Portfolio optimization based on Markowitz mean variance model considering PLI index an‎d prospect theory(case study: crypto currencies)

1/1/1900 12:00:00 AM

With the expansion of the cryptocurrency market an‎d the increase in uncertainties an‎d fluctuations in this area, traditional portfolio optimization models no longer respond to the complexities of investor behavior. The classic Markowitz model, which is based on the assumptions of economic rationality an‎d stability of investor behavior, has limited ability to analyze an‎d predict real decisions of individuals in critical an‎d volatile conditions. In this regard, the use of behavioral approaches such as prospect theory an‎d the Perceived Loss Index (PLI), as tools for modeling psychological factors, alongside traditional frameworks, can provide a solution to improve investment decision-making. In this study, a hybrid portfolio optimization model is presented that combines prospect theory an‎d the PLI index with the Markowitz model. The purpose of this model is to consider investorsʹ behavioral preferences, including loss aversion, the effect of recent experiences, an‎d emotional reactions to market fluctuations, in the investment decision-making process. The designed model was tested under different investor behavioral conditions an‎d compared with traditional an‎d semi-behavioral models. To eva‎luate the model, a case study was conducted on three major cryptocurrencies, including Bitcoin (BTC), Ethereum (ETH), an‎d Binance Coin (BNB). Weekly price data of these assets was extracted from Yahoo Finance website for a six-month period. Expected returns, covariance matrix, an‎d PLI index values ​​were calculated using these data. The optimization problem was solved using SLSQP (Sequential Least Squares Programming) algorithm in Python an‎d Google Colab environment. Next, eight different behavioral scenarios were modeled by varying the loss aversion coefficient (λ) to simulate different investor attitudes towards risk an‎d loss. The overall results of the research show that the simultaneous use of behavioral theories an‎d subjective risk assessment tools can improve portfolio diversification, reduce perceived risk, an‎d increase the modelʹs fit with market realities. The proposed model is not only scientifically structured from a statistical perspective, but also psychologically consistent with real investor behavior, providing an efficient framework for financial decision-making, especially in high-risk markets such as cryptocurrencies.

مالي رفتاري تئوري چشم انداز بهينه سازي پورتفوي زيان گريزي ريسك , مالي رفتاري , تئوري چشم انداز , بهينه سازي پورتفوي , زيان گريزي , ريسك

1. Behavioral finance , 2. Perspective theory , 3. Portfolio optimization , 4. loss aversion , Risk

fatemeh poorhashemi

Dr.ahmad makouei