How Long Does It Take to Climb Out of a Hole?

[Fairman]

How Long Does It Take to Climb Out of a Hole?

Scenario: a trader has a 20 percent drawdown. How long will it take to recover, at different monthly return rates?

A 20 percent loss requires a 25 percent gain to recover, since 0.8 times 1.25 is 1.

Months needed: the natural log of 1.25 divided by the natural log of one plus the monthly return. The natural log of 1.25 is 0.2231.

At 2 percent a month: ln(1.02) is 0.0198. 0.2231 divided by 0.0198 is about 11.3 months.

At 1 percent a month: ln(1.01) is 0.00995. 0.2231 divided by 0.00995 is about 22.4 months.

At 0.5 percent a month: ln(1.005) is 0.00499. 0.2231 divided by 0.00499 is about 44.7 months, almost four years.

So a trader earning a modest half percent a month needs nearly four years to repair a 20 percent drawdown, if no further drawdowns occur.

What does it mean? Drawdown control is worth more than return enhancement at modest levels. Avoiding one 20 percent loss is equivalent to earning an extra 25 percent.

It also shows the danger of chasing: trying to recover in two months requires 12 percent a month, which demands risk levels that cause further losses.

For your plan, set a drawdown limit that you could recover from within a year at your realistic return.

At 1 percent a month, a 10 percent drawdown needs a 11.1 percent gain, ln(1.111) divided by 0.00995, about 10.6 months.

Exercise: compute the recovery time for your own maximum acceptable drawdown.