Diversification is behind the equation 1 + 1 = 1.41. Let's start with a simple example. Suppose you make the investment described in the example in Chapter 1 that pays out $1 with a 50 percent probability and $3 with a 50 percent probability. The expected payout will be $2 [(50% × $1) + (50% × $3)]. The standard deviation (the most common measure of volatility) of the payout is defined as the square root of the expected squared deviation from the mean. (Chapter 1 uses the average absolute return rather than the standard deviation, for simplicity.) Under either outcome, the squared deviation from the mean of $2 is $1, so the expected squared deviation is $1, and the square root of this is also $1.
Now suppose you invest ...