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**Beta calculation details**

The calculation divides the covariance of the stock return with the market return by the variance of the market return

thus: ** beta = cov(ri.rm) / var(rm)** where

stock return ri = (stock price at time w / stock price at time (w-1))-1

market return rm = (index at time w / index at time (w-1))-1

E(ri) = arithmetic mean of stock returns

E(rm) = arithmetic mean of market returns

covariance cov (ri,rm) = sum [ri-E(ri))*(rm-E(rm))]/count(ri-E(ri))*count(rm-E(rm))

variance var(rm) = sum[(rm-E(rm))^2]/count(rm-E(rm))^2