Private Wealth Management puzzles, solved step by step
- Puzzles
- 100
- Traced to a firm
- 3
- Topics
- 13
- Hard
- 30
010Estimate the gold held by a typical urban middle-class Indian family, first in grams and then in rupees at an assumed price per gram.Indian wealth management
Try it first
Which starting point gives the most defensible estimate?
Show the worked solution
About 245 grams, or roughly Rs 24.5 lakh at an assumed Rs 10,000 a gram. Build it by person and occasion: the wife's wedding jewellery about 100 g, older jewellery from the husband's mother about 60 g, festival coins about 50 g, gifts for two children 20 g, and the husband's chain and ring 15 g. Convert to rupees only at the end, at the day's price.
Why estimate grams before rupees?
Ask someone how much their jewellery is worth and they will guess; ask how many bangles and chains they own and they can count. Estimate the physical quantity first, because grams can be pictured and defended, while the price is a separate, changing input you plug in at the end. It also means the estimate survives a change in the gold price: only the last line moves.
A household tally of wedding jewellery, older family jewellery, festival coins, children's gifts and the husband's chain adds to about 245 grams, which at an assumed Rs 10,000 a gram is about Rs 24.5 lakh. How do you sanity check a number like 245 grams?
Check it against the unit people use. Gold prices in India are quoted per 10 grams, so 245 grams is about 24.5 units. A sanity check that uses a different unit or a different route catches estimates that are off by a factor of ten. Then give a range: a family with a recent wedding might hold 400 grams, a young nuclear family nearer 100. Saying the range shows you know the average hides a wide spread.
Source of gold Assumption Grams Wife's wedding jewellery sets, bangles, chains 100 Mother's older jewellery handed down, still at home 60 Festival coins 5 g a year for 10 years 50 Children's gifts 2 children x 10 g 20 Husband's chain and ring worn daily 15 Household total 245 Every row is an assumption you say out loud; together they give about 245 grams for one urban middle-class household. Why does a wealth desk ask this? Because gold is the asset most Indian families hold outside any statement the adviser ever sees. A household balance sheet that leaves it out misses a sizeable share of what the family owns, and the Rs 10,000 price here is only an assumption to be replaced with the current rate.
Where candidates lose it
The common loss is jumping straight to a rupee figure, which sounds like a guess because it is one. It also ties the answer to a gold price the candidate is quoting from memory.
The second loss is giving one number with no range. A single estimate for a quantity that varies this much across families invites the question the candidate cannot answer: how sure are you?
What the interviewer asks next
- How would the estimate change for a family in a smaller town?
- Scale it up: roughly how much gold might the households of one city of 20 lakh families hold?
- Why does it matter for advice that most of this gold never appears on a statement?
036A 35-year-old earns Rs 30 lakh a year and supports a spouse and two young children. Using an income-replacement method, roughly how much life cover does he need?Indian wealth management
Try it first
Before you build it: which number does the cover start from?
Show the worked solution
About Rs 4.2 crore, roughly 14 times his income. After illustrative tax of 20% and his own spending of a quarter of take-home pay, the family loses Rs 18 lakh a year. Replacing that for 25 working years, rising 6% a year and invested at 8%, needs Rs 3.63 crore today. Add the Rs 40 lakh home loan and Rs 50 lakh for the children's education, subtract Rs 30 lakh of existing investments, and the cover is Rs 4.23 crore.
What exactly is the cover replacing?
If a family's shop closed tomorrow, the loss is not its gross sales but the profit that fed the household. Life cover replaces the income the family would stop receiving: his take-home pay, less the share he spent on himself, for the years he would have kept working. Then the lump sums the family would still owe, a home loan and the children's education, are added, and what is already saved is taken off.
The family loses Rs 18 lakh a year once tax and his own spending are removed; over 25 years, rising 6% and discounted at 8%, that stream is worth Rs 3.63 crore today. With the home loan and education added and existing investments subtracted, the cover comes to Rs 4.23 crore. The relationshipC the family's yearly need in today's rupees, Rs 18 lakh g the yearly rise in that need, 6% r what the lump sum earns while it is paid out, 8% n working years left, 25 What it says in wordsThe lump sum is every future year's need, grown by inflation and discounted back at what the money can earn.Which assumptions move the answer most?
The gap between the return and the growth of the need. With a 2-point gap each rupee of annual need costs about Rs 20.2 today; if the need did not grow at all, the same 25 years at 8% would cost only about Rs 11.5. That is why a cover built on a flat income understates the need by about 43%. The years to retirement and the share he spends on himself come next; tax and the loan matter less.
