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Exponential Decay

Exponential Decay

Anti-Martingale

Halve size each level — very conservative.

At a glance

Engine value
anti_marti_exponential
Size at level i
size(i) = base / 2ⁱ
Family
— Size shrinks deeper into — capital protection first.
Risk band
Low risk
Capital profile
Geometric (r=½) — total < 2 × base (bounded).
Best for
Strong trends; when deep levels are likely to keep running.
Orders per level
One entry order and one take-profit per level.
Ladder cost @ 10 levels
1.00× base lot
Versus a flat ladder
0.10× the capital
Deepest rung
0.00× base (0.00× the first rung)
Entry orders resting
10 at 10 levels
Break-even bounce
8.90% from the deepest fill (flat ladder: 5.00%)

What this curve is for

Halving decay: size is 1/2ⁱ. Exposure beyond the first few rungs is negligible and the whole ladder converges to under twice the base lot no matter how deep it goes. It is the cheapest possible tail in the , bought by giving up averaging entirely below the .

How the sizing rule works

Size at level i is 2⁻ⁱ. By level 4 the theoretical size is a sixteenth of base, which is below any venue minimum, so the executed ladder is one base lot near the top and the minimum lot everywhere else.

LevelPer-order sizeOrdersLevel totalCumulativeEntry priceTake-profit
L10.50×10.50×0.50×99.0099.99
L20.25×10.25×0.75×98.0098.98
L30.13×10.13×0.88×97.0097.97
L40.06×10.06×0.94×96.0096.96
L50.03×10.03×0.97×95.0095.95
L60.02×10.02×0.98×94.0094.94
L70.01×10.01×0.99×93.0093.93
L80.00×10.00×1.00×92.0092.92
L90.00×10.00×1.00×91.0091.91
L100.00×10.00×1.00×90.0090.90
Reference configuration: 10 levels, 1% apart, 1% target, base price 100, long. Sizes are in base-lot units.

The ladder, as the engine builds it

Below is the 's own ladder and the trading terminal's chart engine, both driven by buildLadderPlan for this . Change the level count, spread or target and the rung prices, sizes, and chart lines recompute exactly as they would in the .

base lot 100 USDT · long · no stop

Ladder shape — Exponential Decay

LONG · base 100.00 (illustrative) · 10 levels stepping down · 1% apart

Base positionEntry rung (buy)Init target
Opening position & init targets200 USDT
T2
target 2 sell @ 102.00
+2 USDT
T1
target 1 sell @ 101.00
+1 USDT
L0
Market buy · 2 lots @ 100.00
200 USDT

Targets are stacked above the opening buy because a long grid exits higher than it enters.

Entry ladder

Limit buys below the base · L1 nearest, L10 deepest · every amount in USDT

Entry ladder: one row per rung, showing entry and exit price, size, order count, notional, margin, running capital and profit at exit.
LevelSize curveEntry buyUSDTExit sellUSDTFrom base%Sizebase lotsOrdersNotionalUSDTMarginUSDTCum. capitalUSDTProfit at exitUSDT
L1100%99.0099.991.00%0.500×150502500.5
L250%98.0098.982.00%0.250×125252750.25
L325%97.0097.973.00%0.125×112.512.52880.13
L413%96.0096.964.00%0.063×16.256.252940.06
L56%95.0095.955.00%0.031×13.133.132970.03
L63%94.0094.946.00%0.016×11.561.562980.02
L72%93.0093.937.00%0.008×10.780.782990.01
L81%92.0092.928.00%0.004×10.390.393000
L90%91.0091.919.00%0.002×10.20.23000
L100%90.0090.9010.00%0.001×10.10.13000
Levels 1–10 of 10
1 / 1
Ladder cost 0.999×Capital 300 USDTAvg entry 99.34Cycle profit 4
Loading the chart engine…

What depth costs

Bounded at roughly 2× base regardless of depth. Adding levels is effectively free, which makes hundred-level coverage a realistic configuration.

