Drawdowns and the math of getting back

A drawdown is how far your account has fallen from its last high. Every trader has them, including traders with a real edge. What matters is how deep they get, because the math of getting back is not even.

This is one of the quiet reasons most people who day trade lose money. A few large losses dig a hole that takes much longer to climb out of than it took to fall in.

The recovery math

When you lose a percent of your account, you need a larger percent to get back. That's because the gain is measured on a smaller balance.

• Lose 10%, and you need an 11.1% gain to get back to even.
• Lose 20%, and you need a 25% gain.
• Lose 30%, and you need about a 42.9% gain.
• Lose 50%, and you need a 100% gain. You have to double what is left.

Here it is in dollars. A $10,000 account that drops 20% is at $8,000. A 20% gain on $8,000 only gets you to $9,600. You need $2,000 more, which is 25% of $8,000. The formula is the loss divided by what remains.

Small drawdowns are easy to recover from. Deep ones are not. This is why risk per trade and a daily loss limit matter so much. They keep you in the shallow part of the table.

Losing streaks are normal

Even a sound setup will hand you strings of losses. It helps to know how often that happens before it happens to you.

Take a setup that wins half the time. The chance that any five trades in a row, starting at a given trade, are all losers is 1/2 × 1/2 × 1/2 × 1/2 × 1/2. That is 1 in 32, or about 3.1%. That sounds rare.

But you don't take five trades. You take hundreds. Over 100 trades at a 50% win rate, the chance of at least one streak of five or more losses is about 81%. Even with a 60% win rate, the chance over 100 trades is about 46%. I worked these out with a short program, and the point is simple. Over enough trades, a long losing streak is not bad luck. It is expected.

So plan for it. If you risk $50 a trade, five losses in a row is $250 plus costs. Ask yourself now whether you could take that and still follow your rules on trade six. If not, your size is too large.

Trailing drawdown, briefly

Many prop firm accounts use a trailing drawdown. Instead of a fixed floor, the maximum loss level moves up as your account makes new highs. If your balance rises, the floor rises with it. Depending on the firm, it may track your closing balance or your open profit during trades.

This means you can be "up" on the account and still be close to failing it. Each firm defines its rule in its own way, so read the details before you trade one. Prop Firm Duel (my own site) lays out how firms set these rules side by side.

The takeaway

Losses take bigger gains to recover: 10% needs 11.1%, 20% needs 25%, and 50% needs 100%. Losing streaks are close to certain over many trades, so size for them in advance. If you trade an account with a trailing drawdown, know exactly how the floor moves.

Do this today

• Work out your current drawdown from your account's highest balance.
• Multiply your risk per trade by five to see the cost of a normal losing streak.
• Decide whether that streak would change how you trade, and size down if it would.
• If you use an account with a trailing drawdown, write down exactly how its floor moves.

Check yourself

Answer each one in your head, then open it to check.