Private Wealth Management puzzles, solved step by step
- Puzzles
- 100
- Traced to a firm
- 3
- Topics
- 13
- Hard
- 30
025A private bank charges 1% a year on the first Rs 10 crore of a client's assets, 0.6% on the next Rs 20 crore and 0.4% on everything above Rs 30 crore. What is the blended fee rate on a Rs 45 crore client?Private banking
Try it first
Pick the blended rate on Rs 45 crore.
Show the worked solution
About 0.62%. Each slice pays its own rate: 1% on the first Rs 10 crore is Rs 10 lakh, 0.6% on the next Rs 20 crore is Rs 12 lakh, and 0.4% on the last Rs 15 crore is Rs 6 lakh. The total is Rs 28 lakh, and Rs 28 lakh divided by Rs 45 crore is 0.622%. The blend falls as the client grows but never reaches 0.4%.
Why is the answer not 0.4%?
Income tax slabs work the same way. Someone whose income crosses into a higher slab pays the higher rate only on the part above the threshold, not on the whole income. A tiered fee charges each slice of assets at its own rate, so the top rate applies only to the top slice and the blended rate sits between the highest and lowest tiers. The first Rs 30 crore of this client's money is charged exactly as it would be for a Rs 30 crore client.
Each tier's area is its fee: Rs 10 lakh on the first Rs 10 crore, Rs 12 lakh on the next Rs 20 crore and Rs 6 lakh on the last Rs 15 crore, so Rs 28 lakh on Rs 45 crore blends to 0.62%. What does the blend do as the client grows?
It drifts down toward the top tier's rate without reaching it. At Rs 30 crore the blend is 22 over 3,000, about 0.73%; at Rs 45 crore it is 0.62%; at Rs 100 crore it would be 50 over 10,000, 0.50%. For the bank this is the cost of winning large clients: revenue grows more slowly than assets, which is why the revenue marginRevenue divided by assets under management for a book or a whole business, the per-rupee earning rate of the wealth franchise. of a book tells you about its client mix.
The relationship10, 20, 15 the rupee crore in each tier 0.01, 0.006, 0.004 each tier's fee rate 0.28 the total fee in Rs crore, Rs 28 lakh What it says in wordsAdd the fee on each slice, then divide by the total assets.Mention the practical point a banker would. Clients compare the headline top-tier rate across banks, while the bank's income depends on the blend, and moving assets across tiers or between family accounts can change which slices apply. Fee schedules are negotiated, so the tiers here are an illustration.
Where candidates lose it
The trap is 0.4%: applying the top-tier rate to the whole balance, as if the tiers were price bands rather than slabs. It understates the fee by more than a third.
The second trap is averaging the three rates to 0.67%. It ignores that the slices are different sizes, the same error as averaging averages.
What the interviewer asks next
- What is the blended rate on a Rs 25 crore client?
- At what asset level does the blended rate fall to 0.5%?
- The client splits Rs 45 crore across two family accounts of Rs 22.5 crore each. What happens to his total fee?
064How does a private bank make money on one client? Take a Rs 50 crore client with Rs 20 crore under a 1% advisory mandate, Rs 15 crore in funds and notes that pay the bank a 0.8% trail, and a Rs 10 crore loan against securities earning the bank a 2% spread.J.P. MorganCharlotte · 2026
Try it first
Which stream earns the bank the most from this client?
Show the worked solution
About Rs 52 lakh a year, from three streams at once. The advisory fee earns 1% of Rs 20 crore, Rs 20 lakh. Product trails earn 0.8% of Rs 15 crore, Rs 12 lakh. The loan against securities earns a 2% spread on Rs 10 crore, Rs 20 lakh. Together that is about 1.04% of the client's Rs 50 crore, before the cost of the banker and the team who serve him.
What are the three ways a private bank earns on one client?
