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?

Question

Business

Gage Gould

18 December, 01:39

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?

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Answers (1)

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Gina · Answer 1

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