pure and applied mathematics. Mathematics also publishes timely and thorough survey articles on current trends, new theoretical techniques, novel ideas, and new mathematical tools in different branches of mathematics. A submission must be well written and of interest to a substantial number of mathematicians and scientists.

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