Unwinding a Position Before the Close

The scenario: it's 3:00 PM, the market closes at 4:00 PM, and you need to sell a large position — say 100,000 shares — entirely before the close, with no ability to carry it overnight. How do you schedule the selling across the remaining hour? Dumping it all in the first minute risks heavy market impact; waiting until 3:58 risks running out of time to actually get filled, or crashing the price in the final minutes when there's less time for the market to absorb the order.

The default: spread it out, weighted by when liquidity is available

The simplest reasonable answer is a uniform schedule: sell the same number of shares in each equal time slice across the hour, so no single slice demands too much liquidity at once. A better answer accounts for the fact that trading volume isn't uniform across the day — most markets have more volume near the open and close than in the middle, so a schedule that sells a bit more when volume is naturally higher (closer to a volume-weighted schedule) generally achieves lower impact than a strictly uniform one, because you're trading in proportion to how much liquidity is actually available at each moment rather than assuming it's constant.

Worked example: uniform schedule with a simple impact check

100,000 shares to sell over 60 minutes. Under a uniform schedule, sell $100{,}000/60 \approx 1{,}667$ shares per minute. If typical one-minute volume in this name is 20,000 shares, your slice is about 8.3% of a minute's volume — generally a modest enough fraction that per-minute price impact stays small under most simple impact models, where impact roughly scales with (your size / market volume).

Now suppose you instead try to sell it all in the first 5 minutes: $100{,}000/5 = 20{,}000$ shares per minute — the same size as an entire typical minute's total volume, meaning you'd need to be essentially the only seller and buyer in the market simultaneously, which in practice means paying a much worse average price as you exhaust available liquidity at each price level and push through several ticks. Comparing the two: spreading over the full hour keeps each slice a manageable single-digit percentage of natural volume; compressing into 5 minutes pushes each slice to roughly 100% of natural volume, a qualitatively different (and much costlier) situation.

What this means in practice

This scenario is a compressed version of the optimal-execution problem trading desks solve formally (the Almgren-Chriss framework and its variants), but the interview version rewards recognizing the shape of the tradeoff without needing the full optimization: don't sell all at once (impact), don't wait until the very end (you may not get filled, and thin end-of-day liquidity can make a late rush even more damaging), and lean the schedule toward periods of naturally higher volume when they're available, such as the closing auction itself, which many venues use specifically to absorb large size at a single, transparent print.