1. 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 Blue Llama Mining Company (BLM) and Hungry Whale Electronics (HWE). Three- quarters of Joshua's portfolio value consists of BLM's shares, and the balance consists of HWE'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 Strong Normal Probability of Occurrence Blue Llama Mining Hungry Whale Electronics 0.25 22.5% 31.5% 0.45 13.5% 18% Weak 0.30 -18% -22.5% 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 on Blue Llama Mining's stock over the next year is The expected rate of return on Hungry Whale Electronics's stock over the next year is The expected rate of return on Joshua's portfolio over the next year is The expected returns for Joshua'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: PROBABILITY DENSITY Company A Company B -40 -20 0 20 60 40 RATE OF RETURN (Percent) Based on the graph's information, which of the following statements is true? Company A has a smaller standard deviation. O Company B has a smaller standard deviation. The expected rate of return on Blue Llama Mining's stock over the next year is The expected rate of return on Hungry Whale Electronics's stock over the next 6.31% The expected rate of return on Joshua's portfolio over the next year is 5.36% The expected returns for Joshua's portfolio were calculated based on three possibl ns in the market. Such conditions will vary from time to 8.52% time, and for each condition there will be a specific outcome. These probabilities a mes can be represented in the form of a continuous probability distribution graph. 7.57% For example, the continuous probability distributions of rates of return on stocks for two different companies are shown on the following graph: PROBABILITY DENSITY Company A Company B -40 -20 0 20 40 60 RATE OF RETURN (Percent) Based on the graph's information, which of the following statements is true? Company A has a smaller standard deviation. Company B has a smaller standard deviation. The expected rate of return on Blue Llama Mining's stock over the next year is The expected rate of return on Hungry Whale Electronics's stock over the next year is The expected rate of return on Joshua's portfolio over the next year is 9.23% The expected returns for Joshua's portfolio were calculated based on three possible condi 11.45% market. Such conditions will vary from time to time, and for each condition there will be a specific outcome. These probabilities and out be represented in the form of a continuous 10.43% probability distribution graph. 6.00% For example, the continuous probability distributions of rates of return on stocks for two Jmpanies are shown on the following graph: PROBABILITY DENSITY Company A Company B -40 -20 0 20 40 60 RATE OF RETURN (Percent) Based on the graph's information, which of the following statements is true? O Company A has a smaller standard deviation. O Company B has a smaller standard deviation. The expected rate of return on Blue Llama Mining's stock over the next year is The expected rate of return on Hungry Whale Electronics's stock over the next year is The expected rate of return on Joshua's portfolio over the next year is 8.45% The expected returns for Joshua's portfolio were calculated based on thre conditions in the market. Such conditions will vary from time to time, and for each condition there will be a specific outcome. These proba 7.04% d outcomes can be represented in the form of a continuous probability distribution graph. 5.98% For example, the continuous probability distributions of rates of return on two different companies are shown on the following graph: 9.50% PROBABILITY DENSITY Company A Company B -40 -20 0 20 60 40 RATE OF RETURN (Percent) Based on the graph's information, which of the following statements is true? Company A has a smaller standard deviation. Company B has a smaller standard deviation