Why does recovering from a 25% loss require more than a 25% gain?

Keep a running peak

Use an original fictional value series with five ordered observations: $10,000, $12,000, $9,000, $10,800, and $12,000. Assume no deposits, withdrawals, or distributions outside the values shown. The running peak rises to $12,000 at the second observation.

The CFA Institute discussion defines drawdown relative to a preceding peak and notes that measurement frequency affects the result. For this worksheet, each observation is one end-of-period mark. It makes no claim about unobserved movements between marks.

Calculate the peak-to-trough decline

At the $9,000 trough, value divided by the earlier $12,000 peak is 0.75. The drawdown is 0.75 − 1 = −25%. That is the largest observed peak-to-later-trough decline in this stipulated five-point series.

The decline from the initial $10,000 to $9,000 is only 10%, but it answers a different question. Drawdown uses the relevant preceding high, not necessarily the value at the start of the reporting window. Keep the dates or observation numbers of both endpoints.

Calculate recovery from the smaller denominator

To move from $9,000 back to $12,000 requires $3,000 of growth. Divide by the $9,000 remaining balance: $3,000 ÷ $9,000 = one-third, or approximately 33.3333%. A 25% gain would instead produce $11,250 and leave a $750 gap.

The fourth observation, $10,800, is a 20% gain from the trough but still 10% below the peak. The final $12,000 observation completes the stipulated recovery. None of these calculations says when a real investment will recover, or that it will recover at all.

Separate recovery size from recovery duration

A ledger can record peak observation 2, trough observation 3, and first recovered observation 5. Without dates, it cannot translate those intervals into calendar months or years. Adding timestamps would allow a duration calculation, but would not reveal movements between the recorded marks.

The denominator rule also explains other invented cases. A 40% decline leaves 60% of the original balance, so recovery requires 40 ÷ 60 = approximately 66.6667%. A 50% decline requires 100% growth from the remaining half. These are arithmetic requirements, not expected returns.

For a fresh worksheet, record the running peak beside every observation before calculating any decline. This prevents accidentally using a later high as the reference for an earlier trough. Peak-to-later-trough order matters: a high that had not yet occurred cannot describe the preceding loss.

Method, sources, and limits

All values are invented, with ratios checked using decimal arithmetic. The CFA Institute source was opened on 26 October 2026. Maximum observed drawdown describes a chosen series, window, and sampling interval; it is not a worst possible future loss. Contributions can restore an account balance without representing investment recovery, so a real review should distinguish cash added from changes in the measured investment value.