Multi-Objective Linear Programming in Portfolio Selection
The IUP Journal of Financial
Gayatri Biswal, B K Mangaraj and K B Das
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Portfolio theory originally proposed by Markowitz is based on the assumption that the utility of an investor is a function of two factors, viz., mean and variance (or standard deviation) of return. However, the single index model of Sharpe is a statistical representation of return generating process that expresses return on stock in the form of a regression equation. Literature review on investment portfolio management shows that Sharpe’s coefficient is the most commonly used performance measure in the determination of optimal portfolio. Sharpe’s model is a linear programming model of the problem considering ? as the measure of risk. The present paper, building on the above model, proposes a multi-objective linear programming portfolio selection model that ensures a nondominated solution on the efficient frontier based on the outputs of the single index model. Taking Dow Jones Industrial Average (DJIA) as the market index and considering monthly indices along with the monthly prices of 28 securities for the period from March 1999 to March 2015, this model solves a practical portfolio selection problem in a multi-objective framework. The proposed model also shows its superiority over Sharpe’s single index model.
In finance, portfolio selection has always been a challenging task where the fundamental
objective is to combine investments to form a well-diversified portfolio which best serves
and meets the interest of the investors. Markowitz’s (1952) seminal paper was the first to
incorporate risk on investment and considered the effects of diversification when security
risks are correlated (Markowitz, 1999). His insights established that diversification would
reduce risk, but not eliminate it. Hence, he attached enormous importance to portfolio risk
assuming the investors as risk averse and proposed the mean and variance of the portfolio as
the two criteria for portfolio selection, where mean and variance measure portfolio return
and volatility respectively. This led him to postulate that an investor should maximize his
expected portfolio return while minimizing portfolio variance of return.
Financial Risk Management Journal, Dow Jones Industrial Average (DJIA), Single Index Model, Optimal Portfolio Based, Multi-Objective, Linear Programming, Portfolio Selection, Single Index Model.