We studied several different methods of calculating an average. For example, if using historical rates of return, we can calculate either an Arithmetic Mean (AM) or a Geometric Mean (GM). If using projected future rates of return, we calculate an Expected Value instead of either the AM or GM. Assume we have made the following set of projections regarding the possible rates of return for a company we are analyzing:

State of the Economy Probability Return

Recession 25% 2%

Normal 50% 10%

Boom 25% 20%

What is the standard deviation of the expected returns for this stock?