Martingale Strategy Simulator [BackQuant]

Martingale Strategy Simulator [BackQuant]
Purpose
This indicator lets you study how a martingale-style position sizing rule interacts with a simple long or short trading signal. It computes an equity curve from bar-to-bar returns, adapts position size after losing streaks, caps exposure at a user limit, and summarizes risk with portfolio metrics. An optional Monte Carlo module projects possible future equity paths from your realized daily returns.

What a martingale is
A martingale sizing rule increases stake after losses and resets after a win. In its classical form from gambling, you double the bet after each loss so that a single win recovers all prior losses plus one unit of profit. In markets there is no fixed “even-money” payout and returns are multiplicative, so an exact recovery guarantee does not exist. The core idea is unchanged:

• Lose one leg → increase next position size
  
• Lose again → increase again
  
• Win → reset to the base size
  

The expectation of your strategy still depends on the signal’s edge. Sizing does not create positive expectancy on its own. A martingale raises variance and tail risk by concentrating more capital as a losing streak develops.

What it plots

• Equity – simulated portfolio equity including compounding
  
• Buy & Hold – equity from holding the chart symbol for context
  
• Optional helpers – last trade outcome, current streak length, current allocation fraction
  
• Optional diagnostics – daily portfolio return, rolling drawdown, metrics table
  
• Optional Monte Carlo probability cone – p5, p16, p50, p84, p95 aggregate bands
  

Model assumptions

• Bar-close execution with no slippage or commissions
  
• Shorting allowed and frictionless
  
• No margin interest, borrow fees, or position limits
  
• No intrabar moves or gaps within a bar (returns are close-to-close)
  
• Sizing applies to equity fraction only and is capped by your setting
  

All results are hypothetical and for education only.

How the simulator applies it
1) Directional signal
You pick a simple directional rule that produces +1 for long or −1 for short each bar. Options include 100 HMA slope, RSI above or below 50, EMA or SMA crosses, CCI and other oscillators, ATR move, BB basis, and more. The stance is evaluated bar by bar. When the stance flips, the current trade ends and the next one starts.
2) Sizing after losses and wins
Position size is a fraction of equity:

• Initial allocation – the starting fraction, for example 0.15 means 15 percent of equity
  
• Increase after loss – multiply the [u]next[/u] allocation by your factor after a losing leg, for example 2.00 to double
  
• Reset after win – return to the initial allocation
  
• Max allocation cap – hard ceiling to prevent runaway growth
  

At a high level the size after k consecutive losses is
alloc(k) = min( cap , base × factor^k ).
In practice the simulator changes size only when a leg ends and its PnL is known.
3) Equity update
Let r_t = close_t / close_{t-1} − 1 be the symbol’s bar return, d_{t−1} ∈ {+1, −1} the prior bar stance, and a_{t−1} the prior bar allocation fraction. The simulator compounds:
eq_t = eq_{t−1} × (1 + a_{t−1} × d_{t−1} × r_t).
This is bar-based and avoids intrabar lookahead. Costs, slippage, and borrowing costs are not modeled.
Why traders experiment with martingale sizing

• Mean-reversion contexts – if the signal often snaps back after a string of losses, adding size near the tail of a move can pull the average entry closer to the turn
  
• Behavioral or microstructure edges – some rules have modest edge but frequent small whipsaws; size escalation may shorten time-to-recovery when the edge manifests
  
• Exploration and stress testing – studying the relationship between streaks, caps, and drawdowns is instructive even if you do not deploy martingale sizing live
  

Why martingale is dangerous
Martingale concentrates capital when the strategy is performing worst. The main risks are structural, not cosmetic:

• Loss streaks are inevitable – even with a 55 percent win rate you should expect multi-loss runs. The probability of at least one k-loss streak in N trades rises quickly with N.
  
• Size explodes geometrically – with factor 2.0 and base 10 percent, the sequence is 10, 20, 40, 80, 100 (capped) after five losses. Without a strict cap, required size becomes infeasible.
  
• No fixed payout – in gambling, one win at even odds resets PnL. In markets, there is no guaranteed bounce nor fixed profit multiple. Trends can extend and gaps can skip levels.
  
• Correlation of losses – losses cluster in trends and in volatility bursts. A martingale tends to be largest just when volatility is highest.
  
• Margin and liquidity constraints – leverage limits, margin calls, position limits, and widening spreads can force liquidation before a mean reversion occurs.
  
• Fat tails and regime shifts – assumptions of independent, Gaussian returns can understate tail risk. Structural breaks can keep the signal wrong for much longer than expected.
  

The simulator exposes these dynamics in the equity curve, Max Drawdown, VaR and CVaR, and via Monte Carlo sketches of forward uncertainty.

Interpreting losing streaks with numbers
A rough intuition: if your per-trade win probability is p and loss probability is q=1−p, the chance of a specific run of k consecutive losses is q^k. Over many trades, the chance that at least one k-loss run occurs grows with the number of opportunities. As a sanity check:

• If p=0.55, then q=0.45. A 6-loss run has probability q^6 ≈ 0.008 on any six-trade window. Across hundreds of trades, a 6 to 8-loss run is not rare.
  
