Question
In: Finance
Risk and Return Sarah is a financial analyst of a portfolio consisting of the stocks shown...
Risk and Return
Sarah is a financial analyst of a portfolio consisting of the stocks shown below.
The risk free rate is 3% and the market risk premium is 8%.
Stock H, Investment $2mil, Beta 1.4
Stock I, Investment $3mil, Beta 1.0
Stock J, Investment $5mil, Beta -0.2
Compute beta and expected return of portfolio.
Solutions
Expert Solution
Investment in Stock H = $2 mil
Investment in Stock I = $3 mil
Investment in Stock J = $5 mil
Total investment = 2+3+5 = $10 mil
Weight of stock H in the portfolio = wH = Investment in H/Total investment = 2/10 = 0.2
Weight of stock I in the portfolio = wI = Investment in I/Total investment = 3/10 = 0.3
Weight of stock J in the portfolio = wJ = Investment in J/Total investment = 5/10 = 0.5
Beta of stock H = βH = 1.4
Beta of stock I = βI = 1
Beta of stock J = βJ = -0.2
Beta of the portfolio can be calculated using the formula:
Beta of the portfolio = βP = wH*βH+wI*βI+wJ*βJ = 0.2*1.4 + 0.3*1 + 0.5*(-0.2) = 0.48
Now, we can use the CAPM equation to calculate the expected return on this portfolio
Expected return on the portfolio = E[RP] = RF+βP*MRP
where RF= Risk-free rate = 3%, βP = beta of the portfolio = 0.48, MRP = Market risk premium = 8%
Expected return of portfolio = E[RP] = 3%+(0.48*8%) = 3%+3.84% = 6.84%
Answer
Beta = 0.48
Expected return of portfolio = 6.84%
jeff jeffy answered 1 year agoRelated Solutions
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