This module is mostly arithmetic, and it is the arithmetic that everything else in the course rests on. Once you have felt how asymmetrical losses are, position limits stop sounding like timidity and start sounding like accounting.
Lose a percentage of your money and you must gain a larger percentage to get back to where you started, because the gain is computed on a smaller base. The formula is one line:
Lose 20% and $100 becomes $80. Getting $80 back to $100 requires $20 on a base of $80 — 25%, not 20%. The asymmetry is mild at first and then turns vicious:
| Loss | Gain needed to break even | At 8%/yr, years to recover |
|---|---|---|
| −10% | +11.1% | ~1.4 |
| −20% | +25.0% | ~2.9 |
| −33% | +50.0% | ~5.3 |
| −50% | +100.0% | ~9.0 |
| −66% | +200.0% | ~14.3 |
| −80% | +400.0% | ~20.9 |
| −90% | +900.0% | ~29.9 |
The third column is the one that should stay with you. A 50% loss is not “half your money” — it is nine years of good returns spent standing still. And those are years you do not get back, which matters enormously if you are 58 and not at all if you are 24. This is the arithmetic behind the claim that avoiding the deep hole matters more than catching the big winner: the hole compounds against you at exactly the rate the winner compounds for you.
Here is a result that surprises almost everyone the first time. Two portfolios, both with an average annual return of 0%:
Portfolio B lost a quarter of its money while averaging zero. Nothing is wrong with the arithmetic — the problem is that the “average” being quoted is the arithmetic mean, and money compounds at the geometric mean. The gap between them is volatility drag, and it is real money.
The approximation is good for ordinary levels of volatility. Read it carefully: volatility subtracts from your compounded return even when it does not change your average return. A portfolio averaging 9% with 15% volatility compounds at roughly 9 − (0.15² ÷ 2) = 9 − 1.1 = 7.9%. Push volatility to 30% and the same 9% average compounds at roughly 4.5% — you lost nearly half your return to turbulence alone.
This is the mathematical reason risk management pays for itself rather than merely feeling safer. Two strategies with identical expected returns are not equivalent: the smoother one ends with more money. It is also why the marketing figure “average annual return” should always be checked against the compound annual growth rate (CAGR), which is the number you can actually spend.
Maximum drawdown is the largest peak-to-trough decline over a period, measured from the highest value reached to the lowest value that followed before a new high. It answers the question standard deviation cannot: what is the worst this actually got?
It is the single most useful risk statistic for a private investor, for one reason: it is the number you have to live through. Nobody experiences a standard deviation. Everybody experiences watching their account fall by a third.
Time under water is its neglected twin — how long the portfolio stayed below its previous peak. It matters more than depth for anyone drawing an income, and it is psychologically brutal in a way that depth is not. A fast 40% crash that recovers in a year is easier to hold than a 25% decline that grinds sideways for six.
Approximate peak-to-trough declines in broad North American equity indices, on a price basis. Figures are rounded and illustrative — the precise number depends on the index, whether dividends are included, and the exact dates used.
| Episode | Approx. decline | Approx. time to recover |
|---|---|---|
| 1929–1932 (US) | ~86% | Over two decades |
| 1973–1974 | ~48% | Several years |
| 2000–2002 (dot-com) | ~49% | ~5 years |
| 2007–2009 (financial crisis) | ~57% | ~4 years |
| 2020 (COVID) | ~34% | ~5 months |
| 2022 (rates/inflation) | ~25% | ~2 years |
Two things to take from the table. First, the frequency: a serious drawdown is not a freak event, it is a recurring feature. Anyone investing for thirty years should expect to sit through several. Second, the enormous variance in recovery time — five months in 2020, several years in 2000 and 2007. Recovery speed is not something you can plan on, which is exactly why the cash buffer in Module 8 exists.
Scale the arithmetic down to a single position and you get the formula that Module 5 is built on:
A 5% position that falls 50% costs the portfolio 2.5%. A 25% position that falls 50% costs 12.5% — and now you need a 14.3% gain from everything else just to stand still. A 40% position that goes to zero costs 40%, which needs +67% to recover, which at 8% a year is a lost decade caused by one decision.
Educational purposes only; not financial advice. Historical figures are illustrative and past drawdowns are not a forecast of future ones. Always do your own research and consult a licensed advisor.