Question

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?

Answer 1

Beta = 1.46

Step-by-step 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