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Stock and Risk

5. Company XYZ studied the relationship between the states of nature and the corresponding returns for both XYZ stock and the S&P 500 index. This is reported on the table below where we asume that there are 2 states.

Probability XYZ S&P 500
Boom Times 0.8 12.30% 14.20%
Bad Times 0.2 -2.70% -6.80%

i) What is the covariance of returns on XYZ stock with the S&P 500?
ii) If we think of the S&P 500 as the market portfolio, what is the beta of XYZ stock?
iii) Assume that the market is in CAPM equilibrium, what is the market price of risk?
iv) What is the risk free rate?
v) The covariance of XYZ stock with that of General Motors (GM) was computed to be 0.005. What is beta of GM? What is the expected return on GM stock?

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i) What is the covariance of returns on XYZ stock with the S&P 500?

Probability Return on XYZ Probability x Return on XYZ Return on S&P Probability x Return on S&P
Boom 0.8 12.30% 9.8400% 14.20% 11.3600%
Bad 0.2 -2.70% -0.5400% -6.80% -1.3600%
9.3000% 10.0000%

Therefore, expected return on XYZ= 9.3000%
Expected return on S&P= 10.0000%

1 2 3 4 5
Probability Return on XYZ Return on S&P Return on XYZ- Expected return on XYZ Return on S&P- Expected return on S&P 1 x 4 x 5
0.8 12.30% 14.20% 3.00% 4.20% 0.001008
0.2 -2.70% -6.80% -12.00% -16.80% 0.004032
Total= 0.00504

Covariance= 0.00504

ii) If we think of the S&P 500 as the market portfolio, ...

Solution Summary

Solution calculates covariance beta and risk and expected return

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