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: Tyler owns a two-stock portfolio that invests in Blue Llama Mining Company (BLM) and Hungry Whale Electronics (HWE). Three-quarters of Tyler'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 Strong Normal Probability of Occurrence 0.50 0.25 0.25 Blue Llama Mining 35% 21% Hungry Whale Electronics 49% 28% Weak -28% -35% Calculate expected returns for the individual stocks in Tyler's portfolio as well as the expected rate of return of the entire portfolio over the three possible market conditions next year.

Answer 1

Expected return on a stock or portfolio is weighted average of the return on constituents.

For Blue Llama,

E(R) = p1 * R1 + p2 * R2 + p3 * R3

E(R) = 0.50 * 35% + 0.25 * 21% + 0.25 * -28%

E(R) = 17.50% + 5.25% - 7%

E(R) = 15.75%

For Hungry Whale,

E(R) = p1 * R1 + p2 * R2 + p3 * R3

E(R) = 0.50 * 49% + 0.25 * 28% + 0.25 * -35%

E(R) = 24.50% + 7.00% - 8.75%

E(R) = 22.75%

For Tyler portfolio expected return,

E(R) = w1 * r1 + w2 * r2

E(R) = 75% * 15.75% + 25% * 22.75%

E(R) = 11.8125% + 5.6875%

E(R) = 17.50%

Correct statement is - Statement 1

Statement 1 is correct as Company A is spread over lower scale on the graph and hence has lower standard deviation.