# Collateral Ratio

**The Collateral Ratio**is the ratio in which the stablecoins and utility tokens are required to create the fractional-algorithmic stablecoin. For KUSD, it is the ratio between USDC and DOPX. A collateral ratio of 100% means that the user needs 100% worth of USDC and 0% worth of DOPX to mint KUSD, while a collateral ratio of 60% means that the user needs 60% worth of USDC and 40% of DOPX to create KUSD.

Example of KUSD at Collateral Ratio of 60% (Backed by USDC 60% and DOPX 40%)

The general formula of calculating the proportion of KUSD is from this equation:

$KUSD=P_{USDC}\times USDC + P_{DOPX}\times DOPX$

$(1-C_r)( P_{USDC}\times USDC)= C_r(P_{DOPX}\times DOPX)$

Which reads:

*Amount of KUSD is the sum of USDC values and DOPX values where the proportion of USDC value to DOPX value is the Collateral Ratio.*

**Example:**

At a Collateral Ratio of 60%, given that USDC price is $1 and DOPX price is $2, a user wants mint $100 worth of KUSD. The values can be substituted in the formula as follows:

$100 = 1 \times USDC + 2 \times DOPX$

$0.4(1\times USDC) = 0.6(2\times DOPX)$

After solving the system of equations, the user will need to supply 60 USDC and 20 DOPX (this example excludes the minting fees for clarification).

The Collateral Ratio might increase/decrease by 0.25% every hour by taking the price of KUSD as well as other factors (to be described below) into account. Eventually, the Collateral Ratio will reach the equilibrium at each moment in time that signifies the balance between the stablecoin and utility tokens, at which the Collateral Ratio will not change.

The Collateral Ratio will gradually decrease if the price of KUSD has shown that it could be kept on peg for a certain period of time in order to utilize DOPX tokens more and be less dependent on the USDC value.

On the other hand, the Collateral Ratio will increase when the price of KUSD is too volatile, especially when the price is below $1, in order to keep the KUSD price on peg.

Simplified example below shows the relation ship beginning with KUSD price of $1 and Collateral Ratio of 0.9 (not to scale). There are other factors that affect the Collateral Ratio.

Simplified example of relationship between the price of KUSD and Collateral Ratio.

To make sure that the Collateral Ratio reflects the situation of KUSD better, “Growth Rate” is also considered to dynamically adjust the Collateral Ratio. The Growth Rate is calculated by the ratio of the total worth of DOPX across all liquidity pools that has DOPX to the total worth of circulating KUSD in the ecosystem. A higher growth rate implies that DOPX is less volatile, which means less price impact while selling DOPX, as well as indicating that more redemption could be made without having a high impact on the KUSD itself.

Last modified 1yr ago