Suppose you wish to invest a fixed sum of money in to assets that yield returns of X and Y, where X and Y are random quantities. You will invest a fraction in X and the remaining (1 - ) in Y. Because there is variability associated with the returns on these two assets we wish to chooses such that the total risk or variance is minimized. We want to minimize .

Find such that the risk is minimized.

VaraX + (1 - aY