# Drawdown, recovery and time under water

> Maximum drawdown, the gain needed to get back to the peak and how many months a portfolio can stay below it.

- Course: [Long-Term Investing: Index Funds, Risk and Your Own Behavior](https://productovi.com/courses/long-term-investing.md)
- Module: How much can you lose, and for how long?
- Lesson 6/32, ~23 min
- Source: https://productovi.com/courses/long-term-investing/drawdown-recovery

## The crash in years 21 and 22

**Grace:** Still March at Zapas. Yesterday's beta questions were about one bad month. Today, as the PM who writes the risk screen, you need the worst stretch in our synthetic history: the crash of years 21 and 22.

**Ethan:** I know this one. Year 21 was −22%, year 22 was −30%. So the worst case is about −30%, right? That's what I'd put on the screen.

**Grace:** Two bad years don't add up like that; they compound. Let's follow 100 dol. invested at the end of year 19, month by month. At the end of year 20 it had grown to 115.95. That's the **peak**.

**Grace:** Then the slide began. Twenty-four months later, at the end of year 22, the same money was worth 63.32. That's the **trough**. The fall from peak to trough is the **drawdown**.

**100 dol. in Tessaro World, years 20–27, month by month**

| Month of the window | Value |
| --- | --- |
| 1 | 101.19 |
| 2 | 103.3 |
| 3 | 101.85 |
| 4 | 104.28 |
| 5 | 105.31 |
| 6 | 105.94 |
| 7 | 107.83 |
| 8 | 106.96 |
| 9 | 108.55 |
| 10 | 110.6 |
| 11 | 113.03 |
| 12 | 115.95 |
| 13 | 112.36 |
| 14 | 105.39 |
| 15 | 110.03 |
| 16 | 100.9 |
| 17 | 96.26 |
| 18 | 103.09 |
| 19 | 99.17 |
| 20 | 90.05 |
| 21 | 93.02 |
| 22 | 87.72 |
| 23 | 95.09 |
| 24 | 90.43 |
| 25 | 83.78 |
| 26 | 90.94 |
| 27 | 80.8 |
| 28 | 77.21 |
| 29 | 85.28 |
| 30 | 77.9 |
| 31 | 72.8 |
| 32 | 75.6 |
| 33 | 68.15 |
| 34 | 65.87 |
| 35 | 68.93 |
| 36 | 63.32 |
| 37 | 70.82 |
| 38 | 75.1 |
| 39 | 71.76 |
| 40 | 77.9 |
| 41 | 79.96 |
| 42 | 78.08 |
| 43 | 80.93 |
| 44 | 82.19 |
| 45 | 79.27 |
| 46 | 81.21 |
| 47 | 81.98 |
| 48 | 81.04 |
| 49 | 79.48 |
| 50 | 80.92 |
| 51 | 80.51 |
| 52 | 87.04 |
| 53 | 88.97 |
| 54 | 89.86 |
| 55 | 92.96 |
| 56 | 95.46 |
| 57 | 91.99 |
| 58 | 91.44 |
| 59 | 94.26 |
| 60 | 95.64 |
| 61 | 93.79 |
| 62 | 89.24 |
| 63 | 91.45 |
| 64 | 94.7 |
| 65 | 91.51 |
| 66 | 94.18 |
| 67 | 94.1 |
| 68 | 95.6 |
| 69 | 100.29 |
| 70 | 105.25 |
| 71 | 110.75 |
| 72 | 109.99 |
| 73 | 109 |
| 74 | 113.29 |
| 75 | 107.35 |
| 76 | 107.59 |
| 77 | 110.64 |
| 78 | 106.84 |
| 79 | 100.76 |
| 80 | 100.83 |
| 81 | 102.97 |
| 82 | 109.99 |
| 83 | 111.99 |
| 84 | 119.77 |
| 85 | 123.47 |
| 86 | 127.36 |
| 87 | 125.27 |
| 88 | 124.35 |
| 89 | 121.35 |
| 90 | 126.05 |
| 91 | 125.45 |
| 92 | 116.07 |
| 93 | 116.96 |
| 94 | 119.6 |
| 95 | 117.77 |
| 96 | 117.37 |

