# Collateral Ratio and Leverage

Let C.R. be $f\ (> 1)$ i.e. with a collateral of value $c$ one can take a maximum debt of $\frac{c}{f}$. One can then redeposit this debt as collateral to borrow even more ($\frac{c}{f^2}$). The maximum exposure that one can get in total to the collateral asset is

$$
\begin{align*}
&c + \frac{c}{f} + \frac{c}{f^2} + ...\\
=\ & c \left[1 + \frac{1}{f} + \frac{1}{f^2} ... \right]\\
=\ &\frac{fc}{f-1}
\end{align*}
$$

Defining leverage $L$ as the total exposure divided by the intial collateral

$$
\begin{align*}
L = \frac{f}{f - 1}
\end{align*}
$$

A C.R. $f$ of 110% implies a max leverage $L$ of $11$x