A small cap fund has Rs 3,000 crore in 60 stocks averaging Rs 6 crore of daily volume. If a quarter of the fund is redeemed in a month and it trades 20% of daily volume, how many days does a pro rata sale take, and who bears the cost if it sells the liquid names first?

On averages a pro rata sale takes about 10 days, but the least liquid tenth of the portfolio needs about 44 days, so the redemption cannot be met pro rata within a month. Selling the liquid names first meets it in about 19 days and cuts today's trading cost from Rs 7.8 crore to Rs 2.9 crore, but the investors who stay inherit a fund that is 33% thin stocks instead of 25%. They bear the deferred cost.

Start where the interviewer expects. The average holding is Rs 3,000 / 60 = Rs 50 crore, a quarter of it is Rs 12.5 crore, and 20% of Rs 6 crore of volume is Rs 1.2 crore a day. Rs 12.5 crore at Rs 1.2 crore a day is about 10.4 days, and the whole Rs 750 crore over the fund's total selling capacity of Rs 72 crore a day gives the same 10.4. That is the number a slide would show, and it is wrong in the way that matters.

A queue at a bank moves at the speed of the slowest counter if every customer must visit every counter. A pro rata sale is that queue: it is finished only when each stock has sold its quarter, so the slowest stock sets the time, not the average. Liquidity is skewed in small caps: here the most liquid group needs 5.8 days, but the thin group needs 16, the very thin 33 and the least liquid 44. 20 of the 60 stocks cannot be sold pro rata within the month without trading far more than 20% of their volume, which would move their prices against the fund.

The tempting fix is to meet the redemptions from the two liquid groups, selling 58% of each of those holdings. That finishes in about 19 days and costs about Rs 2.9 crore instead of Rs 7.8 crore, but the saving is borrowed from the investors who stay. The thin stocks, untouched, rise from 25% of the fund to 33% of the Rs 2,250 crore that remains, and the average cost of selling the remaining portfolio rises from 1.04% to 1.26% of its value. If redemptions continue, the next investors out face a fund that is harder and dearer to sell, and those who never leave carry the thin stocks into the next fall. Knowing that early leavers get the better deal is exactly what encourages a run.

Act before the redemptions, not during them. Size positions so that every holding can be sold pro rata within the redemption window the fund is prepared to face, which here means holding the thinnest names at well under half their current size or not at all. Keep a cash and large-cap buffer for the first wave, use any tools the rules allow for slowing large outflows, and report a pro rata days-to-liquidate figure, not an average. In India, small and mid cap funds now publish stress-test results showing how long it would take to sell a quarter and a half of the portfolio pro rata; confirm the current method, volume assumptions and disclosure rules before quoting them. Say the limitation too: volumes dry up in exactly the falls that trigger redemptions, so 20% of normal volume may be optimistic.