Suppose an economy has three states: boom, normal, and recession. Assume that the probability of a boom state is 0.2, a normal state is 0.5, and a recession state is 0.3. And there are three stocks in this economy, called Alpha, Beta, and Gamma respectively. The return performance of these stocks has been summarized by the following table:
Alpha 
Beta 
Gamma 

boom 
15% 
28% 
1% 
normal 
6% 
12% 
3% 
recession 
12% 
30% 
20% 
(Please show your intermediate processes, instead of just a final number for your answers. Only round your final answers to two decimal places.)
(a) What is the expected return of Stock Alpha?
(b) What is the variance of Stock Beta?
(c) What is the standard deviation of Stock Gamma?
(d) Suppose you build a portfolio by including these three stocks. The weight of Stock Alpha in your portfolio is 0.2, the weight of Stock Beta is 0.3, and the weight of Stock Gamma is 0.5. What are the expected return, variance, and standard deviation of your portfolio?
(e) Based on what you observe from the calculations and what you learned from the class, could you specify what are the characteristics of portfolios?
a)expected return SUM(R*P+R*P+R*P)
=.024
alpha expected return
BOOM  0.2  15%  0.03  
NORMAL STATE  0.5  6%  0.03  
RECESSION  0.3  12%  .036  
b)variance of stock beta
r =retun
epr = expected return
epr =.03
=(.28.3)^^2*.2+(.12.30^2*.5+(.30.3)*.3
.00008+.02
=.02
c)standard deviation of gamma
expected return =.2
co variance =.1
sd =.316
d) EXOECTED RETURN OF PORTFOLIO
=(w1*r1)+w2*r2) +w3*r3
alpha 
.2  .03 
beta 
.3  .02 
gammma  .5  .01 
=.006+.006+.005
=.02
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