2. 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 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:

Ian owns a two-stock portfolio that invests in Celestial Crane Cosmetics Company (CCC) and Lumbering Ox Truckmakers (LOT). Three-quarters of Ians 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	32.5%	45.5%
Normal	0.45	19.5%	26%
Weak	0.30	-26%	-32.5%

Calculate expected returns for the individual stocks in Ians 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 Ians portfolio over the next year is .

The expected returns for Ians 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 lower risk.

Company B has lower risk.

PROBABILITY DENSITY Company A Company B -40 -20 0 20 40 60 RATE OF RETURN (Percent)