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Exponential Decay
Anti-MartingaleHalve size each level — very conservative.
At a glance
anti_marti_exponentialsize(i) = base / 2ⁱWhat 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.
| Level | Per-order size | Orders | Level total | Cumulative | Entry price | Take-profit |
|---|---|---|---|---|---|---|
| L1 | 0.50× | 1 | 0.50× | 0.50× | 99.00 | 99.99 |
| L2 | 0.25× | 1 | 0.25× | 0.75× | 98.00 | 98.98 |
| L3 | 0.13× | 1 | 0.13× | 0.88× | 97.00 | 97.97 |
| L4 | 0.06× | 1 | 0.06× | 0.94× | 96.00 | 96.96 |
| L5 | 0.03× | 1 | 0.03× | 0.97× | 95.00 | 95.95 |
| L6 | 0.02× | 1 | 0.02× | 0.98× | 94.00 | 94.94 |
| L7 | 0.01× | 1 | 0.01× | 0.99× | 93.00 | 93.93 |
| L8 | 0.00× | 1 | 0.00× | 1.00× | 92.00 | 92.92 |
| L9 | 0.00× | 1 | 0.00× | 1.00× | 91.00 | 91.91 |
| L10 | 0.00× | 1 | 0.00× | 1.00× | 90.00 | 90.90 |
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 .
Ladder shape — Exponential Decay
LONG · base 100.00 (illustrative) · 10 levels stepping down · 1% apart
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
| Level | Size curve | Entry buyUSDT | Exit sellUSDT | From base% | Sizebase lots | Orders | NotionalUSDT | MarginUSDT | Cum. capitalUSDT | Profit at exitUSDT |
|---|---|---|---|---|---|---|---|---|---|---|
| L1 | 100% | 99.00 | 99.99 | 1.00% | 0.500× | 1 | 50 | 50 | 250 | 0.5 |
| L2 | 50% | 98.00 | 98.98 | 2.00% | 0.250× | 1 | 25 | 25 | 275 | 0.25 |
| L3 | 25% | 97.00 | 97.97 | 3.00% | 0.125× | 1 | 12.5 | 12.5 | 288 | 0.13 |
| L4 | 13% | 96.00 | 96.96 | 4.00% | 0.063× | 1 | 6.25 | 6.25 | 294 | 0.06 |
| L5 | 6% | 95.00 | 95.95 | 5.00% | 0.031× | 1 | 3.13 | 3.13 | 297 | 0.03 |
| L6 | 3% | 94.00 | 94.94 | 6.00% | 0.016× | 1 | 1.56 | 1.56 | 298 | 0.02 |
| L7 | 2% | 93.00 | 93.93 | 7.00% | 0.008× | 1 | 0.78 | 0.78 | 299 | 0.01 |
| L8 | 1% | 92.00 | 92.92 | 8.00% | 0.004× | 1 | 0.39 | 0.39 | 300 | 0 |
| L9 | 0% | 91.00 | 91.91 | 9.00% | 0.002× | 1 | 0.2 | 0.2 | 300 | 0 |
| L10 | 0% | 90.00 | 90.90 | 10.00% | 0.001× | 1 | 0.1 | 0.1 | 300 | 0 |
What depth costs
Bounded at roughly 2× base regardless of depth. Adding levels is effectively free, which makes hundred-level coverage a realistic configuration.
| Levels | Ladder cost | Deepest rung | Entry orders | Cost vs 5 levels | Coverage |
|---|---|---|---|---|---|
| 5 levels | 0.97× | 0.03× | 5 | 1.00× | 5% |
| 10 levels | 1.00× | 0.00× | 10 | 1.03× | 10% |
| 20 levels | 1.00× | 0.00× | 20 | 1.03× | 20% |
| 40 levels | 1.00× | 0.00× | 40 | 1.03× | 40% |
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 budget | Levels affordable | Adverse move covered |
|---|---|---|
| 10× base | 200 levels | 200.0% |
| 25× base | 200 levels | 200.0% |
| 50× base | 200 levels | 200.0% |
| 100× base | 200 levels | 200.0% |
| 250× base | 200 levels | 200.0% |
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.
| Excursion | Levels filled | Deployed | Average entry | Mark | Unrealised | Bounce to flat |
|---|---|---|---|---|---|---|
| Shallow dip | L1–L3 | 0.88× | 98.43 | 97.00 | -0.01× | 1.47% |
| Half the ladder fills | L1–L5 | 0.97× | 98.16 | 95.00 | -0.03× | 3.33% |
| Full ladder | L1–L10 | 1.00× | 98.01 | 90.00 | -0.08× | 8.90% |
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
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.
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.
| Mode | Ladder cost | Deepest rung | Break-even bounce | Entry orders | Shallow cycle |
|---|---|---|---|---|---|
| Exponential Decay (this mode) | 1.00× | 0.00× | 8.90% | 10 | 50.0 bps |
| Fixed | 10.0× | 1.00× | 5.00% | 10 | 10.0 bps |
| Square-Root Decay | 4.32× | 0.30× | 5.85% | 10 | 16.4 bps |
| Linear Martingale | 55.0× | 10.0× | 2.38% | 55 | 1.8 bps |
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
- 1Immediate floorThe 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.
- 2Under-participationIf 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
- 1Is 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/gridModeCurveinlib/grid/gridModes.ts, fromgrid_modes.hppand 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/runBacktestSweepover 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.
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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