State the limits: the tax rate, inflation and return are illustrative, the method ignores his future salary growth beyond inflation, and a spouse's own income would reduce the need. The answer is a range around Rs 4 crore, not a precise figure, and a real plan checks it against the family's goals one by one.
Where candidates lose it
The common error is multiplying gross income by a rule-of-thumb multiple and stopping. It skips tax and his own consumption, ignores inflation, and forgets both the loan and the existing savings. The interviewer wants to see the build, not a multiple.
The second loss is discounting at 8% without growing the need, which quietly assumes the family's costs never rise. Say both rates out loud and show the gap between them is what drives the lump sum.
What the interviewer asks next
- How does the cover change if his spouse earns Rs 12 lakh a year?
- What happens to the answer at age 50 with the same income?
- Why might an adviser prefer term cover to an investment-linked policy for this client?
062Estimate the total monthly SIP inflow into mutual funds from a city of 50 lakh people. Build it from households, the share that invest through SIPs and the average SIP size.Mutual fund distributionIndian wealth management
Try it first
Before you build it: what is the first split you make?
Show the worked solution
About Rs 124 crore a month, on these assumptions. Fifty lakh people in households of four is 12.5 lakh households. If half of the top 20% run a SIP of about Rs 8,000, 15% of the middle 40% run Rs 3,000 and 2% of the rest run Rs 1,000, that is 2.1 lakh SIP households and about Rs 123.5 crore. Every input is an illustrative assumption, and the structure matters more than the figure.
Why segment before you multiply?
Estimating the sweets a wedding hall sells, you would not multiply every guest by the same number of laddoos: children, adults and the groom's uncles eat very differently. An average taken across the whole city hides the fact that a small, well-off slice contributes most of the SIP money. Split households into income bands, give each band its own share investing and its own ticket size, and the estimate becomes something you can defend line by line.
Fifty lakh people make 12.5 lakh households; on the illustrative assumptions, upper income households supply 1.25 lakh SIPs worth Rs 100 crore, middle income 75,000 worth Rs 22.5 crore and lower income 10,000 worth Rs 1 crore, about Rs 124 crore a month in total. Segment Households, lakh Share with a SIP Avg SIP, Rs Rs crore a month Upper income 2.5 50% 8,000 100.0 Middle income 5.0 15% 3,000 22.5 Lower income 5.0 2% 1,000 1.0 Total 12.5 16.8% 5,881 123.5 Every share and ticket size is an illustrative assumption, not a reported figure. Upper income households contribute about 81% of the flow, which is why that row deserves the most care. How do you check the answer is sane?
Test it two ways. Per SIP household the average works out to about Rs 5,881 a month, which should look plausible against what families in those bands earn. Per resident it is about Rs 247 a month. A sizing answer is judged on whether each assumption is stated and each check is run, not on hitting a number the interviewer has in mind. If you know an official total for SIP flows, compare your city's share with its share of the country's income, and say which assumption you would move if the two disagree.
Then name the sensitive line. Upper income households supply about 81% of the total, so a change in their share investing or ticket size moves the answer far more than anything in the lower bands. That is where you would spend a real week of research.
Where candidates lose it
The common loss is a single chain: 50 lakh people times some percentage times some average. It produces a number with no way to defend it, and the interviewer's first follow-up breaks it.
The second is presenting assumptions as facts. Say each one is an assumption, give the check, and name the line that moves the answer most.
What the interviewer asks next
- How would your estimate change for a city of the same size but with a younger, salaried population?
- What single piece of data would you ask for to tighten the estimate most?
- How would you estimate the number of mutual fund distributors this city can support?
074Assume, as an illustration and not a reported figure, that portfolio management services manage Rs 4 lakh crore. Using stated fee rates for each type of strategy, estimate the annual fee pool and the share of it paid as performance fees.Wealth management
Try it first
Before the arithmetic: what drives the size of a fee pool?
Show the worked solution
About Rs 6,840 crore a year, with about 21% from performance fees, on these assumptions. Fixed fees of 2% on Rs 1.6 lakh crore, 1% on Rs 1.6 lakh crore and 0.75% on Rs 0.8 lakh crore give Rs 5,400 crore. A 15% share of returns above a 10% hurdle, in a 16% year, adds Rs 1,440 crore. That is a 1.71% blended rate, and the performance part can vanish in a weak year.
How do you structure a fee pool estimate?
A toll road's yearly takings are traffic times toll, lane by lane, because trucks and cars pay different rates. A fee pool is the asset base times the fee rate, computed separately for each strategy because each charges differently, then added. Here the assumptions split Rs 4 lakh crore into 40% fixed-fee equity, 40% equity charging a lower fixed fee plus a performance feeA share of the return above an agreed hurdle rate, paid to the manager only when that hurdle is beaten, usually subject to a high-water mark., and 20% debt and multi-asset strategies. Every share and rate is an illustrative assumption.