• If your size factor is 1.5 and your base is 10 percent, after 8 losses the requested size is 10% × 1.5^8 ≈ 25.6%. With factor 2.0 it would try to be 10% × 2^8 = 256% but your cap will stop it. The equity curve will still wear the compounded drawdown from the sequence that led to the cap.
  

This is why the cap setting is central. It does not remove tail risk, but it prevents the sizing rule from demanding impossible positions
Note: The p and q math is illustrative. In live data the win rate and distribution can drift over time, so real streaks can be longer or shorter than the simple q^k intuition suggests..

Using the simulator productively
Parameter studies
Start with conservative settings. Increase one element at a time and watch how the equity, Max Drawdown, and CVaR respond.

• Initial allocation – lower base reduces volatility and drawdowns across the board
  
• Increase factor – set modestly above 1.0 if you want the effect at all; doubling is aggressive
  
• Max cap – the most important brake; many users keep it between 20 and 50 percent
  

Signal selection
Keep sizing fixed and rotate signals to see how streak patterns differ. Trend-following signals tend to produce long wrong-way streaks in choppy ranges. Mean-reversion signals do the opposite. Martingale sizing interacts very differently with each.

Diagnostics to watch
Use the built-in metrics to quantify risk:

• Max Drawdown – worst peak-to-trough equity loss
  
• Sharpe and Sortino – volatility and downside-adjusted return
  
• VaR 95 percent and CVaR – tail risk measures from the realized distribution
  
• Alpha and Beta – relationship to your chosen benchmark
  

If you would like to check out the original performance metrics script with multiple assets with a better explanation on all metrics please see

Monte Carlo exploration

When enabled, the forecast draws many synthetic paths from your realized daily returns:

• Choose a horizon and a number of runs
  
• Review the bands: p5 to p95 for a wide risk envelope; p16 to p84 for a narrower range; p50 as the median path
  
• Use the table to read the expected return over the horizon and the tail outcomes
  
• Remember it is a sketch based on your recent distribution, not a predictor
  

Concrete examples
Example A: Modest martingale
Base 10 percent, factor 1.25, cap 40 percent, RSI>50 signal. You will see small escalations on 2 to 4 loss runs and frequent resets. The equity curve usually remains smooth unless the signal enters a prolonged wrong-way regime. Max DD may rise moderately versus fixed sizing.
Example B: Aggressive martingale
Base 15 percent, factor 2.0, cap 60 percent, EMA cross signal. The curve can look stellar during favorable regimes, then a single extended streak pushes allocation to the cap, and a few more losses drive deep drawdown. CVaR and Max DD jump sharply. This is a textbook case of high tail risk.
Strengths

• Bar-by-bar, transparent computation of equity from stance and size
  
• Explicit handling of wins, losses, streaks, and caps
  
• Portable signal inputs so you can A–B test ideas quickly
  
• Risk diagnostics and forward uncertainty visualization in one place
  

Example, Rolling Max Drawdown


Limitations and important notes

• Martingale sizing can escalate drawdowns rapidly. The cap limits position size but not the possibility of extended adverse runs.
  
• No commissions, slippage, margin interest, borrow costs, or liquidity limits are modeled.
  
• Signals are evaluated on closes. Real execution and fills will differ.
  
• Monte Carlo assumes independent draws from your recent return distribution. Markets often have serial correlation, fat tails, and regime changes.
  
• All results are hypothetical. Use this as an educational tool, not a production risk engine.
  

Practical tips

• Prefer gentle factors such as 1.1 to 1.3. Doubling is usually excessive outside of toy examples.
  
• Keep a strict cap. Many users cap between 20 and 40 percent of equity per leg.
  
• Stress test with different start dates and subperiods. Long flat or trending regimes are where martingale weaknesses appear.
  
• Compare to an anti-martingale (increase after wins, cut after losses) to understand the other side of the trade-off.
  
• If you deploy sizing live, add external guardrails such as a daily loss cut, volatility filters, and a global max drawdown stop.
  

Settings recap

• Backtest start date and initial capital
  
• Initial allocation, increase-after-loss factor, max allocation cap
  
• Signal source selector
  
• Trading days per year and risk-free rate
  
• Benchmark symbol for Alpha and Beta
  
• UI toggles for equity, buy and hold, labels, metrics, PnL, and drawdown
  
• Monte Carlo controls for enable, runs, horizon, and result table
  

Final thoughts
A martingale is not a free lunch. It is a way to tilt capital allocation toward losing streaks. If the signal has a real edge and mean reversion is common, careful and capped escalation can reduce time-to-recovery. If the signal lacks edge or regimes shift, the same rule can magnify losses at the worst possible moment. This simulator makes those trade-offs visible so you can calibrate parameters, understand tail risk, and decide whether the approach belongs anywhere in your research workflow.