This paper takes into account a set of risky stocks from the Indian equity market with a view to constructing efficient frontiers and examining the optimal portfolio behavior under various constraints. The paper uses Sensex 30 stocks daily prices along with daily BSE Sensex index price data as market benchmark for 10 years starting from 2006 in constructing and optimizing portfolio with the minimum variance and maximum return under different constraints. The paper makes an attempt to identify the efficient frontiers by estimating the average return of the portfolio and iteratively minimizing the standard deviation or risk of the portfolio to the minimum possible level. It is observed that the efficient frontiers shift towards left as constraints are relaxed in its formation. So, according to the study, the most constrained efficient frontier is the one with value-at-risk at 95% and short sales not allowed. The most relaxed efficient frontier is the one with short sales allowed, as it is to the leftmost position in the combined graph created, as shifting of the efficient frontier to the left in the return-risk graph means same returns for lower levels of risk.

Asset allocation is a problem faced by every rational investor. When making investment decisions, a rational investor has to seek a balance between risk and returns. Markowitz (1952) published his seminal work on portfolio selection, in which he established a framework for investment decisions. In the single-period Markowitz model, the rational investor maximizes the expected return of the portfolio and minimizes the risk, measured by the variance of portfolio returns. This theory came to be known as the Markowitz Portfolio Theory (MPT). It assumes that rational investors are risk-averse, meaning that given two portfolios that offer the same expected return, rational investors will prefer the less risky one. An investor can reduce portfolio risk simply by holding combinations of instruments that are not perfectly positively correlated. As part of this study, portfolios were constructed using the Markowitz efficient frontier approach. In this method, portfolios are built to enhance the expected return to their maximum for a provided level of risk as it views portfolio construction in terms of expected return and the corresponding risk. The Markowitz approach works with a few presuppositions: (i) Risk of a portfolio is established on the variance of returns from the described portfolio; (ii) A rational investor is hostile to risk; and (iii) A rational investor either augments his portfolio’s return for a specified level of risk or maximizes his return for the least possible risk. The risk and return are the most important concepts in financial studies. In fact, they are the basics of the modern finance theory, where the mean rate of return is the summation of the distinct one-period rates of return divided by the count of periods, and the risk is the variation in returns caused by the volatility of the stock prices. There are two gauges of this dispersion: variance and standard deviation. Standard deviation is defined as the square root of the variance.

Financial Risk Management Journal, Examination of Efficient, Frontier Under Constraints, Indian Equity Market