Question

Jar Jar forms an aggressive growth portfolio by investing 24% of his savings in GM stock, 21% in Nissan stock, 23% in Subaru stock, 12% in an index fund, and the last 20% is allocated on a bond fund. Assume for simplicity that the index fund is a good proxy to the market portfolio and has a beta equal to 1, whereas the bond fund is a good proxy to the riskless asset. The beta of GM stock is 1.11, the beta of Nissan is 1.46, and the beta of Subaru is 1.66. If the expected return of the market index is 10% and the risk-free asset yields 6%, what are the beta and the expected return of Jar Jar’s portfolio? Give your answer rounded to two decimal places.

Answer 1

Beta of Jar Jar's Portfolio:

It can be calculated as weighted average of individual betas.

So, (w1*Beta1)+(w2*Beta2)+(w3*Beta3)+(w4*Beta4)+(w5*Beta5)

= (0.24*1.11)+(0.21*1.46)+(0.23*1.66)+(0.12*1)+(0.2*0)

= 1.07

Expected return of Jar Jar's Portfolio:

Given expected return of Market index is 10% and risk free asset yields 6%.

Using CAPM, Expected return can be calculated as Rf+Beta*(Rm-Rf)

Expected return of GM stock = 6%+1.11*(10%-6%)= 10.44%

Expected return of Nissan stock = 6%+1.46*(10%-6%)= 11.84%

Expected return of Subaru stock = 6%+1.66*(10%-6%)= 12.64%

So, Expected return of portfolio= (0.24*10.44%)+(0.21*11.84%)+(0.23*12.64%)+(0.12*10%)+(0.2*6%)= 10.30%