Question

Dominic owns a two-stock portfolio that invests in Happy Dog Soap Company (HDS) and Black Sheep Broadcasting (BSB). Three- quarters of Dominic's portfolio value consists of HDS's shares, and the balance consists of BSB'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 Happy Dog Soap Black Sheep Broadcasting Strong 25% 35% Probability of Occurrence 0.50 0.25 0.25 Normal 15% 20% Weak -20% -25% Calculate expected returns for the individual stocks in Dominic'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 Happy Dog Soap's stock over the next year is • The expected rate of return on Black Sheep Broadcasting's stock over the next year is • The expected rate of return on Dominic's portfolio over the next year is The expected returns for Dominic's 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: PROBABILITY DENSITY Company G Company H -40 -20 0 20 40 60 RATE OF RETURN (Percent) Based on the graph's information, which company's returns exhibit the greater risk? Company H Company G

Answer 1

Expected rate of return of each stock = $\sum$ (probability of each scenario * return under each scenario)

Expected return of portfolio E(r) =   p(s)*r(s),

where p(s) is the probability of each scenario,

and r(s) is the expected return of each scenario

Expected return of two-asset portfolio R_p = w₁R₁ + w₂R_2,

where R_p = expected return

w₁ = weight of Asset 1. This is three-quarters, or 0.75

R₁ = expected return of Asset 1

w₂ = weight of Asset 2

R₂ = expected return of Asset 2. This is one quarter, or 0.25.

ДА B C D E Black Probability Happy 1 market p(s) Dog 2 Strong 0.50 25% 3 Normal 0.25 15% 4 Weak 0.25 -20% 5 Expected Return 11.25% Sheep 35% 20% -25% 16.25% Portfolio 27.50% 16.25% -21.25% 12.50%

1 market 2 Strong 3 Normal 4 Weak 5 Expected Return Probability p(s) 0.5 0.25 0.25 Happy Dog Black Sheep 0.25 0.35 0.15 0.2 -0.2 -0.25 =SUMPRODUCT(B2:B4,C2:04) -SUMPRODUCT(B2:B4,02:04) Portfolio =(0.75*C2)+(0.25*D2) =(0.75*C3)+(0.25*D3) =(0.75*C4)+(0.25*D4) SUMPRODUCT(B2:B4,E2:E4)

Company H's returns exhibit higher risk as the returns are more widely distributed around the mean