Consider the following information about three stocks: Rate of Return if State O
ID: 2715944 • Letter: C
Question
Consider the following information about three stocks:
Rate of Return if State Occurs
State of Economy
Probability of
State of Economy
Stock A
Stock B
Stock C
Boom
0.30
50.0%
12.0%
20.0%
Average
0.45
15.0%
-5.0%
6.0%
Recession
0.25
-8.0%
2.0%
-3.2%
Your portfolio manager has invested 30% of your money in Stock A, 50% in Stock B, and the rest in Stock C.
a) What is the expected return of your portfolio?
b) What is the standard deviation of Stock B?
c) What is the covariance between Stocks B and C?
d) What is the correlation coefficient between Stocks B and C?
e) What is the standard deviation of your portfolio?
Consider the following information about three stocks:
Rate of Return if State Occurs
State of Economy
Probability of
State of Economy
Stock A
Stock B
Stock C
Boom
0.30
50.0%
12.0%
20.0%
Average
0.45
15.0%
-5.0%
6.0%
Recession
0.25
-8.0%
2.0%
-3.2%
Explanation / Answer
Expected return of portfolio can be computed by this formula:
E(R) = w1R1 + w2Rq + ...+ wnRn
Whrere
E(R) = Expected return of portfolio
W1 =Weights of investment made in each stock one
R1= Rate of return from stock one
When Boom
Stock A
Stock B
Stock C
Return
0.05
0.12
0.2
Weights
30
50
20
=.5*.30+.12*.50+.2*.20
=.115 or 11.5%
When Average
=.15*.3+(-.05)*.5+.06*.2
=3.2%
When Recession
=(-.08)*.3+.02*.5+(-.032)*.2
=6.96%
b) standard deviation of Stock B
standard deviation of Stock B is .07
Stock A
Stock B
Stock C
Return
0.05
0.12
0.2
Weights
30
50
20
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