Drawdown Recovery Calculator

The drawdown happens once, at time zero, measured against the reference value you selected. Everything after that is either a closed-form identity or a month-by-month simulation, and which one is used depends only on whether new contributions are modelled.

The gain the loss requires

d  = drawdown, as a decimal between 0 and 1
q  = d / (1 - d)

Equivalently, the value remaining is 1 - d of the reference, and it must be multiplied by 1 / (1 - d) to return to it. At d = 1 there is no finite q, and the tool states that rather than printing a very large number.

Time to regain the old balance from returns alone

t = ln(1 / (1 - d)) / ln(1 + r)

r is the effective annual recovery return you entered. Where r is zero or below and there is a loss, the old balance is not reached through returns alone, and the tool says so instead of showing a negative or unbounded duration.

Time to catch the original plan, with no contributions

t = ln(1 / (1 - d)) / ln((1 + r) / (1 + p))

p is the planned annual return of the path that never had the drawdown. Wherer is not above p and both paths receive the same contributions, the recovery path never catches the plan under constant rates. That is arithmetic, not a search that ran out of time, and the tool distinguishes the two.

Converting annual rates to monthly ones

monthly recovery factor = (1 + r) ^ (1/12)
monthly plan factor     = (1 + p) ^ (1/12)

A rate quoted for a year is converted by the twelfth root, so twelve monthly steps reproduce the annual figure exactly. Dividing an annual rate by twelve would describe a different quantity, a nominal rate compounded monthly. This model does not use that form anywhere.

Order of events in each month

[contribution, if you chose beginning of period]
growth at the monthly factor
[contribution, if you chose end of period]
test whether the old balance or the original plan has been reached

Beginning timing adds the first contribution immediately after the drawdown, before any growth. End timing waits until the first selected period has passed. A contribution that restores the balance before any growth has happened is reported as reached immediately after the first contribution, never as zero years of investment recovery.

The original plan receives identical contributions

The recovery path and the original-plan path consume the same schedule: the same amount, on the same dates, at the same frequency and timing. Giving the plan different contribution dates would manufacture a catch-up out of timing rather than performance, which is precisely the error this tool exists to prevent.

A mathematical no-drawdown reference, not a claim about what would have happened.

The return required to recover within a target period

with no contributions:  r = (1 / (1 - d)) ^ (1/T) - 1
with contributions:     solved numerically for the same target

With contributions the model searches deterministically for the effective annual return whose simulated balance reaches the reference at the end of the period, and verifies the result against the target before showing it. Where contributions alone already reach the target, the tool states that no positive return is required rather than implying one is. Where no reliable result can be verified, it says so rather than showing an arbitrary rate.

Where the calculation stops

The 100-year limit is where this calculation stops searching. It is not a forecast horizon.

Assumptions

• The drawdown occurs once, at time zero, and is not repeated.
• Returns are effective annual returns and are constant for the whole period.
• Contributions arrive exactly on schedule and are never missed.
• Both paths receive identical contributions, so any difference between them comes from the return assumptions rather than from the money added.
• Values are not rounded during the calculation; rounding happens only for display.

Recovery arithmetic does not tell you whether holding the same asset is the best decision. A previous value is a reference point, not evidence about future return.

Recovery arithmetic explains the hurdle a loss creates. It does not choose the best path from today, and the amount already lost is not a reason to keep holding anything. A previous value is a reference point you selected, not evidence about what an asset will do next.

This is the reference you selected. The tool does not determine whether returning to that value is probable, necessary, or the best decision from today.

New contributions can rebuild a balance without the investment earning back the full loss.

This tool does not decide

• whether to hold, sell, buy more, average down, or switch to another asset
• whether the reference value you chose is still economically relevant
• whether the return you entered is likely, available, or reasonable
• whether a loss is temporary or permanent
• the effect of tax, inflation, fees, volatility, or the order in which returns arrive

Nothing here is modelled

• Probability of recovery, historical market recovery periods, expected returns, volatility or the order in which returns arrive.
• Inflation, so a nominal recovery is not a recovery of purchasing power.
• Fees, taxes, spreads or transaction costs.
• Leverage, liquidation, margin calls or withdrawals.
• Whether the reference value you chose was a bubble, a fair value, a purchase price or a prior peak. The tool takes it as given because you selected it.
• Anything about your circumstances. This is not financial, legal or tax advice.

Why the percentages behave this way, and why breaking even is not an investment rule: Why Losses Require Disproportionately Larger Gains.