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Beta, Covariance, SML, CML

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1. Morgan Stanley economists have determined the states of nature and corresponding returns for both Morgan Stanley stock and the S&P 500 index. What is the covariance of the returns on Morgan Stanley stock with the S&P 500? What is the beta of Morgan Stanley stock?

Probability Morgan Stanley S&P500
Boom Times 0.8 14.30% 14.20%
Bad Times 0.2 -2.70% -6.80%

2. A friend in finance shows you the following two figures. She asks you a few facts about them. S represents the safe asset. M represents the market portfolio.
a. What is the name of the line segment between S and M in Figure 1?

b. What is the name of the line in figure 2?

c. How can one achieve a portfolio with the characteristics of point B in Figure 1?

d. Point X and Point X' are meant to represent Xerox common stock. In Figure 1 Xerox appears to be riskier than the market portfolio. In Figure 2 it seems to be safer. Is there something wrong with the two figures? If so, explain why Xerox cannot appear as shown. If it is possible that the two figures are correct, explain what must be true about Xerox to cause its representation to be in such a different location in the two graphs.

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Solution Summary

Answers to 2 questions-one on covariance and beta of Morgan Stanley stock, the other on Capital Market Line and Security Market Line

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1. Morgan Stanley economists have determined the states of nature and corresponding returns for both Morgan Stanley stock and the S&P 500 index. What is the covariance of the returns on Morgan Stanley stock with the S&P 500? What is the beta of Morgan Stanley stock?
Probability Morgan Stanley S&P500
Boom Times .8 14.3% 14.2%
Bad Times .2 -2.7% -6.8%

Step 1
Let us first calculate mean return, variance of returns and standard deviation of returns for Morgan Stanley and S&P
Morgan Stanley

Morgan Stanley
return Probability return x Probability Difference from mean Difference 2 Prob x Difference 2
14.30% 0.8 11.44% 3.40% 0.001156 0.0009248
-2.70% 0.2 -0.54% -13.60% 0.018496 0.0036992
Total 1.00 10.90% 0.0046240

Expected return= 10.90%
Variance= 0.004624
Standard deviation=√Variance= 6.80% =√0.004624

S&P500

S&P500
return Probability return x Probability Difference from mean Difference 2 Prob x Difference ...

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