Question

You have a portfolio with $15,000 invested in Stock A with a beta of 2.5, $25,000 invested in stock B with a beta of 0.7, and $10,000 invested in Stock C with a beta of 1.0. If the risk-free rate is 2% and the market risk premium is 6%, what is the required return of the portfolio?

Answer 1

Information provided:

Investment in stock A= $15,000

Beta of stock A= 2.5

Investment in stock B= $25,000

Beta of stock B= 0.7

Investment in stock C= $10,000

Beta of stock C= 1.0

Total investment in portfolio= $15,000 + $25,000 + $10,000= $50,000

Proportion invested in stock A= $15,000/ $50,000 = 0.30*100= 30%

Proportion invested in stock B= $25,000/ $50,000 = 0.50*100= 50%

Proportion invested in stock C= $10,000/ $50,000 = 0.20*100= 20%

Portfolio beta= 0.30*2.5 + 0.50*0.7 + 0.20*1.0

                           = 0.75 + 0.35 + 0.20

                           = 1.30

The expected return of a portfolio is calculated using the Capital Asset Pricing Model (CAPM)

The formula is given below:

Ke=Rf+b[E(Rm)-Rf]

Where:

Rf=risk-free rate of return which is the yield on default free debt like treasury notes

Rm=expected rate of return on the market.

Rm-Rf= Market risk premium

b= beta

Ke= 2% + 1.30*6%

     = 2% + 7.80

     = 9.80%.

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