Dr. Harry M. Markowitz is credited with developing the first modern portfolio analysis model. It provides a theoretical framework for the analysis of risk-return choices. The concept of efficient portfolios has been enunciated in this model A portfolio is efficient when it yields the highest return for a particular level of risk or minimizes risk for a specified level of expected return.

The Markowitz model makes the following assumptions regarding investor behavior:

– Investors consider each investment alternative as being represented by a probability distribution of expected returns over some holding period.

– Investors maximize one period’s expected utility and possess a utility curve, which demonstrates the diminishing marginal utility of wealth.

– Individuals estimate risk on the basis of the variability of expected returns.

– Investors base decisions solely on expected return and variance of returns only.

– At a given risk level, higher returns are preferred to lower returns. Similarly, for a given level of expected returns, investors prefer less risk to more risk.

**Simple Markowitz Portfolio Optimization**

It is possible to develop a fairly simple decision rule for selecting an optimal portfolio for an investor that can take both risks and return into account. This is called a risk-adjusted return. For simplicity, it can be termed the utility of the portfolio for the investor in question. The utility is the expected return of the portfolio minus a risk penalty. This risk penalty depends on portfolio risk and the investor’s risk tolerance.

**The Risk Penalty**

The more risk one must bear, the more undesirable is an additional unit of risk. Theoretically, and as a computational convenience, it can be assumed that twice the risk is four times as undesirable. The risk penalty is as follows:

Risk penalty = Risk squared/Risk tolerance

Risk squared is the variance of the return of the portfolio. Risk tolerance is a number from zero through 100. The size of the risk tolerance number reflects the investor’s willingness to bear more risk for more return. Low (high) tolerance indicates low (high) willingness. Risk penalty is less as tolerance is increased.

**Standard Deviation**

All points on this arc provide a superior combination of risk and return to other combinations with the shaded area, which represent attemptable portfolios. Each portfolio has its own combination of risk and return. The investor’s final choice out of the range depends on his taste.

**Limitation of Markowitz Model**

The Markowitz approach requires several inputs for portfolio analysis. These are the expected return of the securities, variances of their return, and covariances. Calculation of efficient portfolios is easy when the number of securities in the portfolio is two or three. As the number of securities in the portfolio increases, which indeed is the case in real-life situations, the amount of calculations required to be done becomes enormous. Further, in the real world, portfolio analysts do not keep track of correlations between stocks of diverse industries. As such, correlating security to a common index is much more convenient than correlating to a large number of individual securities.

Secondly, the assumption that correlation in the values of two securities depends on the characteristics of these two securities alone is not valid. In fact movement in the value of securities is affected by a variety of other factors. A stock index is a more representative benchmark that incorporates the general economic conditions more authentically.