Question

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Use the information below to answer parts a and b:

A Expected return 10% Beta 0.8

B Expected return 18% Beta 1.2

C Expected return 16% Beta 1.5

Furthermore, the risk-free rate is 3% and expected return of the market portfolio is 13%.

a. Are securities A, B, and C overvalued, fairly valued, or undervalued?

b. Find the beta of a portfolio that invests equally into these three securities.

Answer 1

Using CAPM, Expected return = Risk free rate + Beta * Market risk premium

Market risk premium= Expected return on market portfolio - Risk free rate = 13% - 3% = 10%

a)

Expected return on A as per CAPM = 3% + 0.8* 10% = 11%

Given expected return is 10%,

So A is undervalued

Expected return on B = 3% + 1.2* 10% = 15%

Given Expected return is 18%

So B is overvalued.

Expected return on C = 3% + 1.5* 10% = 18%

Given expected return is 16%

So C is undervalued

b)

If it is equally invested among the three securities, ie 1/3 rd in eac security

Beta of the portfolio = Beta of security * Proportion = (Beta 1* Weight 1 + Beta 2* Weight 2 + Beta 3* Weight 3)=   (1/3 * 0.8 + 1/3 * 1.2 + 1/3* 1.5) = 1.167

= approx 1.17