Drawdown Mathematics Every Copier Should Know

A loss of ten percent needs a gain of about eleven percent to recover. A loss of twenty needs twenty-five. A loss of fifty needs a hundred. The arithmetic is not symmetric, and understanding it changes how a copier sets limits and reads the record of a strategist.

The recovery curve

The gain needed to recover a loss grows faster than the loss itself. Small drawdowns are cheap to recover; deep ones are expensive, and beyond a point they are practically permanent. A strategy that never falls more than fifteen percent can afford modest returns, while one that falls fifty percent needs spectacular ones just to get back to even.

Drawdown and leverage

A strategy with a maximum drawdown of twenty percent at its own risk level will show a drawdown of forty percent for a copier using a risk multiplier of two. The multiplier scales both gains and losses, and because of the recovery curve, it hurts more on the way down than it helps on the way up. Choosing a multiplier is choosing how deep the next drawdown will be.

Reading a published drawdown

The maximum drawdown in a record is the worst drop so far. Three adjustments make it useful:

• Assume the next one will be deeper. Records are finite and the worst case has usually not happened yet.
• Check how long it took to recover. A deep drawdown recovered in a month is a different experience from one that took a year.
• Look at the frequency of smaller drawdowns. Many moderate ones suggest a method that takes regular risk; one large one suggests a single bad decision.

Setting the stop-copy level

Decide the maximum loss you can accept on this copy. Divide by the published maximum drawdown to get the highest multiplier that keeps the published worst case inside your limit. Then reduce it further, because the next drawdown may be deeper. A common rule is to size so that the published worst case would lose about half of your limit, leaving the other half as margin for a worse one.

Deep drawdowns do not only cost money; they cause copiers to leave at the bottom, locking in the loss just before the recovery. A copy sized so that the worst case is tolerable is a copy that survives to see the recovery.

What to watch

Watch your multiplier against the published drawdown, the time the strategist took to recover from past drawdowns, and your own reaction during the current one. If you are checking the account several times a day, the size is too large.