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:

David owns a two-stock portfolio that invests in Happy Dog Soap Company (HDS) and Black Sheep Broadcasting (BSB). Three-quarters of Davids portfolio value consists of HDSs shares, and the balance consists of BSBs 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	Happy Dog Soap	Black Sheep Broadcasting
Strong	0.50	47.5%	66.5%
Normal	0.25	28.5%	38%
Weak	0.25	-38%	-47.5%

Calculate expected returns for the individual stocks in Davids 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 Happy Dog Soaps stock over the next year is .
	The expected rate of return on Black Sheep Broadcastings stock over the next year is .
	The expected rate of return on Davids portfolio over the next year is .

The expected returns for Davids 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.