he risk free rate is 4%, and the expected return on the market is 12%. There is

Question

he risk free rate is 4%, and the expected return on the market is 12%. There is also an asset X with a Beta of 1.5.What is the return on portfolio 1 consisting of 40% of asset X and the rest in an asset with no risk? What is the return on portfolio 2 which is equally weighted in the risk free asset, the market portfolio, and asset X?

Select one:

a. The E(R) on portfolio 1 is 13.6% and the E(R) on portfolio 2 is 10.67%

b. The E(R) on portfolio 1 is 16% and the E(R) on portfolio 2 is 8.8%

c. The E(R) on portfolio 1 is 8.8% and the E(R) on portfolio 2 is 16%

d. The E(R) on portfolio 1 is 16% and the E(R) on portfolio 2 is 8.8%

e. The E(R) on portfolio 1 is 8.8% and the E(R) on portfolio 2 is 10.67%

Explanation / Answer

Expected return (ER) on a stock (asset) = Risk-free Rate + [Beta x (Expected Return in Market - Risk-Free Rate)]

E(R), Asset X = 4% + [1.5 x (12% - 4%)]

= 4% + 12% = 16%

E(R), risk-free asset = 4% + [0 x (12% - 4%)] [Since, Beta of risk-free asset is 0]

= 4%

Now, Expected return on portfolio = (Proportion of 1st Asset x Expected Return of 1st Asset) + (Proportion of 2nd Asset x Expected Return of 2nd Asset)

(1) Portfolio 1 has 40% of Asset X & 60% of risk-free asset

Expected return on portfolio = (40% x 16%) + (60% x 4%)

= 6.4% + 2.4% = 8.8%

(2) Portfolio 2 has 33.3% of Asset X, 33.3% of Market Portfolio & 33.3% of risk-free asset

Expected return on portfolio = 33.3% x (16% + 12% + 4%)

= 33.3% x 32% = 10.67%

So Correct Option (e)

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