A stock has a beta of 1.25 and an expected return of 15 percent. A risk-free ass

Question

A stock has a beta of 1.25 and an expected return of 15 percent. A risk-free asset currently earns 3.2 percent.

What is the expected return on a portfolio that is equally invested in the two assets? (Round your answer to 2 decimal places. (e.g., 32.16))

If a portfolio of the two assets has a beta of 0.75, what are the portfolio weights? (Round your answer to 4 decimal places. (e.g., 32.1616))

If a portfolio of the two assets has an expected return of 9 percent, what is its beta? (Do not round intermediate calculations and round your answer to 3 decimal places. (e.g., 32.161))

If a portfolio of the two assets has a beta of 2.50, what are the portfolio weights? (Negative amount should be indicated by a minus sign.)

A stock has a beta of 1.25 and an expected return of 15 percent. A risk-free asset currently earns 3.2 percent.

Explanation / Answer

a) Expected return from the protfolio

= 0.5 x 15% + 0.5 x 3.2%

= 9.1%

Note the beta of the stock has already been accounted for in calculating the expected return of 15% from the stock

b) The portfolio beta

= W1x beta of the risk free asset + W2 x beta of the stock

Here protfolio beta = 0.75

therefore,

0.75 = W1 x 0 + W2 x 1.25          [as beta of risk free asset = 0]

=> W2 = 0.75 / 1.25 = 0.6

W1 = 1 - W2 = 1 - 0.6 = 0.4

Therefore

weight of the stock = 0.60

weight of the risk free asset = 0.40

c)

First step: Calculation of weights of the individual assets that give an expected return of 9%.

Expeted Portfolio return = W1x return of the risk free asset + W2 x return of the stock

0.09 = = W1x return of the risk free asset + (1 - W1) x return of the stock

0.09 = W1x 0.032 + (1 - W1) x  0.15

=> W1 = 0.50847 = 50.85 % (approximately)

W2 = 1 - 0.5085 = 0.4915 = 49.15%

Second step: Finding Portfolio beta:

The portfolio beta

= W1x beta of the risk free asset + W2 x beta of the stock

= 0.5085 x 0 + 0.4915 x 1.25

=0.6143 = 0.61 (rounded off to two decimal place)

d)

The portfolio beta

= W1x beta of the risk free asset + W2 x beta of the stock

Here protfolio beta = 2.50

therefore,

2.50 = W1 x 0 + W2 x 1.25          [as beta of risk free asset = 0]

=> W2 = 2.50 / 1.25 = 2

W1 = 1 - W2 = 1 - 2 = -1

This is an example of leveraged portfolio, where dollars have been borrowed at risk free rate from the market and has been invested to purchase the risky stock.

weight of the stock = 2

weight of the risk free asset = -1

This means if you have got an investible fund of $100, you have borrowed another $100 at risk free rate of 3.2% and then $200 have been invested in the stock with expected return of 15%

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