Problem 11-25 Portfolio Returns and Deviations [LO 2] If your portfolio is inves
ID: 2767358 • Letter: P
Question
Problem 11-25 Portfolio Returns and Deviations [LO 2]
If your portfolio is invested 36 percent each in A and B and 28 percent in C, what is the portfolios expected return, the variance, and the standard deviation? (Do not round intermediate calculations. Round your variance answer to 5 decimal places (e.g., 32.16161) and input your other answers as a percentage rounded to 2 decimal places (e.g., 32.16).)
If the expected T-bill rate is 4.35 percent, what is the expected risk premium on the portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)
Consider the following information on a portfolio of three stocks:Explanation / Answer
(a) Expected Return of Stock A = (0.15 x 0.04) + (0.53 x 0.12) + (0.32 x 0.18)
= 0.1272 or 12.72%
Expected Return of Stock B = (0.15 x 0.34) + (0.53 x 0.24) + (0.32 x 0.23)
= 0.2518 or 25.18%
Expected Return of Stock C = (0.15 x 0.48) + (0.53 x 0.22) + (0.32 x 0.37)
= 0.3070 or 30.70%
Expected Return of Portfolio = (0.36 x 0.1272) + (0.36 x 0.2518) + (0.28 x 0.3070)
= 0.2224 or 22.24%
Variance of Stock A = 0.15 (0.04 - 0.1272)2 + 0.53 (0.12 - 0.1272)2 + 0.32 (0.18 - 0.1272)2
= 0.00206
Standard Deviation of Stock A = (0.00206)1/2 = 0.0454 or 4.54%
Variance of Stock B = 0.15 (0.34 - 0.2518)2 + 0.53 (0.24 - 0.2518)2 + 0.32 (0.23 - 0.2518)2
= 0.00139
Standard Deviation of Stock B = (0.00139)1/2 = 0.0373 or 3.73%
Variance of Stock C = 0.15 (0.48 - 0.3070)2 + 0.53 (0.22 - 0.3070)2 + 0.32 (0.37 - 0.3070)2
= 0.00977
Standard Deviation of Stock C = (0.00977)1/2 = 0.0988 or 9.88%
Variance of Portfolio = (0.36)2 x (0.0454)2 + (0.36)2 x (0.0373)2 + (0.28)2 x (0.0988)2 + 2 (0.0454) (0.0373) (0.36) (0.36) + 2 (0.0373) (0.0988) (0.36) (0.28) + 2 (0.0988) (0.0454) (0.28) (0.36)
= 0.00330
Standard Deviation of Portfolio = (0.00330)1/2 = 0.0574 or 5.74%
(b) Expected T-Bill Rate = 4.35%
Expected Risk Premium = 22.24 - 4.35 = 17.89%