# 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

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

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.

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