An Apparent Paradox

In the previous post, I noted that a stock's long-term return is approximately its expected return less one-half its variance of return. This applies to portfolios, too.

Consider a stock market made up of stocks that all have the same expected return and the same variance of return. Then each stock has the same long-term return, approximately equal to its expected return less one-half its variance of return.

Now consider a portfolio of these stocks. The portfolio's expected return is the same as each stock's expected return. But, due to diversification, the portfolio's variance of return is less than each stock's variance of return. Consequently, the portfolio's long-term return exceeds that of the stocks.

Apparently, a portfolio's long-term return can be greater than the long-term returns of its stocks!