Private Wealth Management puzzles, solved step by step
- Puzzles
- 100
- Traced to a firm
- 3
- Topics
- 13
- Hard
- 30
013A client with Rs 5 crore can pay an adviser a flat 1% advisory fee on all his assets, or use a distributor who earns a 1.2% trail commission on the 70% of his money held in mutual funds. Which costs him less each year?Indian wealth management
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Which annual bill is smaller, in rupees?
Show the worked solution
The commission route costs less on these numbers: Rs 4.2 lakh a year against Rs 5.0 lakh. The advisory fee is 1% of the whole Rs 5 crore. The trail is 1.2% of only the Rs 3.5 crore held in funds. The two bills would match if 83.3% of his assets earned trail, and the cheaper bill says nothing yet about the quality or independence of the advice.
Why does the higher rate give the smaller bill?
A phone plan charging Rs 2 a minute on calls only can cost less than one charging Rs 1.50 a minute on calls and data together, if you rarely use data. A fee rate means nothing until it is multiplied by the base it is charged on, so fee models are compared in rupees on the client's actual asset mix. Here 1.2% applies to Rs 3.5 crore and 1% applies to Rs 5 crore.
On a Rs 5 crore portfolio the 1% advisory fee is a Rs 5.0 lakh bill, while a 1.2% trail on the Rs 3.5 crore in funds is Rs 4.2 lakh, and the two only match when 83.3% of assets pay trail. What else should the comparison include?
Visibility and incentives. A trail is paid out of the fund's expense ratio, so the client never sees it as a bill, while an advisory fee arrives as an invoice he has to approve. The trail also pays more when more money sits in trail-paying funds, which is a pull away from direct equity, bonds or direct plansVersions of a mutual fund scheme bought without a distributor, with a lower expense ratio because no commission is paid out of them.. If the distributor moved another Rs 1 crore into funds, the trail bill would rise to Rs 5.4 lakh.
The relationship5 the client's assets, Rs crore; 0.01 of a crore is Rs 1 lakh 0.70 the share of assets held in trail-paying funds 0.012 the trail rate a year What it says in wordsMultiply each rate by the assets it is charged on, then compare rupees.Add the regulatory point as a framework, not a fact from memory: Indian rules separate registered advisers who charge fees from distributors who earn commissions, and limit doing both for the same client. The current regulations need checking before any of this reaches a client.
Where candidates lose it
The trap is comparing 1% with 1.2% and declaring the fee cheaper. The rates apply to different bases, and the rupee bill is the only honest comparison.
The second loss is stopping at the cheaper bill. The interviewer wants to hear that the trail is invisible and that it rewards keeping money in funds, because that is how the two models shape advice differently.
What the interviewer asks next
- At what share of assets in funds do the two models cost the same?
- The distributor proposes moving the other Rs 1.5 crore into funds. What happens to his income and the client's bill?
- How would you explain the invisible trail to a client in one sentence?
039A relationship manager looks after 80 client families and loses 15% of them each year to moves, deaths and competitors. How many new families must he win every year just to keep his book the same size?Wealth management
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Quick: how many new families a year keep the book at 80?
Show the worked solution
12 new families a year. Losing 15% of 80 families means 12 walk out each year, so 12 must come in to keep the book at 80. The general rule: a book settles where new families won equals the attrition rate times the book. Win only 8 a year and the book drifts toward 8 / 0.15, about 53 families; it does not collapse, but it shrinks by a third.
Why does attrition set the minimum pace?
A water tank with a leak at the bottom stays level only if the tap fills it as fast as it drains. A client book is the same tank: attrition drains a fixed share each year, so the new families needed are the leak rate times the size of the book. For 80 families at 15% that is 12, which is more than one new relationship a month before the adviser has grown at all.
At 15% attrition an 80-family book loses 12 families a year, so winning 12 keeps it flat. Winning 8 lets it slide to about 59 in ten years on the way to 53, while winning 16 lifts it toward 107. The relationshipN* the book size where gains and losses balance a the yearly attrition rate, 15% What it says in wordsA book settles at the size where the families lost each year exactly equal the families won.What does the number tell a wealth business?
Two things. First, the average family stays about 1 / 0.15, roughly 6.7 years, which caps what each relationship is worth. Cutting attrition from 15% to 10% lowers the new families needed from 12 to 8 a year, the same effect on book size as a 50% jump in new-client wins. That is why wealth firms spend so much on retention and service: it is usually cheaper to keep a family than to find one.
The limitation: families are not equal. Losing a large family and winning a small one keeps the count flat and shrinks the assets. A proper review runs the same arithmetic on assets and revenue, not just on heads.
Where candidates lose it
The slip is answering 15, reading the 15% as a count, or answering zero, as if a good adviser loses nobody. Neither survives a follow-up about how the book behaves over time.
Give 12, then show you see the steady state: the book settles where wins equal attrition times the book. That turns a percentage question into a business insight about retention.
What the interviewer asks next
- How many years does the average family stay at 15% attrition?
- If attrition drops to 10%, where does a book winning 12 families a year settle?
- Why might a relationship manager's assets shrink even while his family count holds steady?
089A relationship manager's book grew from Rs 400 crore to Rs 500 crore over a year in which his clients' portfolios rose 12%. How much net new money did he bring in?Wealth management
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How much of the Rs 100 crore growth is new money?
Show the worked solution
About Rs 52 crore. The market alone would have taken the book from Rs 400 crore to Rs 448 crore, 12% of 400 being Rs 48 crore. The rest of the growth to Rs 500 crore, Rs 52 crore, is net new money: fresh money in less withdrawals. If the new money arrived through the year and earned some of the rise, the figure is nearer Rs 49 crore.
Why separate the market from the money raised?
A shop's sales rise 25% in a year when prices across the market rose 12%. Most of that rise is inflation, not new customers. Assets under management grow from two sources, the market and net new money, and only the second measures what the adviser did. A banker who quotes 25% growth in a year when markets rose 12% is quoting a number he did not earn in full.
The book of Rs 400 crore gains Rs 48 crore from a 12% market and Rs 52 crore of net new money to close at Rs 500 crore, so only about half of the Rs 100 crore growth came from the adviser. The relationshipNNM net new money: new client money in, less money withdrawn 400 x 1.12 where the opening book would be from market moves alone What it says in wordsNet new money is the closing book less what the opening book would have grown to on its own.When is Rs 52 crore not quite right?
The simple version assumes the new money arrived at the year end, so it earned nothing. If new money came in steadily, part of the market's rise was earned on it, so the true net new money is a little lower than the simple subtraction. With money arriving evenly and earning about half the year's 12%, it is 52 divided by 1.06, about Rs 49 crore.
Say also what the figure hides: net new money is inflows less outflows, so Rs 52 crore could be Rs 80 crore raised and Rs 28 crore lost to clients who left. A manager asking this question usually wants both halves.
Where candidates lose it
The common slip is calling all Rs 100 crore new money, or taking 12% off the closing figure instead of the opening one. The market acts on money the adviser already had, so the 12% applies to Rs 400 crore.
The second loss is missing the timing caveat. Give 52, then say it is an upper figure if the money arrived through the year.
What the interviewer asks next
- The market fell 8% and the book still grew to Rs 420 crore. What was net new money?
- Why do wealth firms report net new money separately from assets?
- How would you split net new money into new clients and existing clients?