Question

# Suppose an economy has three states: boom, normal, and recession. Assume that the probability of a...

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%

(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 0.2 0.03 beta 0.3 0.02 gammma 0.5 0.01

=.006+.006+.005

=.02

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