Refer to the following example for part g) Suppose that you consider two stocks, X and Y with their probability distribution. Scenario Probability Stock X's return Stock Y's return Bull market 60% 15% 8% Bear market 40% -5% 2% Expected rate of return on Stock X = 0.6*15% + 0.4*(-5%) = 9% + (-2%) = 7% Expected rate of return on Stock Y = 0.6*8% + 0.4*2% = 4.8% + 0.8% = 5.6% %3D %3D %3D Variance of Stock X's returns = 0.6*(15% - 7%)2 + 0.4*(-5% - 7%)2 = 38.4 + 144 = 182.4 Standard deviation of Stock X = square root of 182.4 = 13.51% %3D %3D Variance of Stoc Y's returns = 0.6*(8% - 5.6%)2 + 0.4*(2% - 5.6%)2 = 3.46 + 5.18 = 8.64 Standard deviation of Stock Y = square root of 8.64 = 2.94% %3D Covariance between Stock X and Stock Y = 0.6*(15% - 7%)*(8% - 5.6%) + 0.4*(-5% - 7%)*(2% - 5.6%) = 28.8 Correlation between Stock X and Stock Y = 28.8/(13.51*2.94) = 0.73 g) Use the following two stocks. Scenario Probability Stock A Stock B Boom 30% 12% 20% Recession 70% 18% 5% i) Find the expected return on each stock. ii) Find the standard deviation of each stock. iii) Find the covariance between two stocks.
Refer to the following example for part g) Suppose that you consider two stocks, X and Y with their probability distribution. Scenario Probability Stock X's return Stock Y's return Bull market 60% 15% 8% Bear market 40% -5% 2% Expected rate of return on Stock X = 0.6*15% + 0.4*(-5%) = 9% + (-2%) = 7% Expected rate of return on Stock Y = 0.6*8% + 0.4*2% = 4.8% + 0.8% = 5.6% %3D %3D %3D Variance of Stock X's returns = 0.6*(15% - 7%)2 + 0.4*(-5% - 7%)2 = 38.4 + 144 = 182.4 Standard deviation of Stock X = square root of 182.4 = 13.51% %3D %3D Variance of Stoc Y's returns = 0.6*(8% - 5.6%)2 + 0.4*(2% - 5.6%)2 = 3.46 + 5.18 = 8.64 Standard deviation of Stock Y = square root of 8.64 = 2.94% %3D Covariance between Stock X and Stock Y = 0.6*(15% - 7%)*(8% - 5.6%) + 0.4*(-5% - 7%)*(2% - 5.6%) = 28.8 Correlation between Stock X and Stock Y = 28.8/(13.51*2.94) = 0.73 g) Use the following two stocks. Scenario Probability Stock A Stock B Boom 30% 12% 20% Recession 70% 18% 5% i) Find the expected return on each stock. ii) Find the standard deviation of each stock. iii) Find the covariance between two stocks.
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Transcribed Image Text:Refer to the following example for part g)
Suppose that you consider two stocks, X and Y with their probability distribution.
Scenario Probability Stock X's return Stock Y's return
Bull market 60% 15% 8%
Bear market 40% -5% 2%
Expected rate of return on Stock X = 0.6*15% + 0.4*(-5%) = 9% + (-2%) = 7%
Expected rate of return on Stock Y = 0.6*8% + 0.4*2% = 4.8% + 0.8% = 5.6%
%3D
%3D
%3D
Variance of Stock X's returns = 0.6*(15% - 7%)2 + 0.4*(-5% - 7%)2 = 38.4 + 144 = 182.4
Standard deviation of Stock X = square root of 182.4 = 13.51%
%3D
%3D
Variance of Stoc Y's returns = 0.6*(8% - 5.6%)2 + 0.4*(2% - 5.6%)2 = 3.46 + 5.18 = 8.64
Standard deviation of Stock Y = square root of 8.64 = 2.94%
%3D
Covariance between Stock X and Stock Y = 0.6*(15% - 7%)*(8% - 5.6%) + 0.4*(-5% - 7%)*(2%
- 5.6%)
= 28.8
Correlation between Stock X and Stock Y = 28.8/(13.51*2.94) = 0.73
g) Use the following two stocks.
Scenario Probability Stock A Stock B
Boom 30% 12% 20%
Recession 70% 18% 5%
i) Find the expected return on each stock.
ii) Find the standard deviation of each stock.
iii) Find the covariance between two stocks.
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