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27 March, 15:36

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 State

Boom 0.25 0.065 0.240 0.260

Growth 0.36 0.065 0.120 0.180

Stagnant 0.24 0.065 0.030 0.090

Recession 0.15 0.065 - 0.110 - 0.200

a. 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. 27 March, 19:10
    0
    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%
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