Mean Variance Optimization
Mean-Variance Analysis
Mean-variance portfolio theory is based on the idea that the value of investment opportunities can be meaningfully measured in terms of mean return and variance of return. Markowitz called this approach to portfolio formation mean-variance analysis. Mean-variance analysis is based on the following assumptions: 1. All investors are risk averse; they prefer less risk to more for the same level of expected return. 2. Expected returns for all assets are known. 3. The variances and covariances of all asset returns are known. 4. Investors need only know the expected returns, variances, and covariances of returns to determine optimal portfolios. They can ignore skewness, kurtosis, and other attributes. 5. There are no transaction costs or taxes.
The Mean-Variance Approach
The mean-variance theory postulated that in determining a strategic asset allocation an investor should choose from among the efficient portfolios consistent with that investor’s risk tolerance amongst other constraints and objectives. Efficient portfolios make efficient use of risk by offering the maximum expected return for specific level of variance or standard deviation of return. Therefore, the asset returns are considered to be normally distributed. Efficient portfolios plot graphically on the efficient frontier, which is part of the minimum-variance frontier (MVF). Each portfolio on the minimum-variance frontier represents the portfolio with the smallest variance of return for given level of expected return. The graph of a minimum-variance frontier has a turning point that represents the Global Minimum Variance (GMV) portfolio that has the smallest variance of all the minimum-variance portfolios. Economists often say that portfolios located below the GMV portfolio are dominated by others that have the same variances but higher expected returns. Because these dominated portfolios use risk inefficiently, they are inefficient portfolios. The portion of
Mean-variance portfolio theory is based on the idea that the value of investment opportunities can be meaningfully measured in terms of mean return and variance of return. Markowitz called this approach to portfolio formation mean-variance analysis. Mean-variance analysis is based on the following assumptions: 1. All investors are risk averse; they prefer less risk to more for the same level of expected return. 2. Expected returns for all assets are known. 3. The variances and covariances of all asset returns are known. 4. Investors need only know the expected returns, variances, and covariances of returns to determine optimal portfolios. They can ignore skewness, kurtosis, and other attributes. 5. There are no transaction costs or taxes.
The Mean-Variance Approach
The mean-variance theory postulated that in determining a strategic asset allocation an investor should choose from among the efficient portfolios consistent with that investor’s risk tolerance amongst other constraints and objectives. Efficient portfolios make efficient use of risk by offering the maximum expected return for specific level of variance or standard deviation of return. Therefore, the asset returns are considered to be normally distributed. Efficient portfolios plot graphically on the efficient frontier, which is part of the minimum-variance frontier (MVF). Each portfolio on the minimum-variance frontier represents the portfolio with the smallest variance of return for given level of expected return. The graph of a minimum-variance frontier has a turning point that represents the Global Minimum Variance (GMV) portfolio that has the smallest variance of all the minimum-variance portfolios. Economists often say that portfolios located below the GMV portfolio are dominated by others that have the same variances but higher expected returns. Because these dominated portfolios use risk inefficiently, they are inefficient portfolios. The portion of