Use of asymmetric loss functions for risk management in portfolio allocation

Abstract

Markowitz framework forms the basis of almost all studies on the stock market data related to portfolio allocation. It rests on the implicit assumption that the outcomes of the positive and negative returns of the same magnitude are valued equally by an investor.However this may not be true in real life. An investor may wish to earn a certain profit from his portfolio, but may be ready to accept a loss only till a fraction of that amount, should the market move in a direction opposite to his expectation.In such a situation, symmetric loss function which is the base of the Markowitz framework is no longer appropriate for modeling the portfolio allocation problem.This is where the study of asymmetric loss functions becomes important. in this report,I have examined the two significant asymmetric loss function - The lin lin squared loss function and the index squared loss function . These function may be more appropriate for modeling the portfolio allocation problem of a risk averse investor . The report studies in detail the lin- lin squared loss function and gives a framework for portfolio allocation for a two stock portfolio when the two stocks are correlated and when they are not. The report also gives the modified markowitz framework developed on the understanding gained from the asymmetric loss functions. A model has been developed for the portfolio allocation of a two stock portfolio using visual basic and excel . Real life data for two stocks have been fed in and the results for different investor preferences have been explained.