LevelsLadder costDeepest rungEntry ordersCost vs 5 levelsCoverage
5 levels0.97×0.03×51.00×5%
10 levels1.00×0.00×101.03×10%
20 levels1.00×0.00×201.03×20%
40 levels1.00×0.00×401.03×40%
Ladder cost is Σ of every rung in base-lot units, excluding the opening L0 batch. At a grid size of 100 USDT, the 10-level ladder commits 100 USDT of notional at 1× leverage.

Read the cost vs 5 levels column as the escalation test. A flat ladder doubles when the depth doubles; anything materially above that is a whose coverage has to be bought rather than simply configured.

Capital budgetLevels affordableAdverse move covered
10× base200 levels200.0%
25× base200 levels200.0%
50× base200 levels200.0%
100× base200 levels200.0%
250× base200 levels200.0%
How far price can move against the grid before it runs out of rungs, per capital budget, at 1% spacing. This is the question a funding decision actually turns on.

Averaging and recovery

With every rung , the volume-weighted average entry is 98.01 against a base of 100 and a deepest rung of 90.00 — so the average sits 20% of the way down the covered range. Getting back to flat from the bottom therefore needs a 8.90% , against 5.00% for a flat ladder of the same depth — 3.90% more work.

ExcursionLevels filledDeployedAverage entryMarkUnrealisedBounce to flat
Shallow dipL1–L30.88×98.4397.00-0.01×1.47%
Half the ladder fillsL1–L50.97×98.1695.00-0.03×3.33%
Full ladderL1–L101.00×98.0190.00-0.08×8.90%
Reference configuration: 10 levels, 1% apart, 1% target, base price 100, long. Sizes are in base-lot units. Deterministic arithmetic, not a simulation: no assumption is made about how price reached each depth.

Size halves every level, so exposure beyond a few rungs is negligible and the total ladder converges to under 2× base. Almost all capital sits near the entry.

Where the exposure sits

Held by the shallowest quarter
87.6% of total size
Held by the deepest quarter
0.7% of total size
Unrealised loss at full fill
0.08× base (8.2% of deployed capital)
Profit if every rung books its target
0.01× base
One shallow cycle, against reserved capital
50.0 bps

The last row is the metric that separates modes. Profit for a full cycle is the target of deployed capital in every , so it cannot discriminate. What differs is how much capital has to sit reserved to earn one shallow cycle: this mode 1.00× base to collect 50.0 bps of it when the first rung completes.

Which market pays this curve

Strong, persistent trends where deep levels are likely to keep running. It is the correct choice when your honest expectation is "this will keep going and I want to be barely involved if it does".

Position halves every level, so deep exposure vanishes fast. Almost all capital sits near the entry; excellent protection against sustained adverse trends. Floored at 1 lot.

The shape of the risk

Almost no capital risk; substantial opportunity cost. The position that matters is the opening batch and the first rung — everything else is a rounding error, so the is closer to "hold a position and harvest bounces" than to a grid.

ℹ
Note:The one-lot bites early here: past 3–4 levels every rung executes at the minimum lot.

Run it over real history

This is the product's grid backtester, not a summary of one. It fetches public candles for the you pick, rebuilds the ladder on the first candle of the , then applies the engine's own fill, take-profit, and stop-loss rules bar by bar. The caveat block inside the is part of the output — read it before trusting a number.

Instrument

BTCUSD

delta-india

Exponential Decay · 10 levels @ 1% · target 1% · 100 USDT / level · 1× · long · no stop

What this does not model

  • Exact intrabar ticks. Bullish/doji candles use open → low → high → close; bearish candles use open → high → low → close. Finer timeframes reduce sensitivity to this deterministic assumption.
  • Queue position. Limit orders are assumed filled when touched, which flatters a maker grid in fast markets.
  • Margin rejection and liquidation. Deep rungs fill here even if the account could not fund them — check the capital requirement.
  • Slippage and funding. Only the fee you set above is charged; funding, borrow and slippage are absent.

Run the ladder over real history

The grid is rebuilt anchored on the first candle of the window, then the engine's own fill, exit, refill and stop-loss rules are applied bar by bar. You get the real fill sequence for this configuration on this instrument.

