3. 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:

Felix owns a two-stock portfolio that invests in Falcon Freight Company (FF) and Pheasant Pharmaceuticals (PP). Three-quarters of Felixs portfolio value consists of Falcon Freights shares, and the balance consists of Pheasant Pharmaceuticalss 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	FF	PP
	Occurrence
Strong	20%	50%	70%
Normal	35%	30%	40%
Weak	45%	-40%	-50%

Calculate expected returns for the individual stocks in Felixs 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 Falcon Freights stock over the next year is .
	The expected rate of return on Pheasant Pharmaceuticalss stock over the next year is .
	The expected rate of return on Felixs portfolio over the next year is .

The expected returns for Felixs 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:

-40-30-20-100102030405060PROBABILITY DENSITYRATE OF RETURN (Percent)Company ACompany B

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

Company A has a tighter probability distribution.

Company B has a tighter probability distribution.

VALUE (Dollars) 0 1 2 3 4 5 6 7 89 10 TIME (Years) VALUE (Dollars) 0 1 2 3 4 5 6 7 89 10 TIME (Years)