08: Assignment-Risk and Rates of Return 2. Statistical measures of stand-alone risk Remember, the expected value of a probability distribution is a statistical measure of the average (mean) value expected to occur during all possible circumstances. To compute an asset's expected return under a range of possible circumstances (or states of nature), multiply the anticipated return expected to result during each state of nature by its probability of occurrence. Consider the following case: Joshua owns a two-stock portfolio that invests in Happy Dog Soap Company (HDS) and Black Sheep Broadcasting (BSB). Three-quarters of Joshua's portfolio value consists of HDS's shares, and the balance consists of BSB's shares. Each stock's expected return for the next year will depend on forecasted market conditions. The expected returns from the stocks in different market conditions are detailed in the following table: Market Condition Probability of Occurrence Happy Dog Soap Black Sheep Broadcasting Strong Normal 0.25 0.45 37.5% 22.5% Weak 0.30 -30% 52.5% 30% 37.5% Calculate expected returns for the individual stocks in Joshua's portfolio as well as the expected rate of return of the entire portfolio over the three possible market conditions next year The expected rate of return an Happy Dog Soap's stock over the next year The expected rate of return on Black Sheep Broadcasting stock over the next year is The expected rate of return on Joshua's portfolio over the next year is