Portfolio Management puzzles, solved step by step

About 800 tonnes a year, on stated assumptions. Weddings: about 1 crore a year at 35 grams each is 350 tonnes. Festivals and gifting: 30 crore households, a quarter buying 4 grams, is 300 tonnes. Investment coins and bars: 5% of households buying 10 grams is 150 tonnes. The total is 800 tonnes. Check it against published industry demand figures before using it anywhere.

How do you start when you have no idea of the answer?

Ask when a family actually walks into a jeweller. It is not random: a wedding, Dhanteras or Akshaya Tritiya, a birth, or a decision to save in coins. Splitting a total into the occasions that drive it turns one number nobody knows into several that anyone can picture. State the base first: about 140 crore people at four to five per household is roughly 30 crore households. That figure and every weight below are assumptions for the estimate, said out loud so the interviewer can challenge them.

How do you sanity check it, and where is it weakest?

Divide back: 800 tonnes over 30 crore households is about 2.7 grams per household per year, a small coin's worth on average, which feels plausible given that most households buy nothing in a typical year and a few buy a lot at a wedding. The weakest input is grams per wedding, because the spread is huge and the average is dragged up by a few large weddings. Moving it by 10 grams moves the total by 100 tonnes. Say that, and say you would check the result against published demand data from the industry before quoting it: an estimate is a structure plus assumptions, not a statistic.

On a multi-asset or wealth desk, the follow-up is usually why it matters: household gold is a large part of Indian savings, so its demand affects imports, the rupee and how much money is left for financial assets.

Roughly 12 crore 5G phones a year, on stated assumptions. Take about 60 crore smartphone users out of 140 crore people. If they replace their phone every 4 years, that is 15 crore replacements, plus about 1 crore first-time buyers, so 16 crore phones. If three quarters of new phones sold are 5G, the answer is about 12 crore. A household check, one phone every two years across 30 crore households, gives 15 crore, close enough.

Why start from users and replacement, not from the population?

Think of how many school shoes a town buys in a year. The number of children matters, but the answer is set by how often each child outgrows a pair. In a market where most people already own the product, yearly sales are the user base divided by the replacement cycle, plus a smaller flow of first-time buyers. Population only tells you the ceiling; the cycle turns the stock of users into a yearly flow.

Which assumptions should you say out loud, and how do you check them?

Every number here is an assumption to be stated, not a fact to be quoted: the user base, the cycle, the first-time flow and the 5G share. The replacement cycle deserves the most care because a one-year change in it swings the answer by between a fifth and a third; the population barely matters by comparison. A three-year cycle gives 15.75 crore and a five-year cycle 9.75 crore. The 5G share is the other moving part, because it changes fast from one year to the next; ask which year the interviewer means.

Then check from a different direction. With about 30 crore households, one new phone per household every two years gives 15 crore phones, close to the 16 crore from the user build. Two methods that land near each other are more convincing than one precise-looking number. For a real estimate, replace every assumption with published industry shipment data and confirm the current figures.

If the interviewer wants value rather than units, multiply by an assumed average selling price and say that 5G phones are skewed to the middle and upper price bands, so the price assumption needs as much care as the cycle.

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.

About 1,200 a year, within a range of roughly 1,000 to 1,500. Size the fleet first: about 100,000 flights a day, three quarters on narrow-bodies, at five flights per jet a day, needs about 15,000 jets. Yearly demand is replacement plus growth: 15,000 over a 25-year life is 600, and 4% growth adds 600. Every input is an assumption to state and then check against published fleet data.

Where do you start with a plane that lasts 25 years?

Think of refrigerators in a city. Almost every home has one, but the shops sell only the ones that break down plus the ones new homes need. For a long-lived asset, yearly sales are a small flow out of a large stock: the stock divided by its life, plus the stock times its growth rate. So the job splits into two parts. Size the fleet from how the planes are used, then turn the fleet into a yearly flow.

How do you size the fleet without knowing it?

From usage, which is easier to guess. Take about 100,000 commercial flights a day worldwide, a round number to state as an assumption. Most flights are short and medium routes, so put three quarters on narrow-bodies: 75,000. A narrow-body on short routes flies several sectors a day; call it five. That needs 15,000 jets. Each assumption is a round number said out loud, so the interviewer can challenge one without losing the structure.

Now sanity-check. 1,200 deliveries is about 8% of the fleet, which sounds right for an asset that lasts decades. If the question asks about one maker, split by an assumed market share; two main makers sharing the market would each deliver around 600. For an asset manager the useful point is the sensitivity: deliveries swing with the growth assumption far more than the fleet does, which is why aircraft makers' order books are so cyclical. Treat every number here as an assumption to check against published fleet and delivery data before using it.

Roughly 40 lakh new cars a year, built from stated assumptions. About 30 crore households, 8% owning a car, gives about 2.4 crore cars. Ownership rising half a point a year adds 15 lakh first-time buyers; a 12-year life means 20 lakh replacements; fleets and second cars add about 5 lakh. Then compare with published industry sales data.

How do you turn a stock of cars into yearly sales?

A school's intake each year is not its total strength; it is the students leaving that year plus any growth in the roll. New car sales work the same way: they are the growth in the number of cars owned plus the cars being replaced, so the answer needs a stock and two flows. Say this structure first; the interviewer is scoring the tree more than the final number.

Which assumption would you defend first, and which would you flag?

Take the population as roughly 140 crore and confirm the current figure; at about 4.7 people per household that is 30 crore households. The 8% ownership share is the number to flag, because ownership is concentrated in cities and in the top income bands. Replacement is the largest flow, so the assumed 12-year life matters most: at 10 years replacements rise to 24 lakh, at 15 they fall to 16.

Finish by naming what you would check. Industry bodies publish domestic sales every month, and an interviewer at a fund expects you to know the order of magnitude. If your estimate is far off, say which branch you would revisit rather than adjusting the total to fit.