# Drawdown: why losses hit harder than gains

> A 50% loss needs a 100% gain to recover: see drawdown, the recovery maths and how the same trades at a bigger size can sink an account that should have grown.

- Course: [Trading Basics: How It Works, How Not to Lose Everything](https://productovi.com/courses/trading.md)
- Module: Can I lose often and still come out ahead?
- Lesson 15/32, ~27 min
- Source: https://productovi.com/courses/trading/drawdown-and-ruin

## Down 50%, up 50%

**Alex Tutor:** Back on your Pebble practice account, a quick puzzle first. Your account falls 50%, then rises 50%. Where are you?

**Nora:** Back at the start, obviously.

**Sofia:** 10,000 minus half is 5,000. Plus half of 5,000 is 7,500. Still down a quarter.

**Alex Tutor:** Right. After a loss, every gain is measured on a smaller base. That's why a fall from the account's highest point, a **drawdown**, is the number to watch. It measures the pain you actually live through.

**Marc:** Every Friday I write down two numbers: the highest my account has ever been, and how far below that it is now. That difference is my drawdown.

**Alex Tutor:** Try it on a smaller fall first. Where is the peak, and how far below it is the account?

> **Exercise:** A Pebble practice account grows to a peak of 12,000, then a bad stretch takes it to 10,200. What is the drawdown, in percent?

![Marc walks a gentle path of small stepping stones while Nora stands on a tall wobbly stack of stones on the rim of a deep valley with a long climb back up; Alex watches with a phone.](https://productovi.com/courses/trading/diagrams/m4-l3-scene.png)

$$
\text{gain needed to recover} = \frac{\text{loss}}{1 - \text{loss}}
$$

*Loss and gain as fractions of the account, e.g. 0.5 / (1 − 0.5) = 1, so 100%*

> **Exercise:** An account falls 50% from its peak. What gain, in percent, does it need to get back to the peak?

**Marc:** Small drawdowns are cheap to fix: a 10% loss needs about 11%. Big ones get expensive fast.

**Nora:** How fast?

**Alex Tutor:** Fill in the table.

> **Exercise:** Match each drawdown with the gain needed to recover it.

## Same trades, two sizes

**Alex Tutor:** Now a real sequence: 40 trades from one plan. Each win makes 2 times the risk, each loss costs 1 times the risk. 15 wins and 25 losses: on average +0.125 of the risk per trade. A positive plan.

**Alex Tutor:** We run it twice on 10,000: once risking 1% of the account per trade, once risking 25%, Nora-style.

**Dataset (CSV):** [One sequence of 40 trades at 1% and at 25% risk](https://productovi.com/datasets/trading/drawdown-and-ruin/m4_equity_two_sizes.csv)

result_units: results in risk units (one risk unit = the planned risk of a trade); +2 means the trade made twice its risk, −1 means it lost its risk. Each trade risks that part of the account at the moment.

**The same trades at two sizes**

| Trade | 1% risk per trade | 25% risk per trade |
| --- | --- | --- |
| 0 | 10000 | 10000 |
| 1 | 10200 | 15000 |
| 2 | 10098 | 11250 |
| 3 | 10299.96 | 16875 |
| 4 | 10196.96 | 12656.25 |
| 5 | 10094.99 | 9492.19 |
| 6 | 10296.89 | 14238.29 |
| 7 | 10193.92 | 10678.72 |
| 8 | 10091.98 | 8009.04 |
| 9 | 9991.06 | 6006.78 |
| 10 | 9891.15 | 4505.09 |
| 11 | 9792.24 | 3378.82 |
| 12 | 9694.32 | 2534.12 |
| 13 | 9597.38 | 1900.59 |
| 14 | 9789.33 | 2850.89 |
| 15 | 9985.12 | 4276.34 |
| 16 | 9885.27 | 3207.26 |
| 17 | 10082.98 | 4810.89 |
| 18 | 9982.15 | 3608.17 |
| 19 | 9882.33 | 2706.13 |
| 20 | 10079.98 | 4059.2 |
| 21 | 9979.18 | 3044.4 |
| 22 | 10178.76 | 4566.6 |
| 23 | 10076.97 | 3424.95 |
| 24 | 9976.2 | 2568.71 |
| 25 | 10175.72 | 3853.07 |
| 26 | 10379.23 | 5779.61 |
| 27 | 10275.44 | 4334.71 |
| 28 | 10172.69 | 3251.03 |
| 29 | 10376.14 | 4876.55 |
| 30 | 10272.38 | 3657.41 |
| 31 | 10169.66 | 2743.06 |
| 32 | 10373.05 | 4114.59 |
| 33 | 10269.32 | 3085.94 |
| 34 | 10474.71 | 4628.91 |
| 35 | 10369.96 | 3471.68 |
| 36 | 10266.26 | 2603.76 |
| 37 | 10471.59 | 3905.64 |
| 38 | 10366.87 | 2929.23 |
| 39 | 10574.21 | 4393.85 |
| 40 | 10468.47 | 3295.39 |

