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)?

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%