Drawdowns and Risk of Ruin

A drawdown is a decline from a previous equity peak. Risk of ruin asks whether a process can cross a chosen failure threshold, such as insufficient margin or a minimum viable account value. Ruin need not mean a balance of zero. An account can lose the ability to hold its positions long before that.

Recovery is asymmetric

A $20,000 account that falls 25% reaches $15,000. It needs $5,000 ÷ $15,000 = 33.33% to return to its peak. More generally, after a fractional loss d, the required recovery is d ÷ (1 − d). A 50% loss requires a 100% gain; a 75% loss requires a 300% gain.

Fixed dollars and fixed fractions differ

Under a simplified model where each losing trade removes 2% of the then-current account, ten consecutive losses leave 0.98¹⁰ = 81.71% of starting equity, an 18.29% drawdown. With a fixed $400 loss on a $20,000 account, ten losses instead leave $16,000, a 20% drawdown. Real contracts are indivisible, and actual losses can exceed a stop-based estimate.

Increasing size to recover a loss changes the risk process. A sequence described as “the same strategy” can become substantially more dangerous if its quantity rises while equity falls.

Why a neat ruin number can mislead

Closed-form formulas often assume independent trades, stable probabilities and fixed payoffs. Options returns can contain rare jumps, changing volatility, assignment and liquidity costs. Several trades can fail together. A calculated 1% ruin probability is only as credible as the assumptions and definition of ruin behind it.

A simulation should state its horizon, funding threshold, return distribution, treatment of correlated losses, transaction costs and resizing rule. Resampling a quiet historical period cannot manufacture crises absent from that sample. Test harsher losses and longer streaks as sensitivity checks, without claiming that a chosen stress exhausts possible outcomes.

Review before increasing risk

Track equity after all liabilities and open-position marks, not just collected premiums. Record maximum drawdown, time below the prior peak and capital needed to keep positions open. Precommit to a review threshold so that an emotional attempt to recover does not silently replace the original plan. The appropriate threshold depends on the investor and account; none of the percentages here is a recommended allocation.