**Nora:** Look at the start! At 25% I'm at 16,875 after three trades. That's my kind of plan.

**Sofia:** So the 25% line is the same trades, just louder.

**Alex Tutor:** Louder both ways: the wins look heroic, and the losses are brutal. Look at trades 7 to 13: seven losses in a row. At 1% the account dips from 10,299.96 to 9,597.38. At 25% it falls from 16,875.00 to 1,900.59.

> **Exercise:** At 25% risk the account fell from a peak of 16,875.00 to 1,900.59. What was the drawdown, in percent? One decimal.

**Nora:** Ten trades ago I was a genius.

**Sofia:** And at the end of all 40 trades?

**Alex Tutor:** At 1%: 10,468.47, up 4.7%. At 25%: 3,295.39, down 67%. Same trades, same positive average. The only difference is the size.

> **Exercise:** Why did the 25% version lose money with the same trades that made money at 1%?

## Risk of ruin

**Alex Tutor:** That's **risk of ruin**: the chance that a losing run takes the account so low that it can't realistically recover, or that you give up. It grows fast with size. Ruin doesn't need zero: most people quit long before the account gets there.

**Marc:** And seven losses in a row isn't rare. In this sequence it happened once in 40 trades, with a plan that's positive on average.

**Alex Tutor:** Quick check before the numbers: when does ruin actually begin?

> **Exercise:** Risk of ruin only matters when an account can fall to exactly zero.

**Alex Tutor:** There's no magic safe number, but the pattern is clear. Halve the risk and a losing run costs roughly half as much, while the gain needed to recover shrinks even faster.

**Alex Tutor:** Put numbers on it. Take one seven-loss run and change only the risk per trade.

> **Exercise:** A plan risks 2% of the account at that moment on each trade and hits seven losses in a row. What is the drawdown after the run, in percent? One decimal.

**Nora:** So oversizing can kill a good plan.

**Alex Tutor:** Yes. A good plan at a reckless size is a bad plan. A small risk per trade keeps drawdowns shallow, where recovery is still ordinary arithmetic.

> **Exercise:** If a plan's average result per trade is positive, it will make money at any position size.

**Marc:** My rule: if my drawdown reaches 10%, I halve my risk per trade and review the journal.

**Nora:** And mine was "double up to win it back".

**Alex Tutor:** The chart shows where that one leads.

> **Exercise:** Nora says: "I'm down 40%. I'll just make 40% back and I'm fine." In 2–3 sentences, explain the maths she's missing and what her size has to do with it.

**Alex Tutor:** Protect the base first. Gains can only grow whatever is left of the account.

> **Key ideas**
>
> - A **drawdown** is the fall from the account's highest point, in percent of that point.
> - The gain needed to recover is **loss ÷ (1 − loss)**: 10% → 11.1%, 20% → 25%, 50% → 100%, 75% → 300%, 90% → 900%.
> - The same 40 trades (+0.125 risk units on average) ended at **+4.7% at 1%** and **−67% at 25%** risk; worst drawdowns 6.8% and 88.7%.
> - **Risk of ruin** grows fast with size. A good plan at a reckless size is a bad plan.

> **Educational, not advice**
>
> This course explains how trading works; it never tells you what to buy or sell. The sequence here is made up to show the arithmetic. Most people who trade lose money, and you can lose all of it. For taxes and rules, check with a licensed professional where you live.

- Previous lesson: [Expectancy: the average trade](https://productovi.com/courses/trading/expectancy.md)
- Next lesson: [Case: compare two trade lists](https://productovi.com/courses/trading/compare-two-trade-lists.md)

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