Private Wealth Management puzzles, solved step by step

Puzzles: 100
Traced to a firm: 3
Topics: 13
Hard: 30

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002A fund advertisement says the scheme returned 150% over the last 10 years. What annual rate of return is that?Returns arithmeticWarm upMutual fund distributionIndian wealth management
Try it first
Answer before you calculate.
Show the worked solution
About 9.6% a year. A 150% return means Rs 1 became Rs 2.5. The yearly rate is 2.5 to the power one tenth, minus one, which is 9.60%. Dividing 150 by 10 to get 15% ignores compounding: 15% a year for ten years would turn Rs 1 into 4.05, not 2.5.
Why is 15% the wrong annual figure?
Think of a child's height chart. If a child grew 50 centimetres over ten years, you could say 5 centimetres a year, because height adds. Money does not add; it multiplies, and each year's gain earns its own gain the next year. An absolute return over many years must be converted to a compounded yearly rate before it can be compared with anything else. Dividing by the number of years overstates the yearly rate, and the overstatement grows with the length of the period.
Rs 1 lakh growing to Rs 2.5 lakh is the advert's 150%, and built year by year it is about 9.6% a year, each year's bar 1.096 times the last; reading it as 15% a year would imply 4.05 times, not 2.5.
How do you get 9.6% without a calculator?
Use doubling as the anchor. At about 9.6% money doubles in roughly 7.5 years, so in ten years it goes a little past double, which matches 2.5 times. You can also bracket it: 1.10 to the tenth is 2.59, a touch above 2.5, so the answer is a touch below 10%. Saying a bracket out loud, just under 10% because 10% gives 2.59, is as convincing to an interviewer as the exact 9.60%.
The relationship
$r = \left(1 + R\right)^{1/n} - 1 = 2.5^{1/10} - 1 \approx 9.6\%$
R the absolute return over the whole period, here 150% or 1.5
n the number of years, here 10
r the compounded annual rate, often called CAGR
What it says in wordsTurn the total return into a growth multiple, take the n-th root, and subtract one.
Why does a wealth interviewer care? Because a client comparing a 150% ten-year fund with a fixed deposit quoting a yearly rate is comparing two different units. The 9.6% is also before any comparison with a benchmarkThe index or reference portfolio a fund is measured against, so its return can be judged relative to what the market gave., which is the next question worth asking.
Where candidates lose it
Saying 15% is the whole trap, and it comes from treating the advert's number as if it were simple interest. It is the most common error clients themselves make, which is exactly why a wealth desk tests it.
The second loss is getting 9.6% but not being able to say why 15% is wrong. Have the one-line check ready: 15% compounded for ten years is about 4 times, not 2.5.
What the interviewer asks next
The same fund returned 40% in the last three years. What is the annual rate over those three?
What did it return a year over the first seven years?
Why do regulators ask funds to show annualised returns for periods over a year?
004Inflation runs at 6% a year. What will Rs 1 lakh buy in 12 years' time, measured in today's money?Inflation and real returnWarm upIndian wealth management
Try it first
Your first instinct: what is Rs 1 lakh worth in today's money after 12 years?
Show the worked solution
About Rs 49,700, roughly half. At 6% a year, prices rise to 1.06 to the power 12, about 2.01 times today's level. Rs 1 lakh therefore buys what Rs 1 lakh divided by 2.01 buys today, which is Rs 49,697. The rule of 72 gives the shortcut: 72 divided by 6 is 12 years to halve the value of money.
Why divide by the price rise instead of subtracting the inflation?
Think of the family grocery bill. If a monthly basket costs Rs 10,000 today and prices double, the same basket costs Rs 20,000. A Rs 10,000 note still exists, but it now buys half a basket. Inflation does not take rupees away; it makes each rupee buy less, so today's value is the future amount divided by how much prices have grown. Prices at 6% for 12 years grow by a factor of 2.01, and that factor goes in the denominator.
