Time under water tracks waiting below a previous wealth peak. Distinguish current age, completed episode length and underwater counts, including equality and unfinished recoveries.
Time under water
Time under water measures how long an investment remains below a previous high-water mark. It describes the time dimension of a drawdown: capital can remain below its old peak for a long spell even when the loss is shallow. A performance report that shows only the size of the loss leaves out how long the investor waited for recovery.
The label needs a clock convention. It can mean the age of the current spell, the length of a completed spell, or a count of underwater observations. Those numbers need not agree. Here, reaching the old high exactly counts as recovery; both an equal high and a new high reset the current clock.
Start the clock at the latest high
Use a positive, unitised total-return wealth index, adjusted for external deposits and withdrawals. Let Wi be its value at observation time ti. The running high-water mark is
Hi=0≤j≤imaxWj.
The latest observation at a high-water mark and the current underwater age are
gi=max{j≤i:Wj=Hj},Ui=ti−tgi.
At an equal or new high, gi=i and Ui=0. Below the high, the date stored in gi stays fixed while elapsed time grows. This is the sampled-time counterpart of the latest-peak duration process in Mahmoud's The Temporal Dimension of Risk, Definitions 3.6 and 3.9.
“Latest” matters when highs repeat. For daily wealth 100, 95, 100, 96 at days 0, 1, 2, 3, the clock reads 0, 1, 0, 1 days. The return to 100 on day 2 closes a two-day episode. The fall to 96 starts another, measured from day 2. Measuring from the first 100 would incorrectly join spells across a recovery under this convention. A strict-new-high convention would treat that equality differently; López de Prado's §14.5.2 describes recovery in terms of exceeding the earlier maximum. State the rule before comparing reports.
One path, three different readings
Consider six synthetic daily observations, one elapsed day apart, with no external cash flows. Values are a wealth index, not currency or a fund track record.
Day
Wealth
Running high
Current underwater age, days
0
100
100
0
1
120
120
0
2
90
120
1
3
108
120
2
4
80
120
3
5
124
124
0
At day 4 the current spell is three elapsed days old, measured from the high of 120 on day 1. The rebound to 108 on day 3 did not reset it. On day 5, 124 exceeds the old high and the current clock resets to zero.
Synthetic daily wealth 100, 120, 90, 108, 80 and 124. The current underwater clock reads 0, 0, 1, 2, 3 and 0 days. The completed episode runs from day 1 to day 5 for four elapsed days; days 2, 3 and 4 are three strictly underwater observations.
Original synthetic no-flow total-return wealth index. Blue points are observations; the dashed line is the running high. Pale bands identify strictly underwater sample dates. Joining wealth observations does not establish the path between them.
Keep these separate in a report:
Current age at day 4:4−1=3 elapsed days. It answers how long the ongoing spell has lasted so far.
Completed episode length:5−1=4 elapsed days, from the last high before the decline to the first observed recovery. Store this when recovery occurs, even though the current clock has become zero.
Strictly underwater observation count: three, at days 2, 3 and 4. It counts records satisfying Wi<Hi, rather than elapsed time between endpoints.
Even the maximum sampled current-clock reading is only three days here; it does not equal the four-day completed episode length. The final interval ends at a reset. Specify which statistic a “longest time under water” field reports, rather than taking the maximum of a sampled current-age column and assuming it measures completed episodes.
The recovery period also needs its starting point: peak-to-recovery includes the decline as well as the rebound; trough-to-recovery starts later. The longest episode need not contain the maximum drawdown. Depth and time answer different questions.
An unfinished spell is not a short recovery
If this record stops at day 4, recovery has not been observed. Report “ongoing; three elapsed days since the day-1 peak,” or “completed duration unknown, at least three days so far.” The eventual episode length is right-censored. Giving it a completed duration of three days, assigning zero, or dropping it from a summary would change the meaning of the report. An average calculated only over completed episodes excludes unresolved spells and must be labelled accordingly.
Window boundaries matter too. If a reporting window starts on day 3 but carries in the known day-1 high, its opening clock is already two days old and reaches three at day 4. Reinitialising the high to 108 on day 3 gives a different clock: zero on day 3 and one on day 4. That measures a reset history. If the earlier peak date is unavailable, the full ongoing age cannot be recovered from the truncated window alone.
Use actual timestamps and state calendar days, trading sessions or another unit. A row count cannot supply elapsed calendar time when weekends, missing marks or irregular observations intervene. Coarse observations can also miss a recovery and a fresh decline between marks; describe the result as observed at the stated frequency. No straight-line interpolation is assumed here.
For the surrounding reporting workflow, Backtest Evaluation connects flow-adjusted wealth, drawdown duration and unresolved recoveries to performance assessment. The full lesson requires membership, with a public preview. Historical waiting times are descriptive evidence; they do not promise a deadline by which the next loss will recover.
Sources
Marcos López de Prado, Advances in Financial Machine Learning (Wiley, 2018), §14.5.2, “Drawdown and Time under Water” — episode duration between high-water marks. Its exceeding-the-previous-maximum wording differs from the equality-as-recovery convention explicitly used here. All wealth paths and calculations above are original synthetic examples.
