Sizing under a drawdown limit
Every fund has a loss at which its capital gets cut. Work back from it to the most the book can run, and see why a loss shrinks the book.
- Size a book's maximum gross exposure from a drawdown limit
- Work out the gain needed to recover from a drawdown
- Back out the stress a book is sized for today
- Show how much smaller a book must be after a loss
The intuition
A climber has 20 meters of rope before the ledge they must not fall past, and any move can slip a certain distance. With 20 meters of slack they can make big moves. After slipping 8 meters only 12 are left, and every move has to be smaller, just when they most want to make up ground.
A hedge fund's drawdown limit is that ledge: the loss from its high point at which its capital gets cut. The cushion is the room left. The risk desk sizes the book so that a bad week, a stated number of standard deviations hitting every position at once, cannot use up the cushion.
Cushion = drawdown limit − drawdown so far. Weekly volatility = annual volatility ÷ √52. Stress loss per dollar of gross = weekly volatility × stress multiple. Maximum gross = cushion ÷ stress loss per dollar. Gain needed to recover a drawdown d = d ÷ (1 − d).
Why it works
- The conventions here: the stress is a stated number of one-week standard deviations (annual volatility ÷ √52) hitting every position at once, the worst case. Gross exposure and the cushion are shares of NAV.
- A drawdown limit is the real limit. Volatility is a forecast; a drawdown is a loss that happened, and it is what investors, prime brokers and platforms act on.
- After a loss the book must shrink. The cushion is smaller, so the same stress allows less gross, just when the manager wants to press.
- Losses need bigger gains to recover: 10% down needs 11.1% up; 50% down needs 100% up.
- Back out the stress a book is sized for to see how close to the edge it runs: fewer than two standard deviations means an ordinary bad week could reach the limit.
- Platforms accept the cost. Cutting after a loss sometimes sells at the bottom; it also stops a manager doubling down and taking the fund with them.
| Cushion: 15% − 5% | 10% of NAV |
| Weekly volatility: 25% ÷ √52 | 3.47% |
| Stress loss per dollar of gross: 3.47% × 2.5 | 8.67% |
| Maximum gross: 10% ÷ 8.67% | 1.15x NAV, or $1,154M |
| If flat on the year: 15% ÷ 8.67% | 1.73x NAV |
| Gain to recover the 5%: 5% ÷ 95% | 5.26% |
Running 2.0x gross, the book is sized for only 10% ÷ (2.0 × 3.47%) = 1.44 standard deviations: an ordinary bad week could reach the limit.
The formulas
The room left.
Volatility scales with the square root of time.
Every position hit at once.
The most the cushion allows.
The gain is earned on a smaller base.
Run it backwards.
Worked example
The cushion first, then weekly volatility, then the stress loss on each dollar of gross. Divide the cushion by it.
See it move
Same fund. Change the drawdown limit, the loss so far, the positions' volatility, the stress the desk sizes for and the gross the fund runs today.
- Raise the loss so far. The cushion and the maximum gross shrink and the gain needed to recover grows; the flat-year maximum does not move.
- Raise the volatility. The maximum gross falls, and today's book is sized for fewer standard deviations.
- Raise the stress multiple. The maximum gross falls; the standard deviations today's book is sized for do not change.
- Raise today's gross. The book is sized for fewer standard deviations and there is more to cut.
Run it backwards
Same fund, reversed: given the gross it runs today, how big a one-week move, in standard deviations, would take it to the limit?
One weekly standard deviation across the whole book costs gross × weekly volatility. Divide the cushion by that.
Three or more is a comfortable margin; fewer than two means an ordinary bad week could reach the limit, and the desk will want gross cut.
Traps
Say it in the interview
“Your fund is down 8% with a 15% drawdown limit. How does that change how you run the book?”
Check yourself
4 fresh questions, with new numbers. Answer each one correctly to finish the chapter. Get one wrong and you will see the full working, then you can try it again with new numbers.
Answers within 1% are marked right. Type the number; $, %, x and M are fine. First tries count toward Learned: the topic is Learned once every chapter is done and 75% of first tries were right.
- Cushion = limit − drawdown so far.
- Maximum gross = cushion ÷ (weekly volatility × stress).
- Gain to recover = d ÷ (1 − d).
- After a loss, the book must shrink.