*Level 100 at the end of year 19, nominal dollars. Month 12 is the end of year 20; month 36 the end of year 22. Synthetic data.*

**Dataset (CSV):** [Tessaro World crash window, 96 months (years 20–27)](https://productovi.com/datasets/long-term-investing/drawdown-recovery/crash_window_monthly.csv)

> **Exercise:** In the crash window, 100 dol. grew to 115.95 at the peak (end of year 20) and fell to 63.32 at the trough (end of year 22). What was the maximum drawdown, in percent, to one decimal (as a positive number)?

**Ethan:** So my −30% understated the worst case by about a third.

**Grace:** Yes. And remember what that 45.4% measures: the fund's own index from its peak to its trough. A user's account can show a different number, because their money went in at different times and prices. When we quote a fall to users, we say which one it is.

## The way back is steeper

**Sofia:** So from 63.32 it needs to rise 45% to get back?

**Grace:** That's the trap. The rise starts from a smaller base. To go from 63.32 back to 115.95 you need 115.95 ÷ 63.32 − 1 = 83.1%. A loss of half needs a gain of 100%.

$$
\text{gain needed} = \frac{1}{1 - \text{drawdown}} - 1
$$

*The gain needed to get back to the peak after a drawdown*

> **Exercise:** After the 45.4% drawdown, the money stood at 63.32 against a peak of 115.95. What gain from the trough was needed to reach the peak again, in percent, to one decimal?

**Sofia:** So the deeper the hole, the steeper the climb out of it.

**Grace:** Exactly, and not in a straight line. Match a few falls with what they need. It's the little table I keep in my head for every risk message we write.

> **Exercise:** Match each drawdown with the gain needed to get back to the peak.

## Time under water

**Ethan:** Fine, but how long did it take?

**Grace:** That's the question users really ask. Down took 24 months. Back to the old peak took another 48, until the end of year 26. So the money was **under water**, below its peak, for 72 months.

**Below the peak, years 20–27**

| Month of the window | Drawdown |
| --- | --- |
| 1 | 0 |
| 2 | 0 |
| 3 | -1.4 |
| 4 | 0 |
| 5 | 0 |
| 6 | 0 |
| 7 | 0 |
| 8 | -0.8 |
| 9 | 0 |
| 10 | 0 |
| 11 | 0 |
| 12 | 0 |
| 13 | -3.1 |
| 14 | -9.1 |
| 15 | -5.1 |
| 16 | -13 |
| 17 | -17 |
| 18 | -11.1 |
| 19 | -14.5 |
| 20 | -22.3 |
| 21 | -19.8 |
| 22 | -24.4 |
| 23 | -18 |
| 24 | -22 |
| 25 | -27.7 |
| 26 | -21.6 |
| 27 | -30.3 |
| 28 | -33.4 |
| 29 | -26.5 |
| 30 | -32.8 |
| 31 | -37.2 |
| 32 | -34.8 |
| 33 | -41.2 |
| 34 | -43.2 |
| 35 | -40.6 |
| 36 | -45.4 |
| 37 | -38.9 |
| 38 | -35.2 |
| 39 | -38.1 |
| 40 | -32.8 |
| 41 | -31 |
| 42 | -32.7 |
| 43 | -30.2 |
| 44 | -29.1 |
| 45 | -31.6 |
| 46 | -30 |
| 47 | -29.3 |
| 48 | -30.1 |
| 49 | -31.5 |
| 50 | -30.2 |
| 51 | -30.6 |
| 52 | -24.9 |
| 53 | -23.3 |
| 54 | -22.5 |
| 55 | -19.8 |
| 56 | -17.7 |
| 57 | -20.7 |
| 58 | -21.1 |
| 59 | -18.7 |
| 60 | -17.5 |
| 61 | -19.1 |
| 62 | -23 |
| 63 | -21.1 |
| 64 | -18.3 |
| 65 | -21.1 |
| 66 | -18.8 |
| 67 | -18.8 |
| 68 | -17.6 |
| 69 | -13.5 |
| 70 | -9.2 |
| 71 | -4.5 |
| 72 | -5.1 |
| 73 | -6 |
| 74 | -2.3 |
| 75 | -7.4 |
| 76 | -7.2 |
| 77 | -4.6 |
| 78 | -7.9 |
| 79 | -13.1 |
| 80 | -13 |
| 81 | -11.2 |
| 82 | -5.1 |
| 83 | -3.4 |
| 84 | 0 |
| 85 | 0 |
| 86 | 0 |
| 87 | -1.6 |
| 88 | -2.4 |
| 89 | -4.7 |
| 90 | -1 |
| 91 | -1.5 |
| 92 | -8.9 |
| 93 | -8.2 |
| 94 | -6.1 |
| 95 | -7.5 |
| 96 | -7.8 |

