Question

Essay

Selection of Asset Portfolio by Markowitz model

Answer 1

Selection of Asset Portfolio by Markowitz model

Individuals vary widely in their asset preferences and risk tolerance. Their income, expenditures and investment requirements vary from individual to individual. Given these, the portfolio selection is not a simple choice of any one portfolio or portfolios, but a right combination of portfolios.

Markowitz model of portfolio analysis yields an efficient frontier which comprises of a set of efficient portfolios. He used the technique of quadratic programming for calculations and selection of assets in a portfolio in an efficient manner. A portfolio is said to be efficient if it offers the maximum expected return for a given level of risk and if it offers the minimum risk for a given level of expected return. Therefore, a Markowitz efficient set is diversification of assets, which lowers portfolio risk.

Assumption of Markowitz Model

1. Investors are risk averse and thus prefer expected return and have a dislike for risk.
2. Investor would like to get the highest possible return for a given level of risk or would like to minimize the risk for a given expected rate of return.
3. Investors make their investment decisions based on expected return and the variance.
4. The markets are efficient and absorb the information quickly and perfectly.

Example:

Suppose you have three portfolios A, B, C with risk and return characteristics as below:

If you are to choose between portfolios A & B, you would choose portfolio A since it gives you the same return as B, but has a lower risk than B. Thus, portfolio A dominates B and is superior or efficient. In the same way, portfolio C dominates B. If one can identify all such efficient portfolios and plot them, one will get what is called the efficient frontier. In the below given figure, 'EF' is the efficient frontier which is the set of efficient portfolios. Portfolios lying above the efficient frontier are desirable but not available. Portfolios below the efficient frontier are attainable but not desirable since they are dominated by efficient portfolios. Conclusion

The key point of the Markowitz analysis is that the risk of a portfolio of risky assets depends on the asset weights and the standard deviations of the asset’s returns and crucially on the correlation of the asset returns. Other things being equal, higher the correlation between asset returns the higher the portfolio standard deviation. When assets are perfectly positively correlated, there is no diversification benefit. Hence as the correlation decreases, the benefits of diversification increase.

The optimal portfolio for a specific investor can be represented as the point where the investor’s highest attainable indifference curve is tangent to the efficient frontier. The place where each investor’s optimal portfolio lies on the efficient curve depends on that investors degree of risk aversion (indicated by the slope of the tangent indifference curve).

The company related and unsystematic risk can be reduced by diversification into various assets and securities whose variability is different.