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.
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.