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# 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.
Long position
Short position
Remove money from the borrowing position, i.e. the trader could recover part of the interest paid in advance
Add money to the lending position, i.e. the trader will get extra income
Remove equity
Add money to the borrowing position, i.e. the trader will pay the interest on the removed equity amount
Remove money from the lending position, i.e. the trader will get less income from the lent amount
The following examples do take into account potential liquidation for low collaterisation ratios. They are indicative to better understand the impact of equity management.
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.

## Long position

Below we will consider the numerical example of a long position opened in position opening where:
• $S_{L}=100.10 \: DAI$
$50 \:DAI$
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 section), where the zero-coupon bond for lending
$ETH$
is used as collateral to borrow
$DAI$
, we find a collaterisation ratio for borrowing of
$CR_{borrow}=\dfrac{99.19}{50.50}=196.07 \%$
.

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
$r_{Q,l}=9\%$
:
• 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
$r_{Q,b}=10\%$
:
• 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
$CR_{borrow}=\dfrac{99.19}{60.78}=163.19\%$
.
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.

## Short Position

Below we will consider the numerical example of a short position opened in position opening where:
• $S_{S}=99.90 \: DAI$
$50 \:DAI$
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 section), where the zero-coupon bond for lending
$DAI$
is used as collateral to borrow
$ETH$
, we find a collaterisation ratio for borrowing of
$CR_{borrow}=\dfrac{152.70}{99.14}=154.02 \%$
.

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
$r_{Q,l}=9\%$
:
• 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
$r_{Q,b}=10\%$
:
• 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
$CR_{borrow}=\dfrac{142.51}{99.14}=143.74\%$
.