Record AR-EXP-052 · Risk and Capital State
Drawdown is the only measurement
that can end the experiment.
Expectancy describes what a system earns. Drawdown describes whether the account is still there to earn it. This page separates the four things traders collapse into a single percentage, measures how much of a decline is caused by ordering rather than by edge, and sets out the structure of a capital-state ladder that reduces deployment before the situation becomes critical.
Interactive demonstration — not a historical backtest
A drawdown is a path.
A drawdown figure is a shadow of one.
"My maximum drawdown is 18%" answers one question and hides three. Depth is the number that gets quoted. Duration, time under water and recovery efficiency are the numbers that decide whether the system is still being traded when the recovery arrives.
Two systems can report the same 18% maximum decline and be completely different objects. One reaches −18% in nine trading days and is back at a new equity peak three weeks later. The other drifts down over five months, sits between −11% and −18% for another four, and does not make a new peak for well over a year. The first is an event. The second is a condition.
Nothing in the headline number distinguishes them. Yet the second one is the system that gets abandoned, re-optimised, or quietly sized up in an attempt to accelerate the recovery — and all three responses are more destructive than the drawdown itself.
The Foundry treats drawdown as four separate measurements, because they fail in four separate ways and they are repaired by four different decisions.
The measurement that is almost always wrong
Drawdown must be measured from the running equity peak, not from starting capital. An account that grows from 10,000 to 15,000 and falls back to 12,000 is 20% in drawdown, not 20% in profit. Measuring from the start makes accumulated gains invisible as risk, which is exactly backwards: those gains are the capital now being lost.
The four measurements
DD(t) = equity(t) ÷ max(equity(0…t)) − 1
The underwater series. Every drawdown measurement on this page is a property of this one function: depth is its minimum, duration is the distance from the zero-crossing before that minimum to the minimum, time under water is the share of the series meaningfully below zero, and recovery efficiency is the ratio of those two distances.
The risk observatory.
Five controls, six consequences. Every reading below is produced by the same outcome ladder that draws the two curves, so the stated drawdown and the drawn drawdown cannot disagree with each other.
Drawdown terrain
The surface above is the underwater curve rendered as terrain. The flat plane is the running equity peak; every valley is an ordering of the same trade population sitting below its own prior high. Lanes running into the distance are twenty-five independent orderings; the dashed plane marks a stated −25% tolerance. Camera travel follows page scroll. The scene is decorative — everything it depicts is stated in the readings and figures below.
Capital controls
Interactive demonstration — not a historical backtest
Reading
—
Simulated demonstration data — illustrative engine output
Median of nine seeded histories at the current configuration.
Decline from the running equity peak across the same modelled history.
Losses and gains
are not the same size.
A 50% decline requires a 100% gain to undo. This is not a rhetorical point about discipline. It is arithmetic, and it is the reason risk control has priority over return generation in every part of the Foundry.
Capital multiplies. Falling by a fraction d leaves (1 − d) of the account. Returning to the prior peak requires multiplying what remains by 1 ÷ (1 − d), so the required gain is d ÷ (1 − d) — a function that is close to linear while d is small and violently convex once it is not.
Below about 15% the asymmetry is a nuisance. Above about 35% it becomes the dominant fact about the account. Past 60%, the required recovery is larger than most systems produce in several good years, which is why a deep drawdown is rarely survived by patience alone — it is survived, if at all, by the position sizing that prevented it.
The third column of the table is the one worth internalising. It converts the required gain into the currency the rest of this laboratory uses: units of risk. At 1% risk per trade, recovering a 40% decline means accumulating just over 51 R of net gain — several hundred trades for most configurations, taken while the system is in its most compressed state.
gain = d ÷ (1 − d)
Required fractional gain to return to the prior peak after a fractional decline of d. The R-unit column is ln(1 ÷ (1 − d)) divided by the fractional risk per trade — the compounding form, which is what an account actually experiences.
| Decline from peak | Gain required | Net R required at 1% risk | Character |
|---|---|---|---|
| 10% | 11.1% | 10.5 R | Ordinary operating range. Recoverable inside a normal run of trades. |
| 20% | 25.0% | 22.3 R | Uncomfortable but structural. Most systems visit here. |
| 30% | 42.9% | 35.7 R | The recovery is now a project, not an episode. |
| 40% | 66.7% | 51.1 R | Beyond most tolerance thresholds. Behaviour usually breaks before capital does. |
| 50% | 100.0% | 69.3 R | The account must double. Few systems do this at reduced size. |
| 60% | 150.0% | 91.6 R | Practically terminal for a discretionary operator. |
| 70% | 233.3% | 120.4 R | Recovery is a different account, not the same one. |
Required gain plotted against decline from peak. The two lines diverge slowly and then not slowly at all: the gap between them is the entire argument for capping risk before it is needed rather than after. This figure contains no simulation — it is the identity gain = d ÷ (1 − d) evaluated across the range.