A family jeweller earns on making charges, on the margin in the gold he sells, and on the gold loan counter at the back of the shop, all from the same customer. A private bank earns a fee for advice, a commission for products it distributes, and a spread on money it lends, and a good relationship uses all three. Each is a balance times a rate, so the whole puzzle is three multiplications and an addition. The lending line is a loan against securitiesA loan secured by the client pledging shares, bonds or fund units he owns, so he can raise cash without selling them., and the bank keeps the difference between what it charges and what the money costs it.
From one Rs 50 crore client the bank earns Rs 20 lakh of advisory fees, Rs 12 lakh of product trail and Rs 20 lakh of lending spread, Rs 52 lakh a year or about 1.04% of the relationship. Why does the lending line matter so much?
Look at the figure: the Rs 10 crore loan earns as much as the Rs 20 crore advisory mandate. Lending earns on a balance the client does not have to move away from anyone else, which is why private banks work hard to offer credit to wealthy clients. The loan also keeps the pledged assets with the bank, which protects the other two streams. The spread is not free money; the bank carries the risk that the pledged securities fall faster than it can sell them.
What should a candidate add after the arithmetic?
Two things. First, cost: a relationship manager and the specialists behind him are paid out of this Rs 52 lakh, so the bank cares about revenue per banker, not just per client. Second, conflict: a product trail pays the bank more if the client holds certain products, which is why rules in many markets, including India, separate paid advice from commission-based distribution. Confirm the current rules; the point for the interview is that you see the incentive.
Where candidates lose it
The first trap is answering a generic bank's model, deposits and loans, and missing that a private bank earns mostly on fees and on the client's assets. The question is about the relationship, not the balance sheet.
The second is summing the balances, Rs 45 crore, and applying one rate. Each stream has its own base and its own rate; keep them apart and the lending line's weight becomes obvious.
What the interviewer asks next
- The client moves Rs 10 crore from products into the advisory mandate. What happens to revenue?
- Markets fall 20%. Which of the three streams falls, and which does not?
- Why might a bank accept a lower advisory fee to win the lending business?
Asked at J.P. Morgan, Private Banking, Charlotte, 2026 (Wall Street Oasis):
What is happening in the US economy right now? How does a bank make money?
076A private bank lists its risks and asks you to name the greatest. Two candidates: credit risk on a Rs 2,000 crore loan book with a 1% default rate and 45% loss given default, or a conduct fine of Rs 60 crore that it expects once every ten years. Which is the bigger risk?UBSNew York · 2026
Try it first
Which risk costs the bank more in an average year?
Show the worked solution
Credit is the bigger risk on expected loss, Rs 9 crore a year against Rs 6 crore, but conduct is the bigger risk in a bad year. Rs 2,000 crore x 1% x 45% is 9; Rs 60 crore x one in ten is 6. If a bad credit year triples defaults to 3%, credit loses 27, still well short of the 60 crore fine landing whole, and the fine also damages the franchise.
Why is the Rs 60 crore headline the wrong number to rank on?
Think of two risks to a household. A leaking tap wastes a little every month; a burglary costs a lot but comes rarely. You cannot compare them by the size of one burglary against one month of leaking, because one is certain and the other is not. Risks are ranked first by expected loss, the chance of the loss times its size, so a large but rare fine and a small but steady credit loss can be put on one scale.
The relationshipPD probability of default, the share of borrowers who stop paying in a year LGD loss given default, the share of the loan not recovered after default EAD exposure at default, the amount lent, here Rs 2,000 crore What it says in wordsCredit's expected loss is the default rate times the share lost times the book, Rs 9 crore a year.The conduct fine goes on the same scale the same way: Rs 60 crore with a one in ten chance each year is Rs 6 crore a year. On the average year credit costs half as much again as conduct. For a private bank the loan book is usually Lombard lendingLoans to wealthy clients secured against their investment portfolios, which the bank can sell if the loan is not repaid. against portfolios, which is why the loss given default here is well below what an unsecured book would suffer.
On expected loss credit ranks first, Rs 9 crore a year against Rs 6 crore for conduct; in a one in ten bad year conduct ranks first, the whole Rs 60 crore fine against Rs 27 crore of credit loss even with defaults tripled. So what do you say is the greatest risk?
