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Key variables and terms

VariableDescriptionValue/Example
rnet_cycler_{\mathrm{net\_cycle}}Net income to the pool per cycle (2 business days), before mgmt & costsTypically 0.00680.0068 (0.68%)
NbaseN_{\mathrm{base}}Base cycles per year (T+2 cadence)Example: 125125
non_selling_days\text{non\_selling\_days}Days/year with near-zero sales (holidays)44
NeffN_{\mathrm{eff}}Effective cycles per yearNbase−⌈non_selling_days2⌉N_{\text{base}} - \left\lceil \frac{\text{non\_selling\_days}}{2} \right\rceil
u\mathrm{u}Operational utilization of deployable capital(0.10⋯1.00)(0.10 \cdots 1.00)
R\text{R}Liquidity reserve ratio (non-deployable)0.100.10 (10%)
ueffu_{\mathrm{eff}}Effective utilization(1−R)⋅u(1 - R)\cdot u
crampc_{\mathrm{ramp}}On/off-ramp cost per cycle USDC↔CLPUSDC\leftrightarrow CLP0.0040.004 (0.40%)
FXyrFX_{\mathrm{yr}}Annual FX impact (loss if unhedged, or forward cost if hedged)—
DyrD_{\mathrm{yr}}Unexpected annual loss (net chargebacks/defaults)—
mgmt\text{mgmt}Annual management fee0.030.03 (3%)

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Core formulas

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Effective utilization

ueff=(1−R)⋅uu_{\text{eff}} = (1 - R)\cdot u

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Effective cycles per year

Neff=Nbase−⌈non_selling_days2⌉N_{\text{eff}} = N_{\text{base}} - \left\lceil \frac{\text{non\_selling\_days}}{2} \right\rceil

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Per-cycle FX component

first one will be use on stage 1 and second one for stage 2

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Unhedged FX (expected loss):

FXper_cycle=FX_lossyrNeff\text{FX}_{\text{per\_cycle}} = \frac{\text{FX\_loss}_{\text{yr}}}{N_{\text{eff}}}

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Hedged FX (forward cost):

FXper_cycle=FX_forward_costyrNeff\text{FX}_{\text{per\_cycle}} = \frac{\text{FX\_forward\_cost}_{\text{yr}}}{N_{\text{eff}}}

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Net per-cycle rate (after costs/losses)

rcycle=max⁡(0,  rnet_cycle−cramp−FXper_cycle−DyrNeff)r_{\text{cycle}} = \max\Big(0,\; r_{\text{net\_cycle}} - c_{\text{ramp}} - \text{FX}_{\text{per\_cycle}} - \frac{D_{\text{yr}}}{N_{\text{eff}}}\Big)

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Gross APY

APYgross=(1+ueff⋅rcycle)Neff−1\text{APY}_{\text{gross}} = \big(1 + u_{\text{eff}}\cdot r_{\text{cycle}}\big)^{N_{\text{eff}}} - 1

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Net APY to LPs

APYnet=(1+ueff⋅rcycle)Neff−1−mgmt\text{APY}_{\text{net}} = \big(1 + u_{\text{eff}}\cdot r_{\text{cycle}}\big)^{N_{\text{eff}}} - 1 - \text{mgmt}

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Monthly equivalent

Monthlyequiv=(1+APYnet)1/12−1\text{Monthly}_{\text{equiv}} = \big(1 + \text{APY}_{\text{net}}\big)^{1/12} - 1

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What each factor does (directional effects)