At 6% inflation, Rs 1 lakh buys Rs 70,496 of today's goods after 6 years and Rs 49,697 after 12 years, so money loses about half its buying power in 12 years, as the rule of 72 predicts.
How do you say this to a client with most of his money in a savings account?
Turn it into a rupee amount he can feel. A fixed deposit that pays less than inflation after tax is losing buying power every year, even though the balance goes up. If his deposit earns 6% before tax and inflation is 6%, his real return after tax is below zero. That is the point of the puzzle: nominal growth is not the same as getting richer. Any real inflation or deposit rate you quote to a client has to be the current published one, confirmed on the day.
The relationship
$PV = \frac{1{,}00{,}000}{(1.06)^{12}} = \frac{1{,}00{,}000}{2.012} \approx 49{,}697$
(1.06)^12 how much prices grow in 12 years at 6% a year
PV the future Rs 1 lakh expressed in today's buying power
What it says in wordsDivide the future rupees by the growth in prices to get their value in today's money.
Check it with the rule of 72: 72 over 6 is 12, the number of years it takes prices to double. Doubled prices mean half the buying power. The exact figure is a shade under half because 1.06 to the 12th is 2.012, a shade over two.
Where candidates lose it
The slip is subtracting: 6% times 12 years is 72%, so Rs 28,000 is left. It treats inflation as a straight line and removes money that is still there. Clients who hear that from an adviser lose trust in every other number that follows.
The other loss is saying Rs 50,000 with no reasoning. Say the rule of 72 first, then the exact figure; it shows you can do it both ways.
What the interviewer asks next
At 4% inflation, how long does it take money to halve?
A client needs Rs 1 lakh a month in today's money at retirement in 24 years. What monthly amount will he need then, at 6%?
Why is a fixed deposit's post-tax real return often negative?
009A client regrets missing two stocks on his 20-stock watchlist that doubled last year. Of the other 18, five halved and thirteen ended flat. What would an equal stake in all 20 have returned?Behavioural trapsWarm upWealth management
Try it first
Before you add it up: what did the whole watchlist return?
Show the worked solution
An equal stake in all 20 would have lost 2.5%. Put Rs 1 lakh in each, Rs 20 lakh in total. The two doubles end at Rs 4 lakh, the five halved end at Rs 2.5 lakh and the thirteen flat end at Rs 13 lakh, which is Rs 19.5 lakh. The winners he remembers were two picks out of a list that lost money as a whole.
Why does the regret feel bigger than the numbers?
Think of someone who says they almost bought a winning lottery ticket because the number was one digit off their birthday. Every number was one choice among many; only the winner gets remembered. Hindsight picks the winners after the result is known, which is a choice the client never actually had at the time. This is hindsight biasThe tendency to believe, after an outcome is known, that it was predictable and that you would have acted on it., and it makes the missed gains feel certain.
The client remembers two stocks that doubled, but an equal Rs 1 lakh in each of the 20 on his watchlist would have turned Rs 20 lakh into Rs 19.5 lakh, a loss of 2.5%.
How do you use the number with the client?
Turn the regret into the decision he actually faced. At the start of the year he had twenty names and no way of knowing which two would double. The honest benchmark for a missed opportunity is the whole set of choices available at the time, not the best one in hindsight. On that benchmark his inaction cost nothing: holding cash lost nothing, while the list lost 2.5%.
The relationship
$\bar r = \frac{2(+100\%) + 5(-50\%) + 13(0\%)}{20} = \frac{200 - 250}{20} = -2.5\%$
2, 5, 13 the number of stocks that doubled, halved and stayed flat
20 the whole watchlist, equally weighted
What it says in wordsThe equal-weight return is the simple average of the 20 returns.
Note the arithmetic quirk it hides. A double and a halving look like mirror images, but the double adds Rs 1 lakh while the halving takes away only Rs 50,000. Five halvings still outweigh two doubles here, and the adviser who can show that in rupees wins the conversation.
