Lesson 19 of 25 · 7 min
Fire sales, and the price impact of forced selling
What a sale costs is set by how fast it must happen, the one variable a forced seller cannot choose.
A forced sale and a chosen sale can be the same shares, in the same size, on the same day, and cost very different amounts. The difference is not the shares. It is the schedule.
Price impact grows with the fraction of normal daily volume a seller takes and with the asset's volatility, but less than proportionally — the widely used approximation is a square root, which captures the fact that spreading an order out helps but never becomes free.
impact = c x sigma x sqrt(Q / (n x ADV))
- impact
- The average shortfall against the starting price, as a decimal fraction.
- c
- A calibration constant for the market in question. Illustratively 0.80.
- sigma
- The asset's typical daily price move, as a decimal.
- Q
- The number of shares to be sold.
- n
- The number of trading days over which the sale is spread.
- ADV
- Average daily volume in the name, in shares.
Put numbers in. A holding of 186,000 shares in a name trading 240,000 shares a day, at 2.4 percent daily volatility and a constant of 0.80. Sold in one day, the square root of 186,000 over 240,000 is 0.8803 and the impact is 1.69 percent, which on a $4,650,000 position is $78,596.83. Spread over five days the ratio becomes 186,000 over 1,200,000, the square root is 0.3937, the impact is 0.76 percent, and the cost is $35,149.57. The $43,447.26 difference is the price of immediacy, and it is the whole of what forcing the sale costs.
A forced seller cannot buy those five days, because a cure window is measured in hours or days and the cheap schedule is measured in weeks. And the cost does not stop at the shares sold. The remaining pledged shares are marked at the new price, so selling part of a holding reduces the lending value of all of it — which is the bridge to the next lesson, because that mark applies to everyone holding the name and not only to the seller.
Key terms
- Price impact
- How far a seller pushes the price against itself by executing. Grows with size relative to normal volume and with volatility.
- Participation rate
- The share of a day's normal volume one order represents. The main determinant of impact, and the only one a seller can usually control.
- Immediacy
- Getting the whole trade done now rather than over days. It is a service with a price, and a forced seller is obliged to buy it.
Worked example
The same shares, two schedules
Illustrative figures. 186,000 shares at $25.00, average daily volume 240,000 shares, daily volatility 2.4 percent, constant 0.80.
- Participation if sold in one day
- 77.5% of a day
- Impact in one day
- 1.69%
- Cost on a $4,650,000 position
- $78,596.83
- Impact spread over five days
- 0.76%
- Cost over five days
- $35,149.57
- Price of immediacy
- $43,447.26
186,000 / 240,000.
0.80 x 0.024 x 0.8803.
0.80 x 0.024 x 0.3937.
The difference between the two schedules.
Forty-three thousand dollars separates the same sale executed under a deadline from the same sale executed without one.
Check yourself
A holding of 94,000 shares at $41.60 trades 310,000 shares a day at 1.9 percent daily volatility, with a constant of 0.80. What does the sale cost in one day, and over four?
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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.