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The beta of a fund is determined as follows: [(n) (sum of (xy)) ]-[ (sum of x) (sum of y)] [(n) (sum of (xx)) ]-[ (sum of x) (sum of x)] where: n = of observations (36 months) x = rate of return for the S&P 500 Index y = rate of return for the fund Beta equation (Stocks) The beta of a stock is determined as follows: [(n) (sum of (xy)) ]- [(sum of x) (sum of y)] [(n) (sum of (xx)) ]-[(sum of x) (sum of x)] where: n = of observations (24-60 months) x = rate of return for the S&P 500 Index y = rate of return for the stock Biased expectations theories Related: pure expectations theory.