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?
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?