You are considering investing in Microsoft stock. From Bloomberg, you download i

Question

You are considering investing in Microsoft stock. From Bloomberg, you download information on its beta coefficient, which is equal to 2. The risk free rate is currently 2% and the return on the S&P 500 index (which you use as a proxy for the market portfolio) is 15%. You estimate that Microsoft’s dividends are expected to grow at 5% per year.

If the standard deviation of returns on Microsoft is 40% per annum and the standard deviation of the S&P 500 is 20%, what is the correlation coefficient between returns on Microsoft and returns on S&P 500 index

Explanation / Answer

Beta = covariance/variance of the S&P index

2 = covariance/(0.2^2)

covariance = 2*0.2*0.2

correlation coefficient covariance/standard dev of Microsoft*standard dev of S&P

correlation coefficient = 2*0.2*0.2/0.4*0.2

correlation coefficient = 1.00

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