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:
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.
- 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
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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