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This is not a perfect solution but perhaps the following approach could also serve you well as an indicator. Assuming you are only using a finite number (e.g. $n$) of bonds with fixed yields $r_i$ you can write $r_f(w_1, \dots,w_n)=\frac{\sum_0^n w_ir_i}{\sum_0^n w_i}$ with most of the weights being zero. Using the quotient rule you can now calculate ...