Calculator
Drawdown-Recovery Markov Simulator
Time to recover from an N% drawdown given monthly Sharpe + skew + kurtosis. Cornish-Fisher Monte Carlo, percentile distribution of recovery months.
Runs in your browser. Nothing you enter is uploaded, and no account or API key is needed.
Inputs
Mean monthly return / monthly volatility. 0.30 ≈ 1.04 annualized (× √12).
4% a month ≈ 13.9% a year. At the same Sharpe, higher volatility recovers faster.
0 = symmetric; negative = more large losses than large gains.
0 = normal tails; positive = fat tails.
Each path starts this far below its peak.
Paths still under water at the horizon count as not recovered.
Same inputs + same seed = same result.
Median recovery (months)
17
Months to regain the peak from a 20% drawdown, across 2,000 simulated paths of i.i.d. monthly returns. One path in twenty takes longer than 55 months.
Recovery distribution (months)
25th percentile
11
fast paths
Median
17
75th percentile
27
slow paths
95th percentile
55
tail
Path outcomes
Recovered within 12 months
30.3%
607 of 2,000
Not recovered within 240 months
0.00%
Counted as longer than the horizon in every percentile
Reading the result
Each path starts at the drawdown and compounds monthly returns r = μ + σ·q, where μ = Sharpe × σ and q is a standard-normal draw reshaped by the Cornish-Fisher expansion for your skew and kurtosis, then rescaled to unit variance so the simulated Sharpe equals your input. Recovery takes roughly ln(1 / (1 − drawdown)) / (μ − σ²/2) months on average; negative skew and fat tails stretch the slow end. Returns are independent month to month, so regime persistence in real strategies makes true recoveries longer.
How to use it
- Enter your strategy's monthly Sharpe and monthly volatility (4% a month is about 14% a year), plus the skew and excess kurtosis of its monthly returns.
- Set the drawdown to recover from (for example 20%), the number of paths and the simulation horizon in months.
- Read the median recovery and the 25th, 75th and 95th percentiles in months. A percentile shown as 'more than' the horizon means that share of paths had not recovered when the simulation stopped.
- Compare the 95th percentile with the longest drawdown you would sit through. If it is longer, the strategy is too risky at this size or needs a tighter kill switch.
- Change the seed to check that the result is stable, and sweep the drawdown and volatility: at the same Sharpe, deeper drawdowns and lower volatility both lengthen recovery.
Questions people ask
Why use a Markov chain to model drawdowns?
The model is a Markov process in the simple sense: each month's equity depends only on the previous month's equity and a fresh random return. It does not estimate drawdown-state transition probabilities from your equity curve. Every path starts at the drawdown you choose and compounds independent monthly returns with your Sharpe, volatility, skew and kurtosis until it regains the peak or hits the horizon.
What's the recovery time output?
Months from the bottom of the drawdown back to the prior peak, summarized as the 25th, 50th, 75th and 95th percentiles across all simulated paths, plus the share recovered within 12 months and the share still under water at the horizon. Paths that never recover count as longer than the horizon, so a percentile can read 'more than 240'.
How many observations do I need?
None: the tool takes summary statistics, not an equity curve. Estimate monthly Sharpe, volatility, skew and excess kurtosis from your own returns; with fewer than about 60 monthly observations those estimates, especially skew and kurtosis, are noisy, so try a range of values. More simulated paths reduce simulation noise, not estimation error.
Does it work for trend-following systems?
Only partly. Trend-followers have long losing stretches followed by sharp gains, which is serial dependence; the simulation draws each month independently, so it captures the skew and fat tails you enter but not the clustering. Treat its recovery times as a lower bound for strategies whose bad months come in runs.
What's the difference between this and Monte Carlo on returns?
It is a Monte Carlo on returns: i.i.d. monthly draws from a distribution shaped by the Cornish-Fisher expansion for your skew and kurtosis and rescaled so the simulated Sharpe and volatility equal your inputs. Compared with a historical bootstrap it can produce losses your sample never saw, but it cannot reproduce volatility clustering or regime persistence, which make real recoveries longer.
Guides, formulas and worked examples
- Guide How to Estimate Drawdown Recovery Time
- Comparison Calmar vs MAR Ratio
- Comparison Max Drawdown vs Ulcer Index
- Formula Maximum Drawdown Formula
- Formula Ulcer Index Formula
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Use it from code
The same calculation as a JavaScript module you can import. It runs where you import it, with no request, key or rate limit.
import { compute } from "https://aifinhub.io/engines/drawdown-recovery-markov.js";