Covariance and Correlation Coefficient
? The covariance measure is affected by both the direction that assets move together and the size of those movements
~~? As a result, the magnitude of cov?RA,RB? is sometimes difficult to interpret
? For this reason we also calculate the correlation coefficient
? Correlation Coefficient: A standardized measure of the way in which the returns from two assets move together
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Covariance and Correlation Coefficient
?A,B ?A,B~~cov?RA,RB??~~ ??RA???RB??1???1
?0.00950???0.9994 0.1288?0.0738
Special case: ??0, ??1, ???1.
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Expected Return, Variance, Covariance
n~E?R????iRi??1R1??2R2????nRn
i?1~~?R?ERi?ER2??????2~???iRi?ERi?1n????2~~?A,B?ERAi?ERARBi?ERB?????????
~~???iRAi?ERARBi?ERBn????????A,B~~cov?RA,RB??~~ ??RA???RB?i?1
We use r, ?, and ? for simplicity.
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Portfolio of Two Risky Securities
? Assume that we invest w proportion of the wealth in security 1 and proportion of 1?w of the wealth in security 2
? The expected return of security 1 is r1, and the expected return of security 2 is r2
? The standard deviation of security 1 is ?1, and the standard deviation of security 2 is ?2
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