Where candidates lose it
The trap is anchoring on the two doubles and guessing a positive return. Candidates who do this repeat the client's own bias back to him, which is the opposite of the job.
The second loss is getting minus 2.5% and not saying what it means for the conversation. The interviewer wants the reframing: judge a decision by the choices available at the time.
What the interviewer asks next
If he had bought any two stocks from the list at random, what is the chance he would have picked both winners?
How would you respond if he wants to buy only last year's winners now?
What other bias sits next to hindsight in a client's review of his own record?
011A client holds a stock bought at Rs 100 and sells a one-month call option with a Rs 110 strike for a premium of Rs 3. What is his maximum gain, and what does he give up if the stock ends the month at Rs 130?Options and structured productsWarm upPrivate banking
Try it first
The stock ends at Rs 130. What is the covered position worth, per share?
Show the worked solution
His maximum gain is Rs 13 a share, and at Rs 130 he gives up Rs 17. Above Rs 110 the call is exercised and the share goes at Rs 110, so the position is capped at Rs 110 plus the Rs 3 premium, Rs 113. At Rs 130 the stock alone would be worth Rs 130. The premium cushions a fall by only Rs 3: below Rs 97 he is losing money.
What exactly has the client sold?
Think of a landlord who takes a small non-refundable deposit from someone for the right to buy his flat at a fixed price within a month. If flat prices jump, the buyer exercises and the landlord gets only the fixed price plus the deposit. A covered call sells the upside above the strike in exchange for a small, certain fee today. The client keeps all the downside of owning the stock, less the premiumThe price the option buyer pays the seller up front, kept by the seller whatever happens next. received.
The covered call is worth Rs 3 more than the stock below the Rs 110 strike, but it is capped at Rs 113 above it, so at a price of Rs 130 the client gives up Rs 17 against simply holding the stock.
When does the trade help and when does it hurt?
Walk the three regions out loud. Below Rs 110 the covered call beats the plain stock by exactly the Rs 3 premium; above Rs 113 it falls behind by every rupee the stock rises. Between Rs 110 and Rs 113 the stock alone catches up. So the trade suits a client who expects the stock to drift sideways and wants some income, and it hurts the client who is secretly hoping for a sharp rally.
The relationship
$V_T = \min(S_T,\,110) + 3 \qquad V_{130} = 110 + 3 = 113$
S_T the stock price at expiry
110 the strike price of the call sold
3 the premium received up front
V_T the value of the stock plus the short call, per share
What it says in wordsThe covered position is worth the lower of the stock price and the strike, plus the premium already banked.
Say the risk plainly, because clients hear the word income and relax. If the stock falls to Rs 70, the position is worth Rs 73: the premium barely registers. A covered call is not protection; it is a trade of upside for a small, steady fee.
Where candidates lose it
The trap is adding the premium on top of the full stock price and saying Rs 133. It forgets that the share is called away at the strike, which is the whole point of the option sold.
The second loss is describing a covered call as a safe income strategy. The downside is almost entirely intact, and a wealth interviewer is listening for whether you tell a client that.
What the interviewer asks next
Where is the breakeven, and what is the position worth if the stock ends at Rs 90?
What changes if he sells a Rs 105 call for Rs 5 instead?
How would you explain this trade to a client who calls it free money?
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?Wealth business economicsWarm upIndian wealth management
Try it first
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 relationship
$\text{Fee} = 0.01 \times 5 = \text{Rs } 5.0\text{ lakh} \qquad \text{Trail} = 0.012 \times 0.70 \times 5 = \text{Rs } 4.2\text{ lakh}$
5 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?
028A husband's Rs 1 crore portfolio made 20% this year. His wife's Rs 4 crore portfolio lost 5%. They ask you what the family earned. What do you tell them?Returns arithmeticWarm upWealth management
Try it first
Answer inside ten seconds: what did the household earn?
