Question

Please show the steps to get the right answers. Thank you!

Show all attempts Jar Jar forms an aggressive growth portfolio by investing 20% of his savings in Ford stock, 23% in Toyota stock, 24% in Kia stock, 10% in an index fund, and the last 23% 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 Ford stock is 1.18, the beta of Toyota is 1.41, and the beta of Kia is 1.81. If the expected return of the market index is 10% and the risk-free asset yields 7%, what are the beta and the expected return of Jar Jar's portfolio? Give your answer rounded to two decimal places. What is the beta of the portfolio? Bp = Your response 10.28 3 Grade: 0/1.0 Correct response 1.09 0.0x1/1 = 0.00 Based on the value of Bp = 1.09, what is the expected return of Jar Jar's portfolio? Give your answer rounded to two decimal places. Ep) = Your response Correct response 122 10.27 * Grade: 0/1.0 0.0x1/1 = 0.00

Answer 1

Solution:-

Calculation of portfolio beta:

The beta of a portfolio is simply the weighted average of betas of individual components of the portfolio. As a simple example, if a portfolio has two assets in equal proportion with asset A having a beta of 1.5 and asset B having a beta of 0.5, the portfolio beta will be as follows:

Portfolio beta (for above example)= Beta A*50% + Beta B*50%= 1.5*50% + 0.5*50%= 1

Thus, we can summarise the formula for calculating beta as follows:

Beta (portfolio of n assets)= (Beta Asset 1 * weight Asset 1) + (Beta Asset 2 * weight Asset 2) + (Beta Asset 3 * weight Asset 3) +...………..+ (Beta Asset n * weight Asset n)

Now, as given in the question we have the following information:

Beta (Ford)= 1.18 ; Weight (Ford)= 20%

Beta (Toyota)= 1.41 ; Weight (Toyota)= 23%

Beta (Kia)= 1.81 ; Weight (Toyota)= 24%

Beta (Market index)= 1 ; Weight (Toyota)= 10%

Beta (Risk free bond)= 0 (Betas of risk free assets are zero) ; Weight (Toyota)= 23%

Using the above information and beta formula as shown above, we calculate beta portfolio as follows:

Beta (Portfolio)= (1.18*20%) + (1.41*23%) + (1.81*24%) + (1*10%) + (0*23%)

Beta (Portfolio)= 1.09

Calculation of portfolio expected return:

As per CAPM, the required rate of return is calculated as follows:

Expected Return= Risk free rate + Beta*Market risk premium

Risk-free rate (Equal to return of risk free bond)= 7%

Market risk premium= Expected return market index - risk free rate= 10%-7%= 3%

Portfolio beta= 1.09

Thus, the expected returns (ER) for portfolio is calculated using CAPM as follows:

ER (Portfolio)= 7% + 1.09*3% = 10.27%