Portfolio Management puzzles, solved step by step

Roughly Rs 6,000 crore a day, on stated assumptions. Assume about 2.5 lakh ATMs, each handling about 80 withdrawals a day: 2 crore withdrawals. Check from demand: 30 crore regular users withdrawing twice a month is 60 crore a month, also about 2 crore a day. At an average of Rs 3,000 a withdrawal, the total is about Rs 6,000 crore a day. Confirm against published payment statistics for a real figure.

Why build the count from the machines and from the people?

If you wanted to know how many cups of tea a railway station sells, you could count the stalls and ask how many cups each pours, or count the passengers and ask how many buy one. A supply-side estimate and a demand-side estimate rest on different assumptions, so when they land close together, each one checks the other. Here both roads meet at about 2 crore withdrawals a day, which is the number that matters; the rupee value is one multiplication away.

Which assumptions need the most care?

Every number here is an assumption to be stated, not a fact to be quoted. The average ticket size is the loosest input: Rs 2,000 against Rs 4,000 moves the answer from Rs 4,000 crore to Rs 8,000 crore a day, a factor of two. Withdrawals per machine vary widely, too, between a busy city branch and a rural machine, so treat 80 as an average across very different sites. The user count is the easiest to reason about from the number of adults with bank cards who still rely on cash.

Say what would change the answer over time. Growth in digital payments lowers withdrawal counts; festivals, salary days and month ends raise them sharply, so an average day hides large swings. Converting to a year, about 365 times the daily figure, is a useful sanity check against any published annual total the interviewer might mention.

For an asset management desk, the point is less the number than the method: a stock-and-flow structure, two independent builds, and a clear statement of which input you trust least. That is the same discipline as sizing a company's addressable market before building a revenue forecast.

Roughly 5 lakh people, within a range of about 3 to 10 lakh. Start from about 18 crore demat accounts, an assumption to confirm, and divide by 1.5 accounts per person: 12 crore individuals. Perhaps 40% hold a meaningful portfolio, 4.8 crore. Wealth is heavily skewed, so assume about 1 in 100 of those hold more than Rs 50 lakh: about 4.8 lakh. A Pareto-tail check gives the same order of magnitude.

Why is the headline account count a trap?

Think of a cricket academy with thousands of registered players. Asking how many could play first-class cricket is not a question about registrations; it is about the very top of the talent curve. Portfolio sizes are highly skewed, so the count above a high threshold is a small slice of the total, and the size of that slice, not the headline, decides the answer. Crores of accounts become a few lakh people above Rs 50 lakh.

How do you defend the 1 in 100?

With a second route. Suppose 20% of the 4.8 crore holders have more than Rs 5 lakh. Wealth tails often thin out like a Pareto distributionA skewed distribution in which the share above any level falls by a fixed power as the level rises, often used for wealth and city sizes.: raise the threshold tenfold and the share falls by a factor of 10 to about 20. Two independent routes landing in the same range is what turns a guess into an estimate. From Rs 5 lakh to Rs 50 lakh is a tenfold rise, so between 4.8 and 9.6 lakh people sit above Rs 50 lakh, which brackets the first answer.

Then say what the number is for, and what it misses. A portfolio management service can also be funded from bank deposits, mutual fund units or property sales, so the true addressable pool is wider than direct equity holders. The Rs 50 lakh minimum and every count used here are figures to confirm against current SEBI rules and depository data; the structure of the estimate is the part to trust.