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Write out the equation for the covariance in the returns of two assets, Asset 1 and...

Write out the equation for the covariance in the returns of two assets, Asset 1 and Asset 2. Using that equation, explain the easiest way for the two asset returns to have a covariance of zero.

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Answer #1

The equation for the covariance of the two assets = Std. deviation of Asset 1 * Std. deviation of Asset 2 * Correlation between the two assets

Now, if one of the two assets is a risk free asset, its standard deviation will be zero. Therefore the covariance also becomes zero

Covariance = Std. deviation of Asset 1 * Std. deviation of Asset 2 * Correlation between the two assets

Now, if we consider the asset 1 to be risk free, its std. deviation is 0 as shown below:

Covariance = 0*Std. deviation of Asset 2 * Correlation between the two assets

Covairance = 0 ( Since zero Multiplied by anything is zero)

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