Crowding and factor overlap
Two risks the volatility number hides: how long it takes to get out, and how much of the stock is really a factor bet.
- Calculate days to exit from trading volume and participation
- Find the largest position a days-to-exit limit allows
- Split a stock's variance into factor and idiosyncratic parts
- Say why crowded positions fall together
The intuition
A cinema empties calmly through one door when the film ends. Shout 'fire' and everyone heads for the same door at once. The door is the same size; what changed is how many people need it at the same moment. A stock many funds own is the crowded cinema: easy to sell on a normal day, hard when they all need to sell together.
Two numbers measure the danger. Days to exit: how many days of normal trading it takes to sell the position without being too big a share of the volume. And factor overlap: how much of the stock's movement is really a broad factor (the market, momentum, its sector), which every fund holding that factor will be selling at the same time.
Days to exit = position ÷ (value traded a day × participation). Factor share of variance = (beta × factor volatility)² ÷ stock volatility². Idiosyncratic volatility = √(stock volatility² − (beta × factor volatility)²).
Why it works
- The conventions here: the fund trades a fixed share of each day's volume (its participation) against average daily value traded. One factor; volatilities are annual.
- Participation is a trade-off. Being a bigger share of volume gets out faster but pushes the price further; a smaller share costs less but leaves the fund exposed for longer.
- Risk desks cap days to exit, so the largest position allowed is the limit × daily value traded × participation.
- Volatilities do not add; variances do. Factor variance plus idiosyncratic variance is the total, so square, subtract and take the square root.
- Idiosyncratic risk is what a stock picker is paid for. If most of the variance is the factor, the position is a factor bet dressed up as a stock pick.
- Crowding shows on the way out. When funds cut risk they sell what they all own, and crowded longs fall together whatever the fundamentals.
| Sellable a day: 40 × 20% | $8M |
| Days to exit: 60 ÷ 8 | 7.5 days |
| Largest position for a 5-day limit: 5 × 8 | $40M, so $20M over |
| Volatility from the factor: 1.2 × 20% | 24% |
| Factor share of variance: 24² ÷ 40² | 36% |
| Idiosyncratic volatility: √(40² − 24²) | 32% |
At 10% participation, days to exit double to 15. And 24% + 32% is not 40%, but 576 + 1,024 = 1,600 = 40².
The formulas
How many normal days it takes to get out.
Run it backwards.
How much of the stock's risk is the factor.
Subtract variances, not volatilities.
Worked example
Square the volatility that comes from the factor, compare it with the stock's total variance, and take the square root of what is left.
See it move
Same stock. Change the position, how much the stock trades each day, the share of volume the fund will be, and the desk's days-to-exit limit. New company and numbers changes the factor split.
- Raise the position. Days to exit rise; the largest position allowed does not move.
- Raise the value traded a day. Days to exit fall and the limit allows a bigger position.
- Raise the participation. Days to exit fall, though in a real market the fund's own selling would now move the price more.
- Raise the desk limit. The largest position allowed rises; days to exit do not change.
Run it backwards
Same stock, reversed: the desk caps days to exit. What is the largest position it allows?
Each day the fund can sell the value traded × its participation. Multiply by the number of days allowed.
The limit assumes normal volume. On the day the thesis breaks, volume may dry up and every holder may be selling, so a position at the limit is effectively over it.
Traps
Say it in the interview
“What risks does a stock position carry beyond its volatility?”
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.
- Days to exit = position ÷ (daily value traded × participation).
- Largest position = limit × daily value traded × participation.
- Factor share = (beta × factor volatility)² ÷ stock volatility².
- Variances add; volatilities do not.