# Equity management

Once a position has been opened, a trader can add or remove equity. Equity is the sum between the initial margin and a trader's P\&L. The table below summarises the impact of each action on the long and short positions.

<table><thead><tr><th width="150"> </th><th>Long position</th><th>Short position</th></tr></thead><tbody><tr><td>Add equity</td><td>Remove money from the borrowing position, i.e. the trader could recover part of the interest paid in advance</td><td>Add money to the lending position, i.e. the trader will get extra income</td></tr><tr><td>Remove equity</td><td>Add money to the borrowing position, i.e. the trader will pay the interest on the removed equity amount</td><td>Remove money from the  lending position, i.e. the trader will get less income from the lent amount</td></tr></tbody></table>

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The following examples do take into account potential liquidation for low collaterisation ratios. They are indicative to better understand the impact of equity management.&#x20;
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{% hint style="warning" %}
In this section, the collatisation ratio for borrowing $$CR\_{borrow}$$ refers to the one on the underlying borrowing protocol and not on the expirabel position itself.
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## Long position

Below we will consider the numerical example of a long position opened in [position opening](https://contango-2.gitbook.io/exchange/protocol/protocol-pricing/position-opening) where:

* $$S\_{L}=100.10 : DAI$$
* the trader has posted $$50 :DAI$$ as margin
* the price to open the long position is $$P\_{O,L} = 100.59 : DAI$$
* $$0.9929 : ETH$$have been lent, i.e. the equivalent of $$0.9929 \*99.90 = 99.19:DAI$$
* the debt (principal + interest) is $$D=50.59 : DAI$$.

Remembering the concept of flash swaps used in the protocol (see the [borrowing and lending](https://contango-2.gitbook.io/exchange/protocol/borrowing-and-lending) section), where the zero-coupon bond for lending $$ETH$$ is used as collateral to borrow $$DAI$$, we find a collaterisation ratio for borrowing of $$CR\_{borrow}=\dfrac{99.19}{50.50}=196.07 %$$.

### Add equity

When equity is added to a position, it is used to repay earlier some debt and hence increase the collaterisation ratio for borrowing $$CR\_{borrow}$$ of the borrowed $$DAI$$. Taking the example of the long position which has been opened, and supposing that the spot price remains the same, let's say a trader wants to add $$20 :DAI$$ at $$T=0.2$$ when $$r\_{Q,l}=9%$$:&#x20;

* the debt recovered is $$20\*{(1+0.09)}^{0.2}=20.35:DAI$$
* The remaining debt is $$D=50.59-20=30.24: DAI$$
* and the new collaterisation ratio for borrowing would be $$CR\_{borrow}=\dfrac{99.19}{30.24}=327.99%$$.

### Remove equity

Since the initial posted $$DAI$$was used to buy the required $$ETH$$, this equity is no more available and a trader cannot simply withdraw it. Hence, if a trader wants to remove some equity to decrease the collaterisation ratio $$CR\_{borrow}$$, the protocol will simply borrow the required $$DAI$$ directly at a fixed rate on an underlying fixed rate protocol. Taking the example of the long position which has been opened, and supposing that the spot price remains the same, let's say a trader wants to remove $$10 :DAI$$ at $$T=0.2$$ when $$r\_{Q,b}=10%$$:&#x20;

* the extra debt (principal + interest) is $$10\*{(1+0.1)}^{0.2}=10.19:DAI$$
* the total debt will become $$D=50.59+10.19=60.78: DAI$$
* and the new collaterisation ratio for borrowing would be $$CR\_{borrow}=\dfrac{99.19}{60.78}=163.19%$$.

{% hint style="info" %}
The mechanism used in Contango to remove equity implies that a trader can remove an amount of equity higher than the initial posted margin. This allows a trader to get out some equity, or crystallise the P\&L, without having to partially close a position.
{% endhint %}

## Short Position

Below we will consider the numerical example of a short position opened in [position opening](https://contango-2.gitbook.io/exchange/protocol/protocol-pricing/position-opening) where:

* $$S\_{S}=99.90 : DAI$$
* the trader has posted $$50 :DAI$$ as margin
* the price to open the short position is $$P\_{O,S} = 102.70 : DAI$$
* $$0.9924: ETH$$ have been borrowed, i.e. the equivalent of $$0.9924\*99.90 = 99.14 :DAI$$
* the lent amount (principal + interest) is $$L=152.70 : DAI$$.

Remembering the concept of flash swaps used in the protocol (see the [borrowing and lending](https://contango-2.gitbook.io/exchange/protocol/borrowing-and-lending) section), where the zero-coupon bond for lending $$DAI$$ is used as collateral to borrow $$ETH$$, we find a collaterisation ratio for borrowing of $$CR\_{borrow}=\dfrac{152.70}{99.14}=154.02 %$$.

### Add equity

Adding equity is equivalent to lend more $$DAI$$, i.e. add more collateral for the debt and increase the collaterisation ratio. Taking the example of adding $$30 :DAI$$ at $$T=0.2$$ when $$r\_{Q,l}=9%$$:&#x20;

* the new lent amount at expiry (principal + interest) is $$30\*{(1+0.09)}^{0.2}=30.52:DAI$$
* the total lent amount is now $$L=152.70+30.52=183.22:DAI$$
* and the new collaterisation ratio for borrowing would be $$CR\_{borrow}=\dfrac{183.22}{99.14}=184.81%$$.

### Remove equity

Removing equity is equivalent to remove money from the lending position. Taking the example of removing $$10 :DAI$$ at $$T=0.2$$ when $$r\_{Q,b}=10%$$:&#x20;

* the lent amount to remove (principal + interest) is $$50\*{(10+0.1)}^{0.2}=10.19:DAI$$
* the remaining total amount is $$L=152.70-10.19=142.51:DAI$$
* and the new collaterisation ratio for borrowing would be $$CR\_{borrow}=\dfrac{142.51}{99.14}=143.74%$$.