# Risk Marketplace

The Risk Marketplace is a weighted constant product automated market maker (AMM) that enables decentralized token trading. The DEX supports two main types of swaps: standard `swaps` and `split-and-swap`  operations.

## 1.  Types of Swaps <a href="#types-of-swaps" id="types-of-swaps"></a>

* **Standard Swap**: Users can trade between underlying assets and the SMART tokens within customized elastic supply pools.
* **Split and Swap**: This function allows users to deposit the underlying token and simultaneously swap one of the resulting SMART tokens for the other in a single, atomic transaction. This is particularly useful for traders who prefer to hold only one type of SMART token.

## 2.  Core Mechanism

The Risk Marketplace uses a weighted constant product invariant to determine token prices and swap outputs. Unlike traditional constant product AMMs (x × y = k), it extends the formula to support multiple tokens with customizable weights:

$$\prod\_{i=1}^{n} B\_i^{W\_i} = k$$

Where:

* $$B\_i$$ = Balance of token (i) in the pool
* $$W\_i$$ = Normalized weight of token (i)
* $$k$$ = Invariant (remains constant during swaps)

This design allows pools to hold 2-8 tokens with arbitrary weight distributions (e.g., 80/20, 60/20/20), enabling more capital-efficient exposure to specific assets.

***

#### Spot Price

The spot price between any two tokens in the pool is derived from their balance and weight ratios:

$$SP\_{i}^{o} = \frac{B\_i / W\_i}{B\_o / W\_o} \cdot \frac{1}{1 - LPFee}$$

Wher&#x65;**:**

* $$B\_i$$: Balance of token *i*, the token being sold by the trader (going into the pool).
* $$B\_o$$: Balance of token *o*, the token being bought by the trader (coming out of the pool).
* $$W\_i$$: Weight of token *i*.
* $$W\_o$$: Weight of token *o*.

***

## 3.  Swap Calculations

#### 3. a)  Output Given Input (Exact In)

When a user specifies an exact input amount, the output is calculated as:

$$
A\_o = B\_o \cdot \left(1 - \left(\frac{B\_i}{B\_i + A\_i \cdot (1 - \text{LPFee})}\right)^{\frac{W\_i}{W\_o}}\right)
$$

Where:

* $$A\_o$$: Output token amount
* $$A\_i$$: Input token amount
* $$B\_i, B\_o$$: Pool balances for tokens (i) and (o), respectively
* $$W\_i, W\_o$$: Weights of tokens (i) and (o)

#### 3. b)  Input Given Output (Exact Out)

When a user specifies an exact output amount, the required input is:

$$
A\_i = \frac{B\_i \cdot \left(\left(\frac{B\_o}{B\_o - A\_o}\right)^{\frac{W\_o}{W\_i}} - 1\right)}{1 - \text{LPFee}}
$$

Where:

* $$A\_i$$: Input token amount needed
* $$A\_o$$: Desired output token amount
* $$B\_i, B\_o$$: Pool balances for tokens (i) and (o), respectively
* $$W\_i, W\_o$$: Weights of tokens (i) and (o)


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://docs.riskprotocol.io/protocol-design-and-specifications/risk-marketplace.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.