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 assets 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:

Juan owns a two-stock portfolio that invests in Celestial Crane Cosmetics Company (CCC) and Lumbering Ox Truckmakers (LOT). Three-quarters of Juans portfolio value consists of CCCs shares, and the balance consists of LOTs shares.

Each stocks 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	Celestial Crane Cosmetics	Lumbering Ox Truckmakers
Strong	0.25	37.5%	52.5%
Normal	0.45	22.5%	30%
Weak	0.30	-30%	-37.5%

Calculate expected returns for the individual stocks in Juans 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 Cosmeticss stock over the next year is .
	The expected rate of return on Lumbering Ox Truckmakerss stock over the next year is .
	The expected rate of return on Juans portfolio over the next year is .

The expected returns for Juans 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:

Based on the graphs information, which of the following statements is true?

Company A has a smaller standard deviation.

Company B has a smaller standard deviation.

Remember, the expected value of a probability distribution is a statistical measure of the average (mean) value expected to occur during all possible expected to result during each state of nature by its probability of occurrence. Consider the following case: Juan owns a two-stock portfolio that invests in Celestial Crane Cosmetics Company (CCC) and Lumbering Ox Truckmakers (LOT). Threequarters of Juan's portfolio value consists of CCC's shares, and the balance consists of LOT's shares. Each stock's expected return for the next year will depend on forecasted market conditions. The expected returns from in different market conditions are detailed in the following table: Calculate expected returns for the individual stocks in Juan'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 Juan's portfolio over the next year is and for each condition there will be a specific outcome. These probabilities and outcomes can bestility distribution graph. For example, the continuous probability distributions of rates of return on stocks for two different companies are shown on the following graph: 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