Question

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: Antonio owns a two-stock portfolio that invests in Celestial Crane Cosmetics Company (COC) and Lumbering Ox Truckmakers (LOT). Three-quarters of Antonio's portfolio value consists of Celestial Crane Cosmetics's shares, and the balance consists of Lumbering Ox Truckmakers'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: Probability of Occurrence Market Condition Strong Normal Weak as the expected rate of return of the entire portfolio over the three Calculate expected returns for the individual stocks in Antonio's portfolio possible market conditions next year . The expected rate of return on Celestial Crane Cosmetics's stock over the next year . The expected rate of return on Lumbering Ox Truckmakers's stock over the next year • The expected rate of retum on Antonio's portfolio over the next years The expected returns for Antonio's portfolio were calculated based on the possible conditions in the market. Such condition will vary from time to

Answer 1

Expected return of CCC = $\sum$ Prob of Occurence * Expected return

= 0.2 * 50% + 0.35 * 30% + 0.45 * -40% = 2.5%

Expected Return of LOT = 0.2* 70% + 0.35 * 40% - 0.45* 50%

= 5.5%

Expected return of Antonio's portfolio = 3/4 * 2.5% + 1/4* 5.5% = 3.25%

Company B has larger standard deviation as it has wider dispersion around the mean. So Company has smaller standard deviation is true.