Koinlytics

Drawdowns and Volatility: The Recovery Math Nobody Runs

Riskbeginner7 min read
Why a 50% loss needs a 100% gain to break even and a 90% loss needs 900%, what realistic crypto drawdowns look like historically, and why volatility is not the same thing as permanent loss.

A 50% drawdown needs a 100% gain to get back to even. An 80% drawdown needs a 400% gain. A 90% drawdown needs 900%. The math is not intuitive because losses and gains are not symmetric: a loss shrinks the base the recovery gain has to work from, so the percentage needed to recover grows faster than the percentage that was lost.

The recovery table

The formula is simple: gain needed = drawdown / (1 - drawdown). The table below shows how quickly it turns ugly.

DrawdownGain needed to break even
10%11%
20%25%
30%43%
40%67%
50%100%
60%150%
70%233%
80%400%
90%900%
95%1,900%

The curve is convex, not linear. The first 50 percentage points of loss need a 100% gain to undo. The next 40 percentage points of loss, from 50% down to 90%, need a further 800 percentage points of gain. Most of the damage from a large drawdown is not in the loss itself, it is in how much harder the recovery becomes past a certain depth.

What realistic crypto drawdowns look like

At the asset class level, drawdowns of 70% to 85% from cycle highs have happened repeatedly, as a recurring pattern rather than an outlier event. Bitcoin drew down roughly 84% peak to trough after the 2017 top and roughly 77% after the 2021 top, cycles loosely bounded by the supply changes covered in the chapter on the Bitcoin halving. Ether has drawn down further in most cycles. Smaller-cap tokens routinely lose 90% or more from their highs, and a large share of them never recover any of it, because the project stops shipping, liquidity dries up, or the token was never backed by anything durable to begin with.

This is the baseline to plan around, not the exception. An asset class where an 80% drawdown is a normal cyclical event has different portfolio math than one where the same drawdown would be a rare crisis. Position sizing is what makes an 80% drawdown in a single holding survivable at the portfolio level, even when it is unremarkable at the level of that one asset.

Volatility is not the same thing as risk of permanent loss

Volatility measures how much a price moves. Risk of permanent loss measures whether the capital comes back. The two are correlated in crypto but not identical, and conflating them produces two opposite mistakes: selling a volatile but structurally sound asset through a drawdown it was always going to have, or holding through a drawdown in an asset that is never coming back, on the assumption that it is just volatility.

The distinguishing question is not how far something has fallen, it is whether the thing that gave it value is still there. Bitcoin after an 80% drawdown is still Bitcoin: the network is running, the supply schedule is unchanged, the reasons someone bought it in the first place are largely intact. A token whose treasury was drained in an exploit, or a stablecoin that broke its peg permanently, has not had a drawdown in the recoverable sense, because the mechanism that was supposed to underpin its value is gone. UST, after the Terra collapse, did not recover from its drawdown, because there was no remaining mechanism to recover with. Telling the two apart in real time, before the outcome is obvious, is the actual skill; after the fact it always looks easy.

Volatility drag on leveraged and rebalanced products

Volatility does direct, mechanical damage to leveraged and rebalanced products even when the underlying asset goes nowhere. A daily-rebalanced 2x or 3x leveraged token multiplies the daily percentage move, not the cumulative one, and repeated rebalancing in a choppy, sideways market erodes value through a mechanism separate from any view on direction. This is a different exposure than a perpetual futures position sized and managed by the holder, since the leveraged token rebalances on a fixed schedule regardless of what the holder would otherwise choose to do.

Take an asset that alternates +10% one day and -10% the next, forever, with no net trend. Unleveraged, one dollar becomes 1.10, then 1.10 x 0.90 = 0.99, down 1% every two days despite zero average daily return, purely from the arithmetic of compounding a gain and a loss of equal size. Apply 3x daily leverage to the same swings, +30% then -30%, and one dollar becomes 1.30, then 1.30 x 0.70 = 0.91, down 9% over the same two days for an asset that round-tripped to exactly where it started. The drag scales roughly with the square of the leverage multiple and with the variance of the returns: choppier, more volatile conditions cause faster decay, independent of whether the underlying ever trends anywhere. This is why leveraged tokens are structurally unsuited to being held through sideways, high-volatility periods, regardless of which direction anyone expects the market to eventually move.

Working with drawdowns in practice

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