Third multiplythe previous product by the probability

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Unformatted text preview: iplythe previous product by the probability of its occurrence. Fourth, find the some of all the weighted products. The result is the covariance. Calculation of covariance between F and G Probability of Occurrence Deviation of F from r hat Deviation of G from r hat Product of deviations Product * P rob. 10% 20% 4 0% 20% 10% 100% -4 % -2% 0% 2% 4% 4% 2% 0% -2% -4 % -0.1600% -0.04 00% 0.0000% -0.04 00% -0.1600% -0.02% -0.01% 0.00% -0.01% -0.02% Covariance = s um = -0.04 8% Calculation of covariance between F and H Probability of Occurrence Deviation of F from r hat Deviation of H from r hat Product of deviations Product * P rob. 10% 20% 4 0% 20% 10% 100% -4 % -2% 0% 2% 4% -6% -4 % -2% 5% 12% 0.24 00% 0.0800% 0.0000% 0.1000% 0.4 800% 0.02% 0.02% 0.00% 0.02% 0.05% Covariance = s um = 0.108% Calculation of covariance between F and E Probability of Occurrence Deviation of F from r hat Deviation of E from r hat Product of deviations Product * P rob. 10% 20% 4 0% 20% 10% 100% -4 % -2% 0% 2% 4% 0% 0% 0% 0% 0% 0.0000% 0.0000% 0.0000% 0.0000% 0.0000% 0.00% 0.00% 0.00% 0.00% 0.00% Covariance = s um = 0.000% CORRELATION COEFFICIENT Like covariance, the correlation coefficient also measures the tendency of two stocks to move together, but it is standardized and it is always in the range of -1 to +1. The correlation coefficient is equal to the covariance divided by the product of the standard deviations. Calculation of the correlation between F and G ρFG = Covariance FG = -0.04 8% = -0.04 8% ρFG = -1.0 SigmaF * SigmaG ÷ ÷ ÷ 2.19% 0.04 8% 2.19% Calculation of the correlation between F and H ρFH = Covariance FH = 0.108% = 0.108% ρFH = 0.935 ÷ ÷ ÷ SigmaF * SigmaH 2.19% 0.116% 5.27% PORTFOLIO RISK AND RETURN: THE TWO-ASSET CASE Suppose there are two assets, A and B. wA is the percent of the portfolio invested in asset A. Since the total percents invested in the asset must add up to 1, (1-w A) is the percent of the portfolio invested in asset B. The expected return on the portfolio...
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