The losing streak that means nothing.
Every trader eventually experiences a run of losses long enough to feel like evidence. In most cases it is not evidence of anything. The expected longest losing run grows with the size of the sample even when the underlying probabilities have not moved at all.
One seeded ordering of 160 outcomes at a 43% hit rate. Bars above the axis are wins, bars below are losses, and the boxed region marks the longest unbroken losing run in this particular ordering. Nothing in the generating process changes at any point in the series — the cluster is a property of ordering, not of deterioration.
For a system that loses with probability q, the expected longest losing run across n trades is approximately ln(n(1 − q)) ÷ ln(1 ÷ q). The important feature of that expression is the logarithm: the streak grows with sample size, slowly but without limit.
A trader with a 45% hit rate who has taken 250 trades should expect to have already lived through a run of about eight consecutive losses. At 2,500 trades the expectation is closer to twelve. Neither number indicates that anything has broken. Both are routinely interpreted as proof that something has.
The practical consequence is a sizing consequence. If the position size cannot survive the streak the sample size implies, the system does not have a psychology problem — it has an arithmetic problem, and it will meet it eventually with certainty.
Where this reasoning stops
The formula assumes independent outcomes. Real trade sequences are not independent: correlated concurrent positions resolve together, and regime persistence clusters both wins and losses. Both effects make the observed streaks longer than the independent estimate, not shorter. The number above is a floor, not a ceiling.
Expected maximum consecutive losses at three hit rates, evaluated from 50 to 5,000 trades. All three curves rise with sample size alone; none of the underlying probabilities change anywhere along the horizontal axis. A 35% hit-rate system is not worse than a 55% one — it simply requires a position size that can absorb roughly twice the streak.
Same trades.
Different order. Different system.
This is the strongest single result the preview engine produces. Hold the strategy, the risk, the friction and the outcome distribution completely fixed, and change nothing but the order in which the trades arrive.
Distribution of maximum drawdown across 200 independently seeded orderings.
Simulated demonstration data — 200 seeded orderings of one fixed configuration
Reference configuration
The shallowest of the 200 orderings reaches —. The deepest reaches —. The median sits at —. Nothing distinguishes these histories except the sequence in which identical outcomes were drawn.
A trader who experienced the shallow ordering would describe the system as well behaved and might reasonably size up. A trader who experienced the deep one would describe the same system as broken and would probably stop trading it. Both would be reasoning from a sample of one.
This is the entire case for evaluating a configuration across a distribution of orderings rather than a single history — and the reason the Foundry never draws a figure from one path where the median of nine is available.
What this does and does not establish
Every ordering above is drawn from the same illustrative outcome ladder, so the spread measures the contribution of sequence to drawdown within a model. It is not a measurement of any market. What transfers to reality is the structure of the finding: when the per-trade distribution is fixed, ordering alone still moves the worst decline by a factor large enough to change every decision a trader would make about the system.
Governance is not free,
and pretending otherwise is a sales pitch.
The same configuration, the same seeds, the same outcome ladder — evaluated with and without a drawdown-gated risk schedule. The comparison is only useful if both sides of it are stated.
Five measures, each evaluated twice on identical seeds.
The gated path is flatter in both directions. It gives up terminal growth in the region where the ungoverned path compounds freely, and it declines less in the region where the ungoverned path does not.
What governance costs
Simulated demonstration data
—
A gated schedule reduces the authorised risk pool as the account falls from its peak. In the favourable orderings — the ones where the decline was temporary and the recovery immediate — that reduction is applied to precisely the trades that would have produced the recovery. The system therefore climbs back more slowly than it would have without the brake.
That is the cost, and it is real. It is paid in every ordering, including the ones that never needed protecting.
What is bought with it is the elimination of the tail. Compression is not designed to improve the median outcome. It is designed to remove the small proportion of orderings in which the account reaches a depth from which the arithmetic of the previous section makes recovery unrealistic. Whether that trade is worth making is a decision about the operator, not about the strategy — but it must be made with both numbers visible.
Capital states, not capital rules.
A single "reduce size in a drawdown" rule is a cliff. A ladder of states is a gradient — and it is reviewed on cycle boundaries rather than after every trade, so a single adverse outcome cannot reclassify the account.
