Question

1. Statistical measures of standalone risk Aa Aa 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: Juan owns a two-stock portfolio that invests in Falcon Freight Company (FF) and Pheasant Pharmaceuticals (PP) Three-quarters of Juan'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 Normal Weak 2090 35% 4590 3890 23% 30% 53% 30% 3890 Calculate expected returns for the individual stocks in Juan'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 Juan's portfolio over the next year is

Answer 1

1. Expected rate of return on FF's stock over the next year = Expected rate of return in strong market condition + Expected rate of return in normal market condition + Expected rate of return in weak market condition

Expected rate of return on FF's stock in strong market condition = P(Occurrence of Strong market condition) * (FF's return given strong market condition) = 20% * 38% = 0.2 * 0.38 = 0.076 or 7.6%

Expected rate of return on FF's stock in normal market condition = P(Occurrence of Normal market condition) * (FF's return given normal market condition) = 35% * 23% = 0.35 * 0.23 = 0.0805 or 8.05%

Expected market rate of return on FF's stock in weak market condition = P(Occurrence of Weak market condition) * (FF's return given weak market condition) = 45% * -30% = 0.45 * -0.30 = -0.135 or -13.5%

Therefore, expected rate of return on FF's stock over the next year = 7.6% + 8.05% - 13.5% = 2.15%

2. Expected rate of return on PP's stock over the next year = Expected rate of return in strong market condition + Expected rate of return in normal market condition + Expected rate of return in weak market condition

Expected rate of return on PP's stock in strong market condition = P(Occurrence of Strong market condition) * (PP's return given strong market condition) = 20% * 53% = 0.2 * 0.53 = 0.106 or 10.6%

Expected rate of return on PP's stock in normal market condition = P(Occurrence of Normal market condition) * (PP's return given normal market condition) = 35% * 30% = 0.35 * 0.30 = 0.105 0r 10.5%

Expected market rate of return on PP's stock in weak market condition = P(Occurrence of Weak market condition) * (PP's return given weak market condition) = 45% * -38% = 0.45 * -0.38 = -0.171 or -17.1%

Therefore, expected rate of return on PP's stock over the next year = 10.6% + 10.5% - 17.1% = 4%

3. Expected return of Juan's portfolio over the next year = (Weight of FF's stock in the portfolio * Expected rate of return on FF's stock over the next year) + (Weight of PP's stock in the portfolio * Expected rate of return on PP's stock over the next year)

= (0.75 * 2.15%) + (0.25 * 4%)

= 1.61% + 1%

= 2.61%

4. Risk comparison

Based on the continuous probability density graph of companies G and H, the probability as well as magnitude of negative rate of return is very low for company G as compared to that for company H. Hence, company H exhibits a greater risk.