Question

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 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:

James owns a two-stock portfolio that invests in Blue Llama Mining Company (BLM) and Hungry Whale Electronics (HWE). Three-quarters of James’s portfolio value consists of BLM’s shares, and the balance consists of HWE’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	Blue Llama Mining	Hungry Whale Electronics
Strong	0.25	27.5%	38.5%
Normal	0.45	16.5%	22%
Weak	0.30	-22%	-27.5%

Calculate expected returns for the individual stocks in James’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 Blue Llama Mining’s stock over the next year is     .
•	The expected rate of return on Hungry Whale Electronics’s stock over the next year is     .
•	The expected rate of return on James’s portfolio over the next year is     .

Answer 1

Expected returns=Sum(probbaility*returns)

1.
=0.25*27.5%+0.45*16.5%+0.30*(-22%)
=7.700%

2.
=0.25*38.5%+0.45*22%+0.30*(-27.5%)
=11.275%

3.
=3/4*7.700%+1/4*11.275%
=8.594%