Measured against other modes

First the arithmetic, then the market. The below is computed from the size curves alone; the underneath replays every one of those ladders over the same real candle , with grid_mode as the only variable.

ModeLadder costDeepest rungBreak-even bounceEntry ordersShallow cycle
Exponential Decay (this mode)1.00×0.00×8.90%1050.0 bps
Fixed10.0×1.00×5.00%1010.0 bps
Square-Root Decay4.32×0.30×5.85%1016.4 bps
Linear Martingale55.0×10.0×2.38%551.8 bps
Reference configuration: 10 levels, 1% apart, 1% target, base price 100, long. Sizes are in base-lot units. Peers are chosen from this mode's own direction plus the flat baseline, so the comparison is meaningful rather than decorative.

Nothing is precomputed here. Press run and the backtester fetches one candle window and replays 4 ladders across it — identical settings, identical bars, grid_mode as the only difference.

When to use it

  • Strong trends where deep levels are likely to keep running.
  • You want the cheapest possible tail risk with maximum coverage.
  • You are trading an whose drawdowns have historically been deep and slow.

When to avoid it

  • You need deep levels to contribute meaningfully to the average entry.
  • The venue's minimum lot is relative to your base lot — the becomes flat immediately.

Tuning

  • Depth is nearly free; spread is the real dial, because it decides how much range those first two meaningful rungs cover.
  • If you want a decaying where level 5 still matters, use square-root or instead.

Running it in production

  • Watch how quickly executed size hits the one-lot — beyond that extra levels add coverage but almost no averaging.
  • Track realised cycles per day. Decay curves earn from frequency, so a falling cycle count is the signal that the market has left the .
  • Check the gap between average entry and . Decay curves keep it wide by design, so recovery expectations must be set from it, not from hope.

How it fails

  1. 1
    Immediate floor
    The one-lot bites by rung 3–4, so the ladder is flat at minimum size. The 's distinctive exists only in the first few rungs.
  2. 2
    Under-participation
    If the does mean-revert sharply, the captures very little of it. That is the deliberate trade, but it should be a chosen one.

Claims worth correcting

“Halving decay is the safe mirror of doubling.”

It is safe, but it is not a mirror: doubling changes the recovery mathematics dramatically, while halving mostly just reduces .

Interaction with the rest of the configuration

  • Spread sets how fast the ladder consumes depth. Widening it buys coverage for the same level count at the cost of fewer .
  • Target sets what each cycle books. Below -trip fees plus slippage, a grid is a fee generator regardless of the .
  • The is the only bound on the tail. Without it, the 's worst case is whatever the market does, not what you planned.

Questions this mode raises

  1. 1
    Is there any point running many levels?
    Yes — coverage. The rungs cost almost nothing, and a minimum-lot rung still carries a take-profit that can complete on a .

Where these numbers come from

  • Sizes and capital: levelMultiplier / gridModeCurve in lib/grid/gridModes.ts, from grid_modes.hpp and the Python engine's lot calculator.
  • Rung and exit prices, , init targets and the stop line: buildLadderPlan — the same builder the and use.
  • Backtest , cycles and P&L: runBacktest / runBacktestSweep over public broker candles, applying the engine's fill, exit, and stop rules.
  • Price charts: the trading terminal's chart engine, with the ladder drawn through its own price-line API.
!
Caution:A backtest is evidence about one , not a . Fees are charged at the rate you set; slippage, funding, , margin rejection and are not modelled. For a growth especially, a profitable window mostly tells you the window did not contain the trend that would have tested it.

Related

  • 1.Grid Modes — Overview — The full taxonomy and how to choose
  • 2.Anti-Martingale family — What every curve in this family has in common
  • 3.Capital Allocation — Sizing an account to a Exponential Decay ladder
  • 4.Stop Loss — Bounding this curve's tail
  • 5.Reading the Ladder Plan — Verifying the curve before deploying
  • 6.Grid Structure — Levels, init batch and base size

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