Suppose the s& p 500 index has an average return of 11.2% with a standard deviation of 23.7%, and the average return on wells fargo stock is 16.3% with a standard deviation of 42.3%. what is the beta for wells fargo is the correlation coefficient between wells fargo stock return and the s& p 500 index return is 0.82?

Beta = 1.46

Explanation:

Firstly, we need to calculate covariance of S&P 500 return and Well Fargo stock return, using below formula:

Correlation coefficient between Wells Fargo stock return and the S&P 500 Index return = Covariance of S&P 500 return and Well Fargo stock return/(Standard deviation of S&P 500 return x Standard deviation of Well Fargo stock return), or

0.82 = Covariance of S&P 500 return and Well Fargo stock return/(0.237 x 0.423). Solve the equation we get Covariance of S&P 500 return and Well Fargo stock return = 0.082.

Secondly, we calculate beta of S&P 500 return and Well Fargo stock return, using below formula:

Beta = Covariance of S&P 500 return and Well Fargo stock return/Variance of S&P 500 return

       = 0.082/(0.237)^2 = 1.46

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