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# The two entries in the diagonal boxes depend on the

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Unformatted text preview: o invested in stock 1. Similarly, the bottom left corner is the variance of stock 2 times the square of the fraction of the portfolio invested in stock 2. The two entries in the diagonal boxes depend on the covariance between stock 1 and 2. The covariance is equal to the correlation coefficient times the product of the two standard deviations on stock 1 and 2. The portfolio variance is obtained by adding the content of the four boxes together: 22 Portfolio variance w12V 12  w2 V 2  2 w1 w2 U12V 1V 2 The benefit of diversification follows directly from the formula of the portfolio variance, since the portfolio variance is increasing in the covariance between stock 1 and 2. Combining stocks with a low correlation coefficient will therefore reduce the variance on the portfolio. Example: - Suppose you invest 50% of your portfolio in Nokia and 50% in Nestlé. The standard deviation on Nokia’s and Nestlé's return is 30% and 20%, respectively. The correlation coefficient between the two stocks is 0.4. What is the portfolio variance? 22 Portfolio variance w12V 12  w2 V 2  2w1 w2 U12V 1V 2 0.5 2  30 2  0.5 2 20 2  2...
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