On an assumed Rs 4 lakh crore, fixed fees contribute Rs 5,400 crore and performance fees Rs 1,440 crore in a 16% year, a pool of Rs 6,840 crore or 1.71% of assets, with 21% of it depending on beating the hurdle. Strategy Assets, Rs crore Fixed rate Fixed fee, Rs crore Performance fee, Rs crore Equity, fixed fee only 160,000 2% 3,200 0 Equity, fixed plus performance 160,000 1% 1,600 1,440 Debt and multi-asset 80,000 0.75% 600 0 Total 400,000 1.35% 5,400 1,440 All asset splits and fee rates are illustrative assumptions. The performance fee assumes the hybrid equity strategies earn 16% before fees against a 10% hurdle, so 15% of the 6 point excess is 0.9% of their assets. Why does the performance share matter to the business?
Because it is the unstable part. Fixed fees fall only as far as assets fall; performance fees can drop to zero in a single year below the hurdle. In that year the pool shrinks from Rs 6,840 crore to Rs 5,400 crore, a blended rate of 1.35%, and a high-water markA rule that no performance fee is paid until the portfolio value climbs back above its previous peak. can keep it at zero for several years after a fall. Say that sentence and you have shown you understand the economics, not just the multiplication. Fee structures and caps are set by regulation; confirm the current rules before quoting real ones.
Where candidates lose it
The trap is multiplying the whole Rs 4 lakh crore by one headline fee, often the highest one, which overstates the pool and hides the mix. Segment first.
The second miss is treating performance fees as a steady stream. The interviewer wants to hear that they depend on beating a hurdle and can disappear in a bad year.
What the interviewer asks next
- What happens to the pool if assets fall 20% and returns miss the hurdle in the same year?
- How would a shift of assets from fixed-fee to hybrid strategies change the pool in a good year and a bad year?
- Why might a manager prefer a fixed fee even at a lower headline rate?
086Estimate the annual market, in rupees, for will-drafting services across India's ten largest cities.Trust and estate administration
Try it first
Which step in this estimate deserves the most scrutiny?
Show the worked solution
Roughly Rs 210 crore a year, on stated assumptions. Take 10 crore people, 2.5 crore households at four each, 40% with property or savings worth protecting, and two adults each: 2 crore people who need a will. If 15% ever write one over a 30-year window, that is 1 lakh wills a year, at a blended Rs 21,000 each.
How do you structure the estimate before any number?
Think of estimating how many cakes a bakery sells for birthdays: you would go from people, to birthdays a year, to the share celebrated with a bought cake, to the price. A market size is a chain of counts and rates, and saying the chain out loud before any number is most of the marks. Here the chain runs from people, to households with something to leave, to adults who need a will, to how many write one each year, to the fee.
Ten crore people become 2 crore adults who need a will, 1 lakh of whom write one each year at an average Rs 21,000, a market of about Rs 210 crore, and the 15% will-making rate is the step that moves it most. Every number in the tree is an assumption to state, not a fact: the population of the ten cities, the household size and the 40% share should be replaced with census and survey figures when you have them. The fee split reflects two very different products: a simple will drafted online or by a local lawyer, and a complex will or estate plan prepared alongside a private wealth adviser.
Which step would you defend least, and what does that tell you?
The 15% lifetime rate of writing a formal will. The estimate is only as good as its least defensible step, so name that step and show what happens when it moves. At 30% the market doubles to Rs 420 crore; at 7.5% it halves. The interviewer will usually push on the weak step, so get there first.
The relationship2 crore adults in households with something to protect 15% / 30 the share who ever write a will, spread over a 30-year window Rs 21,000 the blended fee, 80% simple and 20% complex wills What it says in wordsWills written each year times the average fee gives the yearly market.Close with a sense check from the other side: 1 lakh wills a year across ten cities is about 40 wills a working day in each city, which feels plausible for the number of lawyers and advisers who offer the service.
Where candidates lose it
The common loss is diving into numbers with no structure, so each figure arrives from nowhere and the interviewer cannot follow or challenge it. Say the chain first.
The second loss is defending every assumption equally. Name the will-making rate as the weak step, show the range, and the answer becomes a judgement rather than a guess.
What the interviewer asks next
- How would you size the market for estate planning for families above Rs 25 crore?
- What data would you use to replace the 15% assumption?
- How does a rise in online will services change the fee mix and the market?