Lose half your money and only doubling what's left gets you back to level. Not a 50% gain. A 100% one. The arithmetic is trivial, and almost nobody carries it around properly.
Here's the version that actually happened. Robert Shiller's monthly US series peaked in January 1973. Measured as real total return, with dividends reinvested and inflation stripped out, it fell 50.1% by December 1974. Getting back to level required 100.2%. It got there in January 1985 — twelve years from the peak, to the month.
That's the whole subject in one paragraph. The rest of this is about why the recovery multiple on its own tells you almost nothing, and what has to be bolted onto it before it says anything about how a portfolio gets built.
The ladder
A fall of L needs a gain of L divided by (1 minus L). That's the entire formula. Here's what it produces.
| Fall | Gain needed to get back to level |
|---|---|
| -10% | +11.1% |
| -20% | +25.0% |
| -30% | +42.9% |
| -40% | +66.7% |
| -50% | +100.0% |
| -60% | +150.0% |
| -80% | +400.0% |
| -90% | +900.0% |
The interesting part is the shape, not the endpoints. The curve is nearly flat to about -30% and then it bends hard. Going from a 20% fall to a 30% fall adds 17.9 points to the required gain. Going from 70% to 80% adds 166.7. Depth doesn't cost linearly, and that's why two portfolios with similar volatility can behave nothing alike once one of them takes a real hit. It's also the cleanest reason drawdown and standard deviation measure different things.
Which fall, exactly?
Before the ladder means anything you have to say what fell. Nominal price? Price plus dividends? Adjusted for inflation? The answers diverge enormously, and the 1929 crash is where they diverge most.
Take Shiller's monthly data. On the nominal S&P price index, the market dropped 84.8% between September 1929 and June 1932. That needs a gain of 556.2% to get level. It got there in September 1954 — twenty-five years later. This is the number everyone repeats.
Now measure the same crash as real total return. The fall is 76.8%, needing 331.0%. And the recovery date is November 1936 — seven years and two months after the peak. Same market, same crash, two answers eighteen years apart.
Dividend yields were enormous in the early 1930s, and consumer prices fell about a quarter before reflating. Both worked in the holder's favour. Neither shows up in a price chart. If you only ever see the price line, you'll systematically overstate what deep drawdowns cost a reinvesting holder — which is the same trap that makes published bear market recovery times look longer than they were.
One caveat on all of this. Shiller's monthly figures are averages of daily closes, so every depth here is shallower than the true daily peak-to-trough. The direction of the error is known and it's small relative to the differences between measures.
Britain's 1974 was worse than America's
The Bank of England publishes a spliced monthly UK share price index back to 1709 and a spliced monthly consumer price index from 1914. Put them together and the mid-1970s look brutal.
The UK index peaked in May 1972 and bottomed in December 1974, down 70.9% in nominal terms. That alone needs 243.5% to repair. But UK consumer prices rose 37.5% over those 31 months. In real terms the fall was 78.8%, and the required gain was 372.3%.
The real level of that index didn't get back to its May 1972 mark until February 1987. Just under fifteen years. And this is a price index, so it excludes dividends, which were generous in that era — a reinvesting holder got back sooner. The point isn't the exact date. It's that inflation quietly moved the finish line while everyone was watching the index.
There's a more recent one in the same data. The UK index set its real peak in December 1999, fell 48.8% to March 2009, and needed 95.4% back. As of March 2017, where the Bank's series ends, it was still 9.8% below that 1999 real level. Seventeen years and counting, on price alone.
Bonds don't escape it
This is where the arithmetic stops being an equity story. Shiller's series also carries a real total return index for US ten-year government bonds. It peaked in January 1941. It bottomed in September 1981.
The fall was 58.2% in real terms. The gain needed was 139.4%. It got there in August 1986 — forty-five and a half years after the peak. That's the safe asset. Four decades of negative real compounding, then a five-year sprint at roughly 19.5% a year to close the gap.
Something smaller but recognisable happened again recently. From April 2020 to October 2023 the same real bond index fell 37.3%, needing 59.6% to recover. It hadn't recovered by September 2024, where the data ends. Anyone who treated the bond sleeve as the part that can't take a 40% real hit had already been contradicted by history twice.
The case against making anything of this
The strongest objection is that all of the above is a mathematical triviality dressed as insight. It deserves a proper hearing, because it's largely correct.
Will Morrison made the underlying point twice for CFA Institute, in 2015 and 2018, under the title "The Myth of Volatility Drag". His example is the same one in miniature. Put in $100, lose 10%, gain 10%, end with $99. People read that missing pound as evidence of a force acting on the portfolio. Morrison argues that the difference between an arithmetic and a geometric mean "is in the definition, not from a force".
Push that further and the asymmetry disappears entirely. In log terms, halving is -0.6931 and doubling is +0.6931. Identical magnitudes, opposite signs, perfectly symmetric. Simple percentages only look lopsided because they're floored at -100% and unbounded above. Choose a different but equally valid unit and the drama evaporates.
The second objection is sharper still. The identity applies to everything — cash, gilts, gold, a single share, a house. Minus 50% needs plus 100% wherever it happens. A rule that holds identically for every asset cannot rank assets. So anyone deploying "a 50% loss needs 100%" as a reason to hold less equity is smuggling in a conclusion the arithmetic doesn't contain.
