Friedman proposes the following equation:
$r_{b}(0)+r_{b}(0)\frac{d(\frac{1}{r_{b}(t)})}{dt}=r_{b}(0)-\frac{r_{b}(0)}{r_b^2(t)}\frac{dr_{b}(t)}{dt}$
Where $r_{b}(0)$ is the bond interest rate at the original time,t is time and $1/r_{b}(t)$ is the bond price at a given time.
If we were to calculate the rate of change of the bond interest rate during time, wouldn't it be $r_{b}(0)\frac{dr_{b}(t)}{dt}$? Also, I cannot understand how the left side of the equation is transformed into the right side.
Any help would be greatly appreciated. Thank you.
Not sure about the financial meaning, but the transformation from LHS to RHS is quite easy to explain - it's chain rule.
$\displaystyle \frac{d(\frac 1{r_b(t)})}{dt} = \frac{d(\frac 1{r_b(t)})}{dr_b(t)}\cdot \frac{d r_b(t)}{dt} = -\frac 1{r_b(t)^2}\frac{d r_b(t)}{dt} $