Question

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: Ethan owns a two-stock portfolio that invests in Falcon Freight Company (FF) and Pheasant Pharmaceuticals (PP). Three-quarters of Ethan's portfolio value consists of FF's shares, and the balance consists of PP'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 Falcon Freight Pheasant Pharmaceuticals Strong 20% 35% 49% Normal 35% 21% 28% Weak 45% -28% -35% Calculate expected returns for the individual stocks in Ethan'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 Falcon Freight's stock over the next year is . The expected rate of return on Pheasant Pharmaceuticals's stock over the next year is • The expected rate of return on Ethan's portfolio over the next year is

Answer 1

Solution A: Expected return on Falcon Freight
Market condition	Probability	Falcon	Falcon expected return
	A	B	C=A*B
Strong	20%	35%	7.00%
Normal	35%	21%	7.35%
Weak	45%	-28%	-12.60%
		Expected return	1.75%
Solution B: Expected return on Pheasant pharma
Market condition	Probability	Pheasant	Falcon expected return
	A	B	C=A*B
Strong	20%	49%	9.80%
Normal	35%	28%	9.80%
Weak	45%	-35%	-15.75%
		Expected return	3.85%
Solution C: Calculation of expected return of the portfolio
Company	Expected return	Weight in portfolio	Expected return
	A	B	C=A*B
FALCON	1.75%	75%	1.313%
PHEASANT	3.85%	25%	0.963%
		Expected return	2.275%