Both criticisms land. The recovery multiple, by itself, is not an allocation argument.
Where it starts to bite
The multiple becomes informative the moment you divide it by a growth rate. Time to repair is roughly the log of the recovery multiple divided by the log of one plus expected growth.
Over the 153 January-to-January years in Shiller's data, from 1871 to 2024, US equities compounded at 6.95% real and US ten-year government bonds at 2.44% real. Run the two through the formula. A 50% equity fall takes 10.3 years of average growth to repair. The 37.3% real bond fall of 2020 to 2023 takes 19.4 years at 2.44%.
Read that twice. The smaller loss, in the calmer asset, has the longer expected repair. The asymmetry only turns into an allocation argument when it's paired with expected return, and once it is, it doesn't obviously favour the safer holding. That's a real result, and it's the opposite of the folk conclusion the arithmetic usually gets used to support.
Variance is the second place it bites. Across those same 153 years, US real equity returns averaged 8.48% arithmetically but compounded at 6.95%. The gap is 1.53 points. Half the variance of the series is 1.59 points. For bonds: 2.82% arithmetic, 2.44% compounded, a gap of 0.38 points against half-variance of 0.41. The textbook approximation holds in the actual data, on both assets.
Morrison would say that gap is definitional rather than a force, and he'd be right about the mechanism. It's still the number that turns up in the account. Anything that cuts variance without surrendering as much arithmetic mean lifts the compounded result — which is the entire quantitative case for the assets that genuinely diversified through past crises.
Averages aren't what recoveries do
That 10.3-year estimate assumes average growth, and deep drawdowns are exactly when growth isn't average. The record is wild.
From the June 1932 trough, US real total returns compounded at 39.9% a year and cleared the 1929 peak in 4.4 years. From March 2009, 20.3% a year, and 4.2 years. From December 1974, only 7.3% a year — 10.1 years. Same broad starting hole, repair times differing by a factor of more than two.
Valuation does much of that work. A market that falls hard usually gets cheap, and cheapness raises the following decade's return. So the mechanical estimate badly overstated the wait after 1932 and 2009, and got 1974 about right. Anyone quoting a single "it takes N years to recover" figure is quoting the middle of a very wide distribution.
Where the arithmetic becomes real money
None of it matters to a holder who simply doesn't sell. It matters enormously to one who does.
Morningstar's Mind the Gap 2025 estimated that the average dollar in US funds earned 7.0% a year over the decade to 31 December 2024, against 8.2% for the funds themselves. The 1.2-point annual gap comes from the timing and size of purchases and sales, and amounts to roughly 15% of the funds' total return. It was widest in sector equity funds, at 1.5 points, and narrowest in allocation funds, at 0.1.
Selling into a drawdown is what converts the ladder from a chart into a bill. The holder who leaves at -40% keeps the hole and hands away the recovery that fills it. That's the mechanism behind the measured cost of investor mistiming, and it's why the evidence on rebalancing through the 2008 and 2020 crashes matters more than the depth of either crash.
What would change the conclusion
Several things, and one of them is likely.
The growth rates above are US figures from the market that won. The Global Investment Returns Yearbook 2025, covering 35 markets from 1900 to 2024, puts the long-run real equity return at 5.2% a year and real bonds at 1.7%. Plug 5.2% in and a 50% fall takes 13.7 years of average growth, not 10.3. Plug 1.7% into the bond side and a 50% fall takes 41.1 years. Lower assumed returns make every conclusion here more severe, not less.
Measurement would change it too. The UK figures come from a price index with no dividends, so the real UK drawdowns are overstated for a reinvesting holder, probably by a lot in a high-yield era. And Shiller's monthly averaging understates every depth relative to daily data.
The cleanest falsification would be an asset with a meaningful positive real return and no drawdown deep enough to trigger the bend in the curve. If one exists, the framing collapses. Nothing in 153 years of the US series or 103 years of the UK series looks remotely like that. Equities, government bonds and the price of a share of British industry have all delivered real drawdowns past 35%.
What wouldn't change it is the objection that the identity is trivial. It is trivial. Triviality isn't the same as irrelevance, and the reason to hold the ladder in your head isn't that it ranks assets — it doesn't — but that it prices the cost of a decision to sell at a moment when the required repair is at its largest. That's also why the distinction between risk tolerance and risk capacity does more work than a questionnaire score.
Key takeaways
- A 50% fall needs a 100% gain, a 60% fall needs 150% and an 80% fall needs 400% — the curve stays gentle to 30% and then bends hard.
- US equities fell 50.1% in real total return from January 1973 to December 1974 and didn't regain that level until January 1985, twelve years later.
- The 1929 crash needed 556.2% back on the nominal price index but only 331.0% in real total return, and the two recovery dates sit eighteen years apart.
- US ten-year government bonds lost 58.2% in real total return between January 1941 and September 1981, requiring 139.4% and 45.6 years to get level.
- At 6.95% real growth a 50% loss repairs in 10.3 years; at 2.44% a smaller 37.3% loss takes 19.4, so depth alone doesn't rank assets.