> For the complete documentation index, see [llms.txt](https://docs.world.inc/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.world.inc/details/atlas-math-risk-based-valuation.md).

# ATLAS Math: Risk Based Valuation

## General

The **risk based portfolio valuation** provides a conservative estimate of portfolio value under adverse conditions.

* Market participants must maintain a **positive risk based valuation** at all times.
* If the valuation becomes negative, the account is subject to **liquidation**.
* The exchange operator defines two risk parameters per token:
  * **Risk Price**
  * **Risk Slippage**

## Adjusted Token Balance

For each token, define the **adjusted balance**:

$$
\text{Adjusted Balance(token)} = \text{Token Balance} - \text{Borrowed Quantity with Interest} + \text{Lent Quantity with Haircut}
$$

where:

$$
\text{Lent Quantity with Haircut} = \text{Lend Quantity} \times 0.98
$$

* `tokenBalance` = user’s holdings of the token
* `borrowedQuantityWithInterest` = borrowed amount **plus 10 days of interest**
* `lendQuantity` = total amount lent to others

📌 For efficiency, lending values are aggregated as the **sum of all borrowed positions with the maximum 10-day interest rate**.

## Margin & Portfolio Valuation

The **risk-based valuation** of the portfolio is:

$$
\text{Risk Based Valuation} = \text{Adjusted Bal(BaseToken)} + \sum\_{\text{Non-base tokens}} \text{Token Value}
$$

### Token Value

For each non-base token:

$$
\text{tokenValue} = \min(\text{tokenValue}*{high}, \text{tokenValue}*{low})
$$

where:

$$
\text{tokenValue}*{high} = \text{adjustedBal(token)} \times \text{adjustedTokenPrice}*{high} + \text{aggregatePerpValue}\_{high}
$$

$$
\text{tokenValue}*{low} = \text{adjustedBal(token)} \times \text{adjustedTokenPrice}*{low} + \text{aggregatePerpValue}\_{low}
$$

### Adjusted Token Prices

The adjusted token prices are computed as:

$$
\text{adjustedTokenPrice}*{high} = \text{price}*{mark} \times \Big(1 + \text{riskPrice} - \text{riskSlippage} \times \text{sign}(\text{adjustedBal(token)})\Big)
$$

$$
\text{adjustedTokenPrice}*{low} = \text{price}*{mark} \times \Big(1 - \text{riskPrice} - \text{riskSlippage} \times \text{sign}(\text{adjustedBal(token)})\Big)
$$

### Adjusted Perp Values

For perpetual positions, we compute high and low valuations:

$$
\text{aggregatePerpValue}*{high} = \sum*{\text{perp positions}} \text{perpValue}(\text{markPrice} \times (1 + \text{riskPrice}))
$$

$$
\text{aggregatePerpValue}*{low} = \sum*{\text{perp positions}} \text{perpValue}(\text{markPrice} \times (1 - \text{riskPrice}))
$$

### Perpetual Position Valuation

The **perp value** at a given price is:

$$
\text{Perp Value(price)} = \text{PNL from price movement + Funding Fees at that price}
$$

## SDKs & Optimization

[#sdks](#sdks "mention") have the above formulas built in, so you can test and simulate margin requirements for different position sets.


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