Question

Obi-wan forms an aggressive growth portfolio by investing 20% of his savings in GM stock, 21% in Nissan stock, 24% in Kia stock, 14% in an index fund, and the last 21% 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 1.13, the beta of Nissan is 1.41, and the beta of Kia is 1.72. If the expected return of the market index is 14% and the risk-free asset yields 3%, what are the beta and the expected return of Obi-wan’s portfolio? Give your answer rounded to two decimal places. What is the beta of the portfolio?

Answer 1

Given:

Funds	Weight	Beta
GM Stock	20%	1.13
Nissan Stock	21%	1.41
Kia Stock	24%	1.72
Index Fund	14%	1
Bond Fund	21%	0

The beta of the portfolio is obtained by the sum of Weight * Beta for every investment in the portfolio.

Funds	Weight	Beta	Weight * Beta
GM Stock	20%	1.13	0.226
Nissan Stock	21%	1.41	0.2961
Kia Stock	24%	1.72	0.4128
Index Fund	14%	1	0.14
Bond Fund	21%	0	0
		Total	1.0749

Hence, Beta of the portfolio = 1.08

Given that Return on Market Index = 14%, Risk free rate of return = 3%, we can calculate the Expected return of portfolio using CAPM Model.

ER = Rf + Beta * (Rm - Rf)

where ER is the Expected returns

Rf is the Risk free rate of return = 3%

Beta = 1.0749

Rm is the Return from the market = 14%

Hence, ER = 0.03 + 1.0749 * (0.14 - 0.03)

ER = 0.03 + 1.0749 * 0.11

ER = 0.03 + 0.118239

ER = 0.148239

Hence, Expected Returns of Obi-wan's portfolio is 14.82%