INTRODUCTION

An investment in a risky security always includes the possibility of a loss or bad performance. An investor, therefore, would like to explore the issue of risk management in a portfolio, a list of financial assets held by the investor. The major issue here is to maintain a balance of the portfolio, that is, how to choose a combination of the assets so that for a given expected return the overall risk is minimized.

Since the pioneering contribution of Markowitz (1952) the mean-variance model of asset choice has been used extensively in finance. In Chapter 3 we examined the implications of the quadratic utility function that shows a preference for higher expected return and an aversion for variance in the portfolio choice problem with two prospects. But for arbitrary distributions and utility functions it is not possible to define expected utility over expected returns and variances of the prospects. However, the mean-variance model of portfolio choice is immensely popular because of its extensive empirical applications and analytical tractability. It will be shown that the risks of individual assets (variances) in the portfolio are not sufficient to understand the risks of the portfolio itself. The interaction (covariance) between any two assets plays an important role in this context. This chapter, therefore, develops analytical relations between the means and the variances of feasible portfolios.