all Verizon LTE 10:59 AM 35%) Reader View Available E connect Chapter T 11 166 p

Question

all Verizon LTE 10:59 AM 35%) Reader View Available E connect Chapter T 11 166 pints 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. a. What is the expected returm on a portfolio that is equally invested in the two assets? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return b. If a portfolio of the two assets has a beta of.97, what are the portfolio weights? (Do not round intermediate calculations and round your answers to 4 decimal places, e.g., 32.1616.) c. If a portfolio of the two assets has an expected return of 12.7 percent, what is its beta? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g-, 32.16.) Beta d. If a portfolio of the two assets has a beta of 2.57, what are the portfolio weights? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 4 decimal places, e.g., 32.1616.) ?mo

Explanation / Answer

Answer to Part a.

Portfolio Expected Return = (Weight of Stock 1 * Return on Stock 1) + (Weight of Stock 2 *
Return on Stock 2)
Weight of Stock 1 = Weight of Stock 2 = 0.50
Portfolio Expected Return = (0.50 * 0.135) + (0.50 * 0.0465)
Portfolio Expected Return = 0.0675 + 0.02325
Portfolio Expected Return = 0.09075
or Portfolio Expected Return = 9.075 or 9.08%

Answer to Part b.

Weight of Stock 1 = x
Weight of Stock 2 (Risk Free Stock) = 1- x

Portfolio Beta = 0.97

Beta of Risk Free Stock = 0

Portfolio Beta = (Weight of Stock 1 * Beta of Stock 1) + (Weight of Stock 2 *
Beta of Stock 2)
0.97 = (x * 1.37) + [(1 – x) * 0)
0.97 = 1.37x + 0
x = 0.71

Weight of Stock 1 = 0.7080
Weight of Stock 2 (Risk Free Stock) = 1 – 0.7080 = 0.2920

Answer to Part c.

Portfolio Expected Return = (Weight of Stock 1 * Return on Stock 1) + (Weight of Stock 2 *
Return on Stock 2)
Weight of Stock 1 = x
Weight of Stock 2 (Risk Free Stock) = 1- x

0.127 = (x * 0.135) + [(1-x) * 0.0465]
0.127 = 0.135x + 0.0465 – 0.0465x
0.127 = 0.0885x + 0.0465
0.0805 = 0.0885x
x = 0.9096

Weight of Stock 1 = 0.9096
Weight of Stock 2 (Risk Free Stock) = 1 – 0.9096 = 0.0904

Portfolio Beta = (Weight of Stock 1 * Beta of Stock 1) + (Weight of Stock 2 *
Beta of Stock 2)
Portfolio Beta = (0.9096 * 1.37) + (0.0904 * 0)
Portfolio Beta = 1.246152 + 0
Portfolio Beta = 1.25

Answer to Part d.

Weight of Stock 1 = x
Weight of Stock 2 (Risk Free Stock) = 1- x

Portfolio Beta = 2.57

Beta of Risk Free Stock = 0

Portfolio Beta = (Weight of Stock 1 * Beta of Stock 1) + (Weight of Stock 2 *
Beta of Stock 2)
2.57 = (x * 1.37) + [(1 – x) * 0)
2.57 = 1.37x + 0
x = 1.8759

Weight of Stock 1 = 1.8759
Weight of Stock 2 (Risk Free Stock) = 1 – 1.8759 = -0.8759

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