FactorEffectExplanation
Operational utilization (u)↑ ⇒ ueffu_{\mathrm{eff}} ↑ ⇒ APY ↑More of the pool is actually earning the per-cycle rate.
Reserve ratio (R)↑ ⇒ (ueff)(u_{\mathrm{eff}}) ↓ ⇒ APY ↓More cash is held idle; safer liquidity, lower yield.
Per-cycle income (rnet_cycle)(r_{\mathrm{net\_cycle}})↑ ⇒ (rcycle)(r_{\mathrm{cycle}}) ↑ ⇒ APY ↑Top-line spread improvement lifts every cycle before compounding.
On/Off-ramp cost (cramp)(c_{\mathrm{ramp}})↑ ⇒ (rcycle)(r_{\mathrm{cycle}}) ↓ ⇒ APY ↓It’s a per-cycle drag; streamlining rails/batching helps.
FX (unhedged loss or forward cost)↑ ⇒ (rcycle)(r_{\mathrm{cycle}}) ↓ ⇒ APY ↓Trade-off between cost and volatility; short duration helps.
Unexpected annual loss (Dyr)(D_{\mathrm{yr}})↑ ⇒ (rcycle)(r_{\mathrm{cycle}}) ↓ ⇒ APY ↓Allocated per cycle as (Dyr/Neff)(D_{\mathrm{yr}}/N_{\mathrm{eff}}).
Effective cycles (Neff)(N_{\mathrm{eff}})↑ ⇒ more compounding ⇒ APY ↑Fewer non-selling days and smoother ops preserve cycles.
Management fee (mgmt = 3% AUM)↑ ⇒ APY ↓Subtracted at the end; linear effect on the net.

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Worked example ~23.28% net APY (compounded)

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Assumptions

VariableValueNotes
uu0.800.80Operational utilization
RR0.100.10Reserve ratio ⇒ ueff=0.72u_{\mathrm{eff}} = 0.72
NbaseN_{\mathrm{base}}125125Base cycles per year
non_selling_days\text{non\_selling\_days}44⇒ Neff=123N_{\mathrm{eff}} = 123
rnet_cycler_{\mathrm{net\_cycle}}0.00680.00680.68% per cycle
crampc_{\text{ramp}}0.0040.0040.40% per cycle
FXloss_yrFX_{\mathrm{loss\_yr}}0.000.00FX unhedged with zero expected drift
DyrD_{\mathrm{yr}}0.020.022% unexpected annual loss
mgmt\text{mgmt}0.030.033% AUM

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Per-cycle net rate

rcycle=0.0068−0.004−0−0.02123≈0.0026374r_{\text{cycle}} = 0.0068 - 0.004 - 0 - \frac{0.02}{123} \approx 0.0026374

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Gross APY

APYgross=(1+0.72⋅0.0026374)123−1≈0.2628\text{APY}_{\text{gross}} = \big(1 + 0.72 \cdot 0.0026374\big)^{123} - 1 \approx 0.2628

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Net APY

APYnet≈0.2628−0.03=0.2328  (23.28%)\mathrm{APY}_{\mathrm{net}} \approx 0.2628 - 0.03 = 0.2328\;(23.28\%)

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Monthly equivalent

(1+0.2328)1/12−1≈1.76% per month(1 + 0.2328)^{1/12} - 1 \approx 1.76\%\ \text{per month}

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Summary

MetricDescriptionValue
uuOperational utilization0.80
RRLiquidity reserve ratio (non-deployable)0.10
NbaseN_{\mathrm{base}}Base cycles per year125
NeffN_{\mathrm{eff}}Effective cycles per year123
crampc_{\mathrm{ramp}}On/Off-ramp cost per cycle USDC↔CLPUSDC\leftrightarrow CLP0.004
FXyrFX_{\mathrm{yr}}Annual FX impact (loss if unhedged, or forward cost if hedged)0.00
DyrD_{\mathrm{yr}}Unexpected annual loss (net chargebacks/defaults)0.02
mgmt\text{mgmt}Annual management fee0.03
rcycler_{\mathrm{cycle}}Per-cycle net rate0.0026374
APYgross\text{APY}_{\text{gross}}Gross APY26.28%
APYnet\text{APY}_{\text{net}}Net APY23.28%
Monthlyequiv\text{Monthly}_{\text{equiv}}Monthly equivalent1.76%
This example assumes a 2% unexpected annual loss, which is typical for credit card networks. In practice, the loss rate is much lower, closer to 0.1-0.2%.