Mean-variance analysis gives investors a framework to assess the tradeoff between risk and return as mean-variance analysis quantifies the relationship between expected return and portfolio variance (or standard deviation).

Mean-variance analysis is the theoretical foundation of Modern Portfolio Theory established by Professor Harry Markowitz and much of the material covered in this module traces its roots concept.

Mean-Variance Assumptions

The assumptions underlying the mean-variance analysis are summarized below:

• Investors are risk averse in that they prefer higher return for a given level of risk (variance, standard deviation), or they want to minimize risk for a given level of returns. The degree of risk aversion may vary from investor to investor

• Example: An investor is presented with two portfolios:

• Portfolio A offers 12% annual return with 25% standard deviation;

• Portfolio B offers 12% annual return with 20% standard deviation;

• A risk averse investor will choose portfolio B.

• Expected returns, variances, and covariances for all assets are known by all investors.

• Investment returns are normally distributed so only returns, variances, and covariances are needed to derive the optimal portfolio.

• There are no transaction costs and no taxes. So, before-tax and after-tax returns are the same making all investors equal.

The mean-variance analysis is used to identify optimal/efficient portfolios.