The role of mean variance analysis in the area of portfolio management - Essay Example

It is therefore computed as the Variance of the returns: Var(R) = [R-E(R)]2 However, the importance of means and variances of assets are far more apparent in the construction and management of an investment portfolio. Essentially an investment portfolio is best understood simply as a combination of individual assets/investments that are held together by the investor at any point in time. But, the importance of risks and returns of individual assets is limited to the significance it has for the risk and return of the entire portfolio (Linter, 1965).

It is how the portfolio performs that is the primary concern for the investor. Presumably, due to the additive property of means, the returns from the portfolio equal a simple weighted average of the returns on the individual securities that constitute the portfolio. We can calculate expected returns from a portfolio of investments as functions of probable returns from the portfolio given the probability distributional properties of the returns or alternatively as weighted averages of expected returns of the individual returns.

The weights on the expected returns for are simply the shares of wealth invested in each asset as a proportion of the total wealth invested on the portfolio (Markowitz, 1952). The variance of the portfolio however is less than the weighed average of the variances of the individual investments provided the returns to these investments are not independent, i.e., their correlation is not zero. Since the objective of creating a portfolio is to minimize risks through combining assets with correlated returns, the variance of the portfolio typically is smaller than the weighted average of the individual investment variances.

The implication of this outcome is that risk can be lowered for any given return by diversifying the portfolio since the variance of the total portfolio includes additional covariance terms and more negatively related assets imply a smaller value for this term (Sharpe, 1964). For a portfolio with more than 2 assets, the portfolio risk is captured by the variance-covariance matrix of the returns of the portfolio. The investor’s problem is to maximize the expected returns from a portfolio for a given level of risk or alternatively minimizing the risk subject to a given expected portfolio return.

This can be reformulated as a problem of choosing the weights on the individual assets to minimize the variance of the portfolio for a given expected return. The set of weights that ensure this comprises the efficient set. Theories of optimal portfolio selection are concerned with constructing the most optimal set of weights for individual assets that ensure maximal returns or minimize risk. Thus, the formulation is that of a constrained optimization problem where either the mean returns of the portfolio are the objective function and the variance serves as the constraint or vice-versa.

Here in lies the importance of Mean-Variance analysis for portfolio management. However, Mean-Variance analysis of portfolio management has the following drawbacks: Prudent investors may be concerned with more than just the mean and the variance of the distribution of returns. The mean and the variance are the first two moments of any distribution and if the returns of the portfolio follow a normal distribution, then it is fully characterized by just the first two mom