L3 Ladder rendered from the MARS capital-state specification · AR-MARS-GATE · Automatic state transition and pool re-authorisation is intended production behaviour, not a capability of this preview.
Each state carries a brake posture rather than a single multiplier: what the system is permitted to do, how much of the authorised pool may be deployed, and which populations remain enabled. Moving down the ladder is automatic and immediate. Moving back up is deliberate and slower, because a single favourable cycle is not evidence that the condition has passed.
The steps are placed so that the first compression happens early enough to matter. A brake that engages at −25% is applying a small reduction to a problem that is already most of the way to the convex part of the recovery curve. The whole point is to act while the correction is still cheap.
Calibration is not published here
The drawdown boundaries between these states, the pool percentages attached to each one, and the tier ceilings that interact with them are part of the MARS workbook product and are not published on this site. What is public is the structure: capital authority is a function of drawdown from the running peak, it is reviewed on cycle boundaries, and it steps down before the situation is critical rather than after.
Why a hard stop exists,
and why it sits high.
Every state below the top of the ladder is a compression. The last one is not. System Lock withdraws deployment authority entirely: no new positions, no exceptions, no discretionary override, and no resumption until the cause has been identified in writing.
A graduated brake handles a bad sequence. It does not handle a broken assumption — a framework deployed into a regime it was never suited to, a friction level that has changed without being noticed, or an execution problem that has been quietly widening for months. In those cases each additional trade is not a draw from the distribution the operator believes they are trading. It is a draw from a worse one that has not been characterised yet.
Why the boundary is set above the point of no return
What the lock is not
It is not a stop-loss on the strategy and it is not a verdict. It is a suspension of deployment authority pending diagnosis. The most common failure of the mechanism is not that it triggers too early — it is that it is disabled by the operator at the moment it first becomes relevant, which is the moment it was built for.
Eight ways risk is
routinely mismeasured.
None of these are exotic. All of them are common, and each one makes a system look safer than it is in a specific, identifiable way.
The intuition is that a larger position recovers the deficit faster, and it is correct — in the orderings where the next trades win. In the orderings where they do not, the increased size is applied to an account that has already lost its cushion, which is how a 25% drawdown becomes a 55% one in a fraction of the time it took to reach 25%.
The asymmetry is structural: raising risk in a drawdown increases the variance of an outcome whose downside is bounded by ruin and whose upside is bounded by the recovery curve. Every governance layer in this laboratory does the opposite, and that is the single design decision most responsible for the difference in the tail.
A system that wins 70% of the time feels safe because losing feels rare. What determines the drawdown is not the frequency of losses but the product of their frequency and their size — and high hit rates are usually purchased by accepting a worse loss-to-win ratio, a heavier tail, or a higher probability of gapping through the stop.
In the archetype constants used by this engine, mean reversion carries the highest baseline hit rate and roughly five times the shock-loss probability of trend following. The comfortable equity curve and the catastrophic tail come from the same design choice.
An account that runs from 10,000 to 16,000 and back to 12,000 will be described by many journals as "up 20%". It is in a 25% drawdown. Measuring from the deposit rather than the running peak makes every gain permanently invisible to the risk calculation, which means the risk measurement gets less accurate exactly as the account gets larger.
This is also the error that makes trailing governance impossible: a gate schedule measured from starting capital never engages on an account that is nominally in profit, no matter how much of that profit has already been given back.
Four open positions at 1% each is described as 4% of open risk spread across four bets. If those positions are 70% correlated, the effective number of independent bets is closer to one and a half. The exposure is real; the diversification is largely notional.
Correlation is also state-dependent, and it moves in the wrong direction: it rises toward one in exactly the conditions that produce the largest adverse moves. The Risk-Off Shock regime in the Foundry's taxonomy carries a correlation coefficient of 0.92 for this reason. Raise the correlation limit on the observatory above and watch the drawdown reading move without any change to the per-trade edge.
Average drawdown across a record is a measure of typical discomfort. It says almost nothing about capital survival, because the account is not ended by the typical decline. It is ended by the worst one, and the worst one is a tail statistic that an average is specifically constructed to suppress.
The honest presentation is a distribution: median, upper decile, and the maximum observed across many orderings — which is precisely what Figure 6 shows. A single average drawdown figure should be treated as a summary of the comfortable part of the record.
Six months without a decline deeper than 8% is usually taken as evidence that the system's drawdown profile is around 8%. It is more often evidence that the sample is short and the regime has been favourable. Figure 6 makes the point without any appeal to market conditions at all: among 200 orderings of one unchanged configuration, a substantial share never exceed a shallow decline, and those are the orderings that get mistaken for the system.
