H10 - Gains from Diversification A Two-Security...

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Gains from Diversification: A Two-Security Illustration W. L. Silber The nice thing about diversification is that it almost always produces gains to a portfolio in the form of increased return that exceeds the cost in terms of increased standard deviation. The only exception is the case of correlation equal to one. This is nicely illustrated with a simple numerical example. Recall that the expected return, R, on a two-asset portfolio is: (1) 2 2 1 1 R X R X R + = , where R 1 and R 2 are the expected returns on security 1 and 2 and X 1 and X 2 are the weights invested in each. The standard deviation ( 29 s on the portfolio is: (2) 2 / 1 2 1 2 1 2 2 2 2 2 1 2 1 ] 2 [ r s s s s s X X X X + + = , where 1 s and 2 s are the standard deviations of asset 1 and 2 and r is the correlation of returns. Suppose we have the following information: 24 . 13 . 2 1 = = R R 136 . 064 . 2 1 = = s s If X 1 =1 and X 2 =0, then the return on the portfolio is .13 and the standard deviation is .064, all the same as asset 1.
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H10 - Gains from Diversification A Two-Security...

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