*How far Tessaro World stood below its highest level so far, in percent. Zero means a new peak. Synthetic data.*

![Tessaro World fell 45.4% in 24 months, needed +83.1% and 48 more months to regain its peak: 72 months under water in dollars and 11 years after inflation.](https://productovi.com/courses/long-term-investing/diagrams/m2-l2-crash-anatomy.png)

*The way back is longer than the way down.*

**Sofia:** And after inflation?

**Grace:** Longer. In real terms the year-20 peak was regained only in year 31: 11 years. Someone who invested everything at the top waited over a decade to be whole in buying power.

> **Exercise:** Put the events of the Tessaro crash in the order they happened.

> **Exercise:** A user who invested at the very peak asks how long recovery took last time. Which answer should the app give?

**Ethan:** Can't we just show the dollar chart? It ends at a new high.

**Grace:** A new high in dollars, yes. But our users plan in buying power: a flat, school fees, a pension. The real line is the one that matches their goals, so that's the one the goal screen shows.

> **Exercise:** At the end of year 26 the Tessaro index was back above its year-20 peak in dollars, so an investor from the peak had also recovered their buying power.

**Ethan:** OK, my screen said −30%. The honest numbers are −45%, six years to get back, eleven after inflation. That's a scary screen.

**Grace:** Scary now is better than surprised later. Users who saw this before investing are the ones who stay. Write him the reply for the FAQ.

> **Exercise:** Ethan proposes an FAQ line: "Markets always bounce back within a year or two." In 2–3 sentences, rewrite it honestly with the Tessaro crash numbers.

> **Key ideas**
>
> - A **drawdown** is the fall from a peak; the **maximum drawdown** of Tessaro World was 45.4% (115.95 → 63.32) over years 21–22.
> - Losses compound: −22% and −30% make −45.4%, not −52%.
> - Gain needed = 1 ÷ (1 − loss) − 1: −10% needs +11.1%, −30% needs +42.9%, −50% needs +100%; the Tessaro crash needed +83.1%.
> - **Time under water**: 24 months down, 48 back, 72 in total in dollars; in real terms the peak returned only in year 31, 11 years later.
> - Count from the peak and say whether it's nominal or real.

> **Educational, not advice**
>
> This course explains how long-term investing works; it never tells you what to buy. Investments can fall, and you can get back less than you put in. Check the current rules where you live or ask a licensed professional.

**Grace:** Next: if a fall can last 11 years in real terms, how long does a user need to hold to be fairly safe from a loss? We'll count every window.

- Previous lesson: [Volatility and a typical bad year](https://productovi.com/courses/long-term-investing/volatility-bad-year.md)
- Next lesson: [Holding period and the chance of a loss](https://productovi.com/courses/long-term-investing/holding-period.md)

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