The useful question is not "what has the drawdown been" but "what depth is consistent with this configuration across the orderings I have not yet lived through".
A 22% decline that resolves in five weeks and a 22% decline that persists for fourteen months are reported identically and experienced completely differently. Time under water is the variable most strongly associated with abandonment, and abandonment converts a temporary drawdown into a permanent one.
Any risk statement that reports depth without duration and time under water is describing a third of the object. The observatory above reports all four measurements together for this reason.
Position size is calculated so that the stop equals 1R. The calculation quietly assumes the stop is honoured at the stated price. Gaps, weekend repricing, thin liquidity and correlated shock all produce losses materially larger than 1R, and they arrive clustered rather than scattered.
Every archetype in this engine carries an explicit shock-loss probability for this reason, ranging from roughly 1% for trend following to nearly 6% for mean reversion. It is a small term that accounts for a large share of the deepest orderings, because it fires precisely when several positions are already adverse.
How these numbers are produced.
Nothing on this page reads market data. Every figure is generated in the browser from a deterministic model, and the same seed always produces the same result.
01 · Median of nine seeded histories
A single simulated path is an anecdote. Every drawdown figure quoted in a readout is the median across nine independently seeded histories of the same configuration, and the curve drawn beside it is the history whose terminal return sits in the middle — so the number and the picture describe the same path rather than two different ones.
02 · Block-level concurrency
Trades are grouped into blocks the size of the effective concurrent position count. Equity is updated once per block rather than once per trade, which is what actually happens when several positions are open simultaneously — and it is why raising concurrency deepens drawdown even when per-trade expectancy is unchanged.
03 · Correlation clustering
Within a block, each trade draws from a shared random driver with probability equal to the correlation limit. At a 70% limit, most positions in a block resolve with the same sign. This is the mechanism by which "four positions" quietly becomes "one position held four times", and it is applied to drawdown, not just to a reported exposure figure.
04 · Gate compression
When governance is enabled, the risk applied to each block is multiplied by a factor determined by the current drawdown from the running peak, reviewed at block boundaries. Past the lock boundary the factor is zero and the history is drawn flat. The compression schedule used in this preview is a demonstration structure, not the MARS workbook calibration.
05 · Shock-loss term
A fixed proportion of losing outcomes is drawn from a wider distribution between 1.8R and 3.7R rather than from the ordinary loss band, representing a stop that did not hold. Without this term, high hit-rate archetypes model as almost free, which is the single most misleading property a risk model can have.
06 · Risk-of-ruin proxy
The ruin reading is a diffusion approximation: exp(−2 · netEV · U ÷ sd²), where U is the number of R units of cushion between the current equity and a 40% decline, and sd is the modelled dispersion of a single outcome in R. It assumes constant fractional sizing and therefore overstates ruin risk when the governance layer is engaged and understates it when correlation is high.
What this page cannot tell you.
A risk model that is not honest about its own boundaries is a marketing asset. These are the boundaries.
The outcome distribution is assumed, not measured
Every result here follows from an outcome ladder whose parameters are design constants. If the real distribution has a heavier left tail than the model, every drawdown figure on this page is optimistic — and heavier-than-assumed left tails are the normal case, not the exception.
Stationarity is assumed within a history
The model draws every trade in a history from the same distribution. Real edges decay, friction levels change, and regimes cluster. A drawdown produced by a deteriorating edge looks identical to one produced by an unlucky ordering while it is happening, and this page cannot distinguish them.
Correlation is modelled as a single scalar
One correlation limit is applied uniformly within a block. Real correlation is pairwise, asymmetric, and rises under stress. The engine's treatment captures the direction of the effect and understates its severity in exactly the conditions that matter most.
Nothing here is a forecast or a guarantee
No governance structure guarantees survival. A gate ladder reduces the probability of reaching a depth from which recovery is implausible; it does not eliminate it, and it cannot protect an account whose underlying framework has no edge. Risk control does not create expectancy — it decides how long you have to find out whether you had any.
Behaviour is not modelled at all
The largest single risk to most accounts is the operator's response to a drawdown, and no line of this engine simulates it. The four measurements at the top of this page exist because they are the ones that predict that response — but predicting it is not the same as modelling it.
Continue the investigation
Drawdown is one constraint.
It is never the only one.
Depth is produced jointly by risk per trade, concurrency, correlation, regime permission and friction. Change any one of them in isolation and the reading moves; change the wrong one and it moves in the direction that feels like an improvement. The Parameter Laboratory exposes all 159 controls against the same engine that generated this page.
Research concept · all datasets simulated · see the risk disclosure