Problem 1 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 Average Poor 0.2 40% 15% 7% 0.3 15% 30% 7% 0.3 5% -5% 7% Recession 0.2 -20% 5% 7% Your portfolio manager has invested 30% of your money in Stock A, 50% in Stock B, and 20% in Stock C. a) What is the expected return of your portfolio? b) What is the covariance between Stocks A and B? c) What is the correlation coefficient between Stocks B and C? d) What is the standard deviation of your portfolio? Hint: Instead of using the portfolio variance formula for three stocks, you can save time by calculating the return on the portfolio for all four states of the economy, and then calculate the standard deviation of these portfolio returns.
Problem 1 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 Average Poor 0.2 40% 15% 7% 0.3 15% 30% 7% 0.3 5% -5% 7% Recession 0.2 -20% 5% 7% Your portfolio manager has invested 30% of your money in Stock A, 50% in Stock B, and 20% in Stock C. a) What is the expected return of your portfolio? b) What is the covariance between Stocks A and B? c) What is the correlation coefficient between Stocks B and C? d) What is the standard deviation of your portfolio? Hint: Instead of using the portfolio variance formula for three stocks, you can save time by calculating the return on the portfolio for all four states of the economy, and then calculate the standard deviation of these portfolio returns.
Chapter8: Analysis Of Risk And Return
Section: Chapter Questions
Problem 22P
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Transcribed Image Text:Problem 1
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
0.2
40%
15%
7%
Average
Poor
Recession
0.3
15%
30%
7%
0.3
5%
-5%
7%
0.2
-20%
5%
7%
Your portfolio manager has invested 30% of your money in Stock A, 50% in Stock B, and 20% in Stock C.
a) What is the expected return of your portfolio?
b) What is the covariance between Stocks A and B?
c) What is the correlation coefficient between Stocks B and C?
d) What is the standard deviation of your portfolio? Hint: Instead of using the portfolio variance formula for three
stocks, you can save time by calculating the return on the portfolio for all four states of the economy, and then
calculate the standard deviation of these portfolio returns.
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