Say both rankings, then pick with a reason. Expected loss tells you what to price and provision for; the bad year tells you what can hurt capital and the name, and for a bank that lives on client trust the bad year usually decides. A conduct fine rarely comes alone: clients leave, regulators restrict new business, and the cost runs well past the Rs 60 crore. That is why many private banking interviewers expect you to land on conduct and reputation as the greatest risk, and to show the arithmetic that says credit costs more on an ordinary year. The 3% bad-year default rate is an assumption; say it as one.
Where candidates lose it
Most candidates answer from the headline: Rs 60 crore sounds bigger than a 1% default rate, so conduct wins. They never weight the fine by its one in ten chance, and the interviewer hears a guess dressed as a judgement.
The opposite trap is stopping at expected loss and calling credit the winner. Give both numbers, 9 against 6 and 27 against 60, and say which one decides for a business that sells trust.
What the interviewer asks next
- Loss given default rises to 70% because collateral falls with the market. Does the ranking change?
- How would you set capital against each of these two risks?
- Name a risk on the wealth side of the bank that has neither a default rate nor a fine attached.
Asked at UBS, Private Wealth Management, New York, 2026 (Wall Street Oasis):
What is the broad range of risks a bank has, and what is the greatest risk?
100A relationship manager costs the bank Rs 60 lakh a year all in. Client assets yield 0.9% a year in revenue, and the bank wants revenue of three times the adviser's cost. How large a book must the adviser manage?Private banking
Try it first
Pick the book size.
Show the worked solution
Rs 200 crore. The bank wants revenue of three times Rs 60 lakh, which is Rs 1.8 crore a year. Each rupee of client assets brings in 0.9 paise, so the book must be Rs 1.8 crore divided by 0.009, which is Rs 200 crore. If the revenue yield slips to 0.75%, the same adviser needs Rs 240 crore.
How do the three numbers fit together?
A shop assistant earning Rs 30,000 a month has to help sell enough goods, at the shop's margin, to cover her pay several times over, because the rent, stock and the owner's profit come from the same margin. An adviser's required book is cost times the coverage the bank wants, divided by the revenue each rupee of assets earns. Coverage above one pays for the office, the platform, compliance and the bank's profit.
The relationshipcost the adviser's all-in cost to the bank, Rs 60 lakh a year coverage revenue as a multiple of that cost, here 3 yield revenue as a share of client assets, 0.9% a year What it says in wordsThe book needed is the revenue the bank wants from the adviser divided by what each rupee of assets earns.An adviser costing Rs 60 lakh at three times coverage must bring in Rs 1.8 crore a year, which at a 0.9% revenue yield needs a Rs 200 crore book, and a fall in yield to 0.75% raises that to Rs 240 crore. Which of the three numbers is the most fragile?
The yield. Revenue yield falls as clients move to cheaper products and larger clients negotiate fees, so the same adviser needs a bigger book every year just to stand still. A drop from 0.9% to 0.75%, which a shift towards advisory fees on large accounts could produce, lifts the required book from Rs 200 crore to Rs 240 crore, 20% more.
Add the time dimension too. A new adviser rarely starts with Rs 200 crore; the bank funds a ramp of two or three years while the book is built, and that ramp is part of the true cost of hiring. The coverage ratio and yield here are illustrative, and a bank's own figures vary widely by segment.
Where candidates lose it
The common slip is dividing cost by yield and stopping at about Rs 67 crore, which only pays the adviser's salary and leaves nothing for the rest of the bank. The coverage multiple is the step people drop.
The second slip is misplacing the decimal: 0.9% is 0.009, not 0.09. Say "0.9 paise per rupee" out loud and the order of magnitude stays right.
What the interviewer asks next
- The bank lowers the coverage it wants to 2.5 times. What book is needed?
- How long would it take a new adviser to build Rs 200 crore at Rs 50 crore of net new money a year?
- Why do revenue yields tend to fall as client size rises?
