3. Statistical measures of standalone 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: Darnell owns a two-stock portfolio that invests in Celestial Crane Cosmetics Company (CCC) and Lumbering Ox Truckmakers (LOT). Three-quarters of Darnell'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: Market Condition Probability of Occurrence 20% CCC LOT 20% 28% Strong Normal 35% 45% Weak 12% -16% 16% -20% Calculate expected returns for the individual stocks in Darnell'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 on Celestial Crane Cosmetics's stock over the next year is The expected rate of return on Lumbering Ox Truckmakers's stock over the next year is The expected rate of return on Darnell's portfolio over the next year is Market Condition Probability of Occurrence 20% LOT Strong 28% 20% 12% Normal 35% 16% Weak 45% -16% -20% Calculate expected returns for the individual stocks in Darnell'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 on Celestial Crane Cosmetics' stock over the next year is The expected rate of return on Lumbering Ox Truckmakers's stock over the next year is The expected rate of return on Darnell's portfolio over the next year is The expected returns for Darnell's portfolio were calculated based on three possible conditions in the market. Such conditions will vary from time to time, and for each condition there will be a specific outcome. These probabilities and outcomes can be represented in the form of a continuous probability distribution graph. For example, the continuous probability distributions of rates of return on stocks for two different companies are shown on the following graph: ? Company A 2 Company A PROBABILITY DENSITY Company B 40 50 60 -30 20 10 0 10 20 30 40 RATE OF RETURN (Percent) Based on the graph's information, which of the following statements is true? Company A has a tighter probability distribution. Company B has a tighter probability distribution 80 888 Calculate expected returns for the individual stocks in Darnell's portfolio as well as the expected rate of return of the entire portfolio over possible market conditions next year. . The expected rate of return on Celestial Crane Cosmetics's stock over the next year is . The expected rate of return on Lumbering Ox Truckmakers's stock over the next year is The expected rate of return on Darnell's portfolio over the next year is 1.35% 1.20% The expected returns for Darnell's portfolio were calculated based on three possible condi time, and for each condition there will be a specific outcome. These probabilities and out 0.85% probability distribution graph. 1.00% ne market. Such conditions will vary from be represented in the form of a continu For example, the continuous probability distributions of rates of return on stocks for two different companies are shown on the following grap Company A ITY DENSITY Company B Calculate expected returns for the individual stocks in Darnell'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 on Celestial Crane Cosmetics's stock over the next year is The expected rate of return on Lumbering Ox Truckmakers's stock over the next year is The expected rate of return on Darnell's portfolio over the next year is 2.49% The expected returns for Darnell's portfolio were calculated based on three possible conditi 1.43% market. Such conditions will vary from time to time, and for each condition there will be a specific outcome. These probabilities and outco be represented in the form of a continuous 2.73% probability distribution graph. 2.20% For example, the continuous probability distributions of rates of return on stocks for two dil mpanies are shown on the following graph: Company A BILITY DENSITY Company B 0 Calculate expected returns for the individual stocks in Darnell'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 on Celestial Crane Cosmetics's stock over the next year is The expected rate of return on Lumbering Ox Truckmakers's stock over the next year is The expected rate of return on Darnell's portfolio over the next year is The expected returns for Darnell's portfolio were calculated based on the 1.76% conditions in the market. Such conditions will vary from time to time, and for each condition there will be a specific outcome. These proba 1.30% ]d outcomes can be represented in the form of a continuous probability distribution graph. 1.56% For example, the continuous probability distributions of rates of return on two different companies are shown on the following graph: 1.10% Company A BILITY DENSITY Company B