Question

Use a risk-free rate of 3% and a market return of 7%. You have a portfolio with $10,000 invested in Stock A with a beta of 0.9, $20,000 in Stock B with a beta of 1.8, and $20,000 in Stock C with a beta of 2.0. What is the beta and required return of the portfolio?

Answer 1

According to CAPM ,

Required return = riskfree rate + beta*(marketreturn - risk free rate)

return of A = 3% + 0.9(7% - 3%) = 6.6%

B = 3% + 1.8(7% - 3%) = 10.20%

C = 3% + 2(7% - 3%) = 11%

Beta of portfolio = weighted average Beta

=

Return on a portfolio = weighted average return

=

first lets calculate weight of each stock in the portfolio

total value of portfolio = 10,000 + 20,000 + 20,000 = 50,000

Weight of A = 10,000 / 50,000 = 0.2 or 20%

Weight of B = 20,000 / 50,000 = 0.4 or 40%

Weight of C = 20,000 / 50,000 = 0.4 or 40%

Beta of portfolio = (0.2*0.9) + (0.4*1.8) + (0.4*2)

= 1.7

Return on portfolio = (0.2*6.6%) + (0.4*10.20%) + (0.4*11%)

= 9.80%