Portfolio Management puzzles, solved step by step

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  1. 073Estimate how many individuals in India hold a direct equity portfolio worth more than Rs 50 lakh, the minimum ticket for a portfolio management service.Market sizing and estimationHardIndian wealth managementIndian asset management

    Try it first

    Which step decides the answer most?

    Show the worked solution

    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.

    From accounts to the tail: the skew of wealth decides the answerDemat accountsround assumption; confirm with depository data18 croreIndividuals, 1.5 accounts eachmany investors hold more than one12 croreHolding a meaningful portfolio, 40%many accounts are dormant or tiny4.8 croreAbove Rs 50 lakh, about 1 in 100set by how skewed wealth isabout 4.8 lakhCross-check: if 20% of holders have over Rs 5 lakh and the tail thins like a Pareto curve with exponent 1.0 to 1.3,the count above Rs 50 lakh is 4.8 to 9.6 lakh. Same order of magnitude: a few lakh people.
    About 18 crore demat accounts shrink to 12 crore individuals and 4.8 crore with meaningful portfolios, and only about 1 in 100 of those holds more than Rs 50 lakh, which is roughly 4.8 lakh people.

    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.

    The relationship
    N=181.5×0.40×0.01 crore=4.8 lakhN = \frac{18}{1.5} \times 0.40 \times 0.01 \text{ crore} = 4.8 \text{ lakh}
    18demat accounts, crore, a round assumption
    1.5accounts per individual
    0.40share holding a meaningful portfolio
    0.01share of those above Rs 50 lakh
    What it says in wordsAccounts to people, people to active holders, then the thin top slice above the threshold.

    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.

    Where candidates lose it

    The trap is quoting the demat account count, or some large share of it, as the answer. It confuses accounts with people and the whole distribution with its top slice, and it lands a hundred times too high.

    The second loss is presenting assumptions as facts. Say each number as a round assumption, show the skew check, and give a range, not a single figure said with false precision.

    What the interviewer asks next

    • How would the answer change if the threshold rose to Rs 1 crore?
    • What data would you use to test the 1 in 100 assumption?
    • Why might the addressable market for this service be larger than the count of direct equity holders?