Asset allocation is one of the most important and difficult challenges investors face, but thanks to Harry Markowitz we have an elegant and widely accepted theory to guide us. In his classic article “Portfolio Selection,” Markowitz reasoned that investors should not choose portfolios that maximize expected return, because this criterion by itself ignores the principle of diversification.^{1} He proposed that investors should instead consider variances of return, along with expected returns, and choose portfolios that offer the highest expected return for a given level of variance. Markowitz called this rule the E‐V maxim.

Markowitz showed that a portfolio's expected return is simply the weighted average of the expected returns of its component asset classes. A portfolio's variance is a more complicated concept, however. It depends on more than just the variances of the component asset classes.

The variance of an individual asset class is a measure of the dispersion of its returns. It is calculated by squaring the difference between each return in a series and the mean return for the series, and then averaging these squared differences. The square root of the variance (the standard deviation) is usually used in practice because it measures dispersion in the same units in which the underlying return is measured.

Variance provides a reasonable gauge of the risk of an asset ...

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