Peak-to-trough loss measures an ordered fall from an earlier peak to a later low. Separate loss amounts, percentages, current drawdown and the recovery gain.
Peak-to-trough loss
Peak-to-trough loss is the fall from an investment's earlier peak value to its subsequent low during a decline. It describes capital lost along the way, even when the investment eventually finishes above its starting value. Always say whether the loss is an amount or a percentage of the peak: those answer different questions about the same episode.
One decline, two measurements
Take a synthetic total-return wealth index observed at equally spaced times:
100,120,90,108,80,124.
There are no deposits or withdrawals; investment income is included. The peak at 120 comes before the trough at 80. Between them, the rebound to 108 does not regain the peak, so it does not end the decline episode.
The absolute loss is
120−80=40 index points.
The fractional loss uses the earlier peak as its denominator:
120120−80=31=3331%.
Forty index points is not a 40% loss. Nor is it automatically a currency loss: this example is an index. For a no-flow account measured in currency, the same subtraction would instead be in that currency.
A synthetic wealth index follows 100, 120, 90, 108, 80 and 124 at observations 0 through 5. The earlier peak is 120 at observation 1 and the later trough is 80 at observation 4. The vertical loss is 40 index points, or one-third of the peak. The final 124 occurs after the trough.
Original synthetic total-return index with no external flows. The bracket measures the fall from the earlier 120 peak to the later 80 trough; straight segments only join the observations.
The final 124 cannot replace 120 as the peak for that loss: 124 happened after 80. The record's unrestricted high-minus-low range is 124−80=44 index points. That range combines two extrema without requiring a loss to occur between them in time. Peak-to-trough measurement preserves the order an investor actually experienced.
Episode loss, current drawdown and the record maximum
An episode's peak-to-trough loss describes that particular decline. Drawdown at a chosen observation describes the distance below the running historical peak at that time. Maximum drawdown selects the largest such loss across the specified record, under a declared amount or percentage convention.
For positive wealth Wt, write
Ht=0≤s≤tmaxWs,At=Ht−Wt,Dt=HtHt−Wt.
Here At is the current loss amount and Dt its positive fractional magnitude. At 108, these are 12 index points and 10%. At 80, they reach 40 points and 3331%. At the final 124, both current measures are zero because wealth has made a new high. The earlier episode's 40-point loss remains in the historical record.
In this particular path, that episode also supplies the maximum loss across all observations. That need not hold for every selected episode. Moreover, across different episodes, the largest loss amount and the largest percentage loss can come from different peaks, because the percentage denominators differ. A negative signed-drawdown convention reports the same fractional loss with a minus sign; it does not describe a different economic fall.
The climb back has a smaller base
Recovering the old peak from the trough requires
80120−80=50%.
The 33⅓% fall was measured against 120; the 50% recovery gain is measured against 80. The two percentages therefore do not cancel. The later observation of 124 is above the old peak, but the path alone says nothing about how likely another recovery will be. Loss depth also does not give a recovery period: dates and a stated recovery convention are needed for that.
For strategy comparisons, apply this measurement to consistently valued, flow-adjusted wealth. A withdrawal can lower an account balance without being an investment loss, and sparse observations can miss an intervening trough. Backtest Evaluation develops the linked-return construction and the drawdown calculation together. The full lesson requires membership, with a public preview.
Sources
Giuseppe A. Paleologo, Advanced Portfolio Management: A Quant’s Guide for Fundamental Investors (Wiley, 2021), §9.1, pp. 149–151 — losses measured from a strategy's high-water mark and their role in loss-management decisions. The numerical path and figure here are original synthetic examples.
