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:

Joshua owns a two$-$stock portfolio that invests in Happy Dog Soap Company $($HDS$)$ and Black Sheep Broadcasting $($BSB$).$ Three$-$quarters

of Joshua's portfolio value consists of HDS$\text{'}$s shares, and the balance consists of BSB$\text{'}$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 Happy Dog Soap Black Sheep Broadcasting

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 Happy Dog Soap's stock over the next year is

The expected rate of return on Black Sheep Broadcasting'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:

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.