8 March, 20:58

# Use the following information to answer the questions.State of Economy Probability of State Return on Asset J in State Return on Asset K in State Return on Asset L in StateBoom 0.25 0.065 0.240 0.260Growth 0.36 0.065 0.120 0.180Stagnant 0.24 0.065 0.030 0.090Recession 0.15 0.065 - 0.110 - 0.200a. What is the expected return of each asset?b. What is the variance and the standard deviation of each asset?c. what is the expected return of a portfolio with 9% in asset J, 51% in asset K, and 40% in asset L?d. What is the portfolio's variance and standard deviation using the same asset weights from part (c) ?

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1. 8 March, 22:29
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1a Return J=6.5% k=9.39% l=12.14%

1b. variance and standard deviation respectively

J=4.64%, 21.53% K=3.47%, 18.64% L=2.52%, 15.89%

1c. 10.23%

1d. 17.8%

Explanation:

1a Expected return

J = (0.25*0.065) + (0.36*0.065) + (0.24*0.065) + (0.15*0.065) = 0.065

K = (0.25*0.240) + (0.36*0.120) + (0.24*0.030) + (0.15*-0.110) = 0.0939

L = (0.25*0.260) + (0.36*0.180) + (0.24*0.090) + (0.15*-0.200) = 0.1214

1b average return = 0.2803 (0.065+0.0939+0.1214)

Variance

J = (0.2803-0.065) ²=0.04635/4.64%

standard deviation = √0.04635=0.2153/21.53%

K = (0.2803-0.0939) ²=0.03474/3.47%

standard deviation = √0.03474=0.1864/18.64%

L = (0.2803-0.1214) ²=0.02524/2.52%

standard deviation = √0.02524=0.1589/15.89%

Ic. portfolio return

= (0.09*0.065) + (0.51*0.0939) + (0.40*0.1214) = 0.1023/10.23%

1d. Varance

(0.09*0.0464) + (0.51*0.03474) + (0.40*0.02524) = 0.03199/3.1%

Standard deviation of portfolio

(0.09*0.2153) + (0.51*0.1864) + (0.40*0.1589) = 0.1780/17.8%