A stock has a beta of 1.37 and an expected return of 13.5 percent. A risk-free a

Question

A stock has a beta of 1.37 and an expected return of 13.5 percent. A risk-free asset currently earns 4.65 percent.

What is the expected return on a portfolio that is equally invested in the two assets? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

If a portfolio of the two assets has a beta of 0.97, what are the portfolio weights? (Do not round intermediate calculations. Round your answers to 4 decimal places (e.g., 32.1616).)

If a portfolio of the two assets has an expected return of 12.7 percent, what is its beta? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

If a portfolio of the two assets has a beta of 2.57, what are the portfolio weights?

A stock has a beta of 1.37 and an expected return of 13.5 percent. A risk-free asset currently earns 4.65 percent.

Explanation / Answer

A) Expected return of portfolio E(Rp) = (0.135 +0.0465) / 2

= 0.09075 or 9.075%

B) Beta = 0.97

Ws = Weight of the stock

Beta = Ws (1.37) + (1-Ws)(0)

0.97 = 1.37 Ws + 0 - 0Ws

Ws = 0.97 / 1.37

= 0.708

Therefore Weight of risk-free asset WRf = 1-0.708

= 0.292

C) E(Rp) = 12.7% = 0.127

E(Rp) = 0.135 Ws +0.0465 (1-Ws)

0.127 = 0.135 Ws +0.0465 (1-Ws)

0.127 = 0.135 Ws +0.0465 - 0.0465Ws

0.0885 Ws = 0.0805

Ws = 0.0805 / 0.0885

= 0.9096

Beta = 0.9096 (1.37) + (1 -  0.9096) (0)

= 1.2461

D) Beta = 2.57 = Ws (1.37) + (1-Ws) (0)

Ws = 2.57 / 1.37

= 1.875

WRF= 1 - 1.875

= -0.875

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