Question

You have been managing a $5 million portfolio that has a beta of 1.70 and a required rate of return of 13%. The current risk-free rate is 5.75%. Assume that you receive another $500,000. If you invest the money in a stock with a beta of 0.85, what will be the required return on your $5.5 million portfolio? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

The return on market of first portfolio is unknown which is required to calculate the required return of the second portfolio

Portfolio 1

As per capital asset pricing mode,

Re = Rf + (Rm – Rf) x Beta

Where,

Re = Required rate of return = 13%

Rf = Risk free rate = 5.75%

Rm = Return on market

Beta = Beta of the stock = 1.70

So, putting these values in the above equation we get,

13 = 5.75 + (Rm – 5.75) x 1.70

So, Rm – 5.75 = (13 – 5.75) / 1.70

So, Rm = 4.26 + 5.75

= 10.01%

So, putting the value of Rm in CAPM equation for second portfolio we get,

Re = 5.75 + (10.01 – 5.75) x 0.85

= 9.38%

Now, return of the portfolio is the weighted average of the return of the stocks of the portfolio

This is calculated in the following table

Calculations	A	B = A / 5.5 million	C	D = B x C
Particulars	Value	Weight	Return	Weighted average return
Portfolio A	5,000,000	0.909091	13.00	11.818182
Portfolio B	500,000	0.090909	9.38	0.8527273
Total	5,500,000			12.67

So, the return of the portfolio is 12.67%