ZivoeMath.sol

Mathematics for Yield Distributions

Introduction

This contract facilitates mathematics, intended solely for the YDL.

Note: This contract is deployed and tracked via ZivoeYDL, see ZivoeYDL.sol and for further information on the derivation of the equations, see

State Variables

Type	Name	Description
uint256	BIPS	Private constant, 10000
uint256	WAD	Private constant, 10**18
uint256	RAY	Private constant, 10**27

Sections

Read Functions

• ema() - Calculates the current EMA (exponential moving average).

• juniorProportion() - Calculates proportion of yield attributable to junior tranche.

• seniorProportion() - Calculates proportion of yield distributble which is attributable to the senior tranche.

• seniorProportionBase() - Calculates proportion of yield attributed to senior tranche (no extenuating circumstances).

• seniorProportionShortfall() - Calculates proportion of yield attributed to senior tranche (shortfall occurence).

• yieldTarget() - Calculates amount of annual yield required to meet target rate for both tranches.

Read Functions

ema()

Calculates the current EMA (exponential moving average).

function ema(
    uint256 bV, 
    uint256 cV, 
    uint256 N
) external pure returns (uint256 eV);

Type	Name	Description
uint256	bV	The base value (typically an EMA from prior calculations).
uint256	cV	The current value, which is factored into bV.
uint256	N	Number of steps to average over.

Returns

Type	Name	Description
uint256	eV	EMA-based value given prior and current conditions.

juniorProportion()

Calculates proportion of yield attributable to junior tranche.

function juniorProportion(
    uint256 eSTT,
    uint256 eJTT, 
    uint256 sP,
    uint256 Q
) external pure returns (uint256 jP);

Type	Name	Description
uint256	eSTT	ema-based supply of zSTT (units = WEI)
uint256	eJTT	ema-based supply of zJTT (units = WEI)
uint256	sP	Proportion of yield attributable to seniors (units = RAY)
uint256	Q	senior to junior tranche target ratio (units = BIPS)

Returns

Type	Name	Description
uint256	jP	Yield attributable to junior tranche in RAY.

seniorProportion()

Calculates proportion of yield distributable which is attributable to the senior tranche.

function seniorProportion(
    uint256 yD,
    uint256 yT,
    uint256 eSTT, 
    uint256 eJTT, 
    uint256 Y, 
    uint256 Q, 
    uint256 T
) external pure returns (uint256 sP);

Type	Name	Description
uint256	yD	yield distributable (units = WEI)
uint256	yT	ema-based yield target (units = WEI)
uint256	eSTT	ema-based supply of zSTT (units = WEI)
uint256	eJTT	ema-based supply of zJTT (units = WEI)
uint256	Y	target annual yield for senior tranche (units = BIPS)
uint256	Q	multiple of Y (units = BIPS)
uint256	T	# of days between distributions (units = integer)

Returns

Type	Name	Description
uint256	sP	Proportion of yD attributable to senior tranche.

seniorProportionBase()

Calculates proportion of yield attributed to senior tranche (no extenuating circumstances).

function seniorProportionBase(
    uint256 yD, 
    uint256 eSTT, 
    uint256 Y, 
    uint256 T
) public pure returns (uint256 sPB);

Type	Name	Description
uint256	yD	yield distributable (units = WEI)
uint256	eSTT	ema-based supply of zSTT (units = WEI)
uint256	Y	target annual yield for senior tranche (units = BIPS)
uint256	T	# of days between distributions (units = integer)

Returns

Type	Name	Description
uint256	sPB	Proportion of yield attributed to senior tranche in RAY.

seniorProportionShortfall()

Calculates proportion of yield attributed to senior tranche (shortfall occurence).

function seniorProportionShortfall(
    uint256 eSTT, 
    uint256 eJTT, 
    uint256 Q
) public pure returns (uint256 sPS);

Type	Name	Description
uint256	eSTT	ema-based supply of zSTT (units = WEI)
uint256	eJTT	ema-based supply of zJTT (units = WEI)
uint256	Q	multiple of Y (units = BIPS)

Returns

Type	Name	Description
uint256	sPS	Proportion of yield attributed to senior tranche in RAY.

yieldTarget()

Calculates amount of annual yield required to meet target rate for both tranches.

function yieldTarget(
    uint256 eSTT,
    uint256 eJTT, 
    uint256 Y, 
    uint256 Q, 
    uint256 T
) public pure returns (uint256 yT);

Type	Name	Description
uint256	eSTT	ema-based supply of zSTT (units = WEI)
uint256	eJTT	ema-based supply of zJTT (units = WEI)
uint256	Y	target annual yield for senior tranche (units = BIPS)
uint256	Q	multiple of Y (units = BIPS)
uint256	T	# of days between distributions (units = integer)

Returns

Type	Name	Description
uint256	yT	yield target for the senior and junior tranche combined.