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Does financing a portfolio on margin affect the variance of a portfolio?
Variance of a single asset is defined as follows: σ2 = Σi(Xi - μ)2 where Xi's represent all the possible final market values of your asset and μ represents the mean of all such market values.  The portfolio's variance is defined as σp2 = Σiwi2σi2 where, σp is the portfolio's variance, and wi stands for the weight of the ith asset.  Now, if you include the borrowing in your portfolio, that would classify as technically shorting at the borrowing rate. Thus, this weight would (by the virtue of being negative) increase all other weights. Moreover, the variance of this is likely to be zero (assuming fixed borrowing rates). Thus, weights of risky assets rise and the investor's portfolio's variance will go up. Also see, CML at wikipedia.