Hedge Funds puzzles, solved step by step

About 25 trading days, roughly five weeks. The market trades 0.2% of the shares a day and you take at most a fifth of that, so you can sell 0.04% of the company a day. A 1% stake divided by 0.04% a day is 25 days. In the desk's language the position is five days of volume, and exiting it without moving the price takes a month.

What is the one division that answers it?

Emptying a water tank through a tap that you are only allowed to open a fifth of the way: how long it takes is the tank size divided by the flow you actually use. Days to exit equals position size divided by your daily selling capacity, and capacity is market volume times your participation cap. Here that is 1% over (0.2% x 20%), or 1% over 0.04%: 25 days. Keeping everything in percent of shares means you never need the share count or the price.

Why does a portfolio manager care about this number?

Because the price can move a long way in 25 days. A position you cannot exit quickly carries more risk than its daily volatility suggests: if the stock falls 2% a day for a week, you have sold only a fifth of it. That is why many desks cap a position at a set number of days of volume, often a few days, and why liquidity sits beside volatility in position sizing. The measure has a name, days to liquidatePosition size divided by the volume you can realistically trade in a day; a common liquidity limit on hedge fund books., and interviewers like hearing it.

Say the limitations. Volume is not steady; it dries up exactly when you most want to sell, and in a sell-off everyone is trying to do the same thing. A 20% participation rate also moves the price against you, so the real exit costs more than the screen price. A stronger answer adds that you would stress the calculation with half the normal volume, which gives 50 days.

40%. Measure everything in units of the average loss. Each trade wins 1.5 units with probability p and loses 1 unit otherwise, so the expected result per trade is 1.5p minus (1 - p). Setting that to zero gives p = 1/2.5 = 40%. At a 45% hit rate the book makes 0.125 units a trade, so a trader who is wrong more often than right can still run a good business.

Why is a hit rate below 50% not a problem on its own?

A street vendor selling umbrellas can stand idle most days and still do well, because the rainy days pay for the dry ones. What decides whether a trading book makes money is the hit rate times the size of the wins against the miss rate times the size of the losses, not the hit rate alone. A win-loss ratio of 1.5 moves the breakeven from 50% down to 40%.

What does the general rule look like?

For a win-loss ratio R the breakeven hit rate is 1 over (1 + R). At R = 1 it is 50%, at R = 1.5 it is 40%, at R = 2 it is 33% and at R = 3 it is 25%. This is why portfolio managers are reviewed on both numbers together. A falling hit rate is fine if the winners are running further, and a rising hit rate is a warning sign if it comes from cutting winners early and letting losers run.

What would you add before calling 45% a good business?

Costs and sample size. Commission, slippage and financing come off every trade, winners and losers alike, so they raise the breakeven. If costs run at 0.05 units a trade, the book needs 1.5p - (1 - p) = 0.05, a hit rate of 42%. And a ratio of 1.5 measured over twenty trades is noisy; say you would want a longer record before trusting either number.

About Rs 12,500 crore. Each stock allows 5% of Rs 50 crore, Rs 2.5 crore a day. Across 200 stocks that is Rs 500 crore a day, and across 250 days Rs 1,25,000 crore a year. A book turned over 10 times a year needs 10 rupees of trading for every rupee of capital, so the book can be Rs 1,25,000 crore divided by 10. Treat it as a ceiling, not a working size.

What does capacity actually mean?

Picture a juice stall that can squeeze 500 glasses a day. How many regular customers can it serve? That depends on how often each one comes. If every regular drinks a glass a day, 500; if each comes once in ten days, 5,000. A strategy's capacity is the capital it can run before its own trading exceeds what the market will absorb, so it is tradable volume divided by how often the book must be traded.

How do you build the number out loud in the room?

Go one multiplication at a time and say each one. 5% of Rs 50 crore is Rs 2.5 crore per stock per day. Two hundred stocks make Rs 500 crore a day. Two hundred and fifty days make Rs 1,25,000 crore a year. Dividing by a turnover of 10 gives Rs 12,500 crore, and the step people drop is the last one: capacity is not a day's or a year's volume.

Why is turnover the lever that matters most?

Every input enters in proportion, but the market and the risk team set the others, while the strategy itself sets its turnover, and turnover varies far more across strategies. A strategy that turns over 50 times a year has a capacity of Rs 2,500 crore on this universe; one that turns over twice a year has Rs 62,500 crore. That is why fast strategies close to new money early and slow ones can run large books.

Why is the real capacity lower than this ceiling?

The estimate assumes the strategy trades evenly every day and in every stock. It does not. Trades cluster when signals fire, which is often when others trade too, and the thinner names in the list hit the 5% limit long before the larger ones. The definition of turnover matters as well: if 10 times means buying 10 times the book and also selling it 10 times, the traded value doubles and capacity halves to Rs 6,250 crore. Say which definition you used, and add that trading costs rise before the hard limit, so returns fade well before the ceiling.