The margin system

Exposures

Instruments in REYA have linear exposures to these risk factors. Explicitly, this means that if risk factors are a multivariate random variable $R_t$ of $n$ factors, then each instrument determines a vector $E_t$such that the price of the instrument is

$$P_t=E_t'R_t$$

This means in particular that the entries of $E_t'$ transform the risk factors into token amounts. As a consequence, note that the exposure vector will often be a function of more than just time: for example, if a given risk factor is the relative (percentual) returns $r_{t,i}$ of some asset, then $e_{t,i}$ will generally have the price $p_{t,i}$ as a factor to transform the percentual return $r_{t,i}$ into an absolute return $p_{t,i}r_{t,i}$ in token amount. For example, if a user holds exposure of two units of ETH when its price is $1500, then their exposure is $3000.

Finally, note that by linearity, exposures are additive, meaning that a portfolio’s exposure is simply the weighted sum (with portfolio weights) of the exposure vectors of each component.

The risk matrix

Having established the fundamental framework, pools in REYA take as risk parameters an $n\times n$ matrix $A$, as well as two multipliers $\lambda_M$ and $\lambda_I$. Given this matrix, REYA computes the liquidation margin requirement for a portfolio exposure vector $E$ as

$$\mathrm{LMR}=\sqrt{E'AE}$$

and then $\mathrm{MMR}=\lambda_M\mathrm{LMR}$ and $\mathrm{IMR}=\lambda_I\mathrm{LMR}$.

The matrix $A$of course, must be carefully chosen and updated for the system to appropriately margin portfolios. The cases of multivariate normal and Student's t-distribution are instructive in getting intuition about the risk matrix.

However, REYA will generally rely on a more flexible version, where the components can be independently adjusted according to risk estimates mixing, e.g., Value-at-Risk and Expected Shortfall methods.