You are considering investing in Microsoft stock From Bloomb

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

Solution

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