Show the worked solution
The household earned 0%. The husband's 20% on Rs 1 crore is a gain of Rs 20 lakh. The wife's minus 5% on Rs 4 crore is a loss of Rs 20 lakh. Together they started with Rs 5 crore and ended with Rs 5 crore. The simple average of 7.5% is wrong because it gives the small account the same weight as the large one.
Why does the simple average mislead?
Two children score 100 on a 10-mark test and 40 on a 100-mark test. Their average percentage is 70, but they got 50 marks out of 110, which is 45%. A household's return is the change in its total rupees divided by the rupees it started with, so each account counts in proportion to its size. Averaging percentages silently treats a Rs 1 crore account and a Rs 4 crore account as equals.
Drawn to size, the husband's Rs 20 lakh gain and the wife's Rs 20 lakh loss are blocks of exactly the same length, so they cancel. The simple average of the two returns is 7.5%, but the rupee-weighted return on the Rs 5 crore family pool is 0%.
The relationship
$R_{\text{household}} = \frac{1}{5}(20\%) + \frac{4}{5}(-5\%) = 4\% - 4\% = 0\%$
1/5 and 4/5 each account's share of the Rs 5 crore family pool at the start of the year
20% and -5% each account's own return
What it says in wordsThe family's return is each account's return weighted by its share of the family's money.
Why does this matter in a wealth review?
Consolidated reporting is one of the first things a family office client asks for, and it is where this error shows up. If the adviser's report leads with the husband's 20%, the family feels rich while its total wealth has not moved at all. The same trap appears when a relationship manager quotes the average return across a client's funds instead of the return on the client's money.
One limit: this weighting assumes no money moved in or out during the year. If the wife added Rs 1 crore in March, you would need a time-weighted or money-weighted calculation, which is a different question.
Where candidates lose it
Saying 7.5% is the whole trap, and it is said fast because both numbers are in front of you. The interviewer wants to hear you ask how big each account is before you combine anything.
Give the rupee answer, then name the rule in one line: weight returns by money, not by account. That line is what shows you would build a consolidated report correctly.
What the interviewer asks next
What if the wife's account had been Rs 2 crore instead?
The husband added Rs 50 lakh halfway through the year. How does that change the calculation?
How would you present this result to a couple who each think their own account did better?
031A taxable bond yields 7.5% and a tax-free bond of similar quality and tenor yields 5.4%. For a client paying tax at an illustrative 30% slab, which one pays him more?Tax arithmeticWarm upIndian wealth management
Try it first
Pick one before you calculate.
Show the worked solution
The tax-free bond pays him more: 5.4% against 5.25%. The taxable bond's 7.5% loses 30% to tax, leaving 7.5 x 0.7 = 5.25%. Put the other way, the tax-free 5.4% is worth 5.4 / 0.7 = 7.71% to a taxable investor at this slab, which is more than 7.5%. On Rs 1 crore the difference is about Rs 15,000 a year.
What is the fair way to compare the two yields?
Two job offers: Rs 20 lakh with a company flat thrown in, or Rs 23 lakh with no flat. You do not compare 20 with 23; you compare what each leaves you after rent. Yields are compared on what the client keeps, which means after his own tax, not on the number printed on the term sheet. Either shrink the taxable yield by the tax rate, or gross the tax-free yield up to its taxable equivalent.
The relationship
$y_{\text{after}} = y\,(1-t) = 7.5 \times 0.7 = 5.25\% \qquad y_{\text{eq}} = \frac{y_{tf}}{1-t} = \frac{5.4}{0.7} = 7.71\%$
y the taxable bond's yield, 7.5%
t the client's marginal tax rate, an illustrative 30%
y_tf the tax-free bond's yield, 5.4%
What it says in wordsEither take the tax off the taxable yield or add it back onto the tax-free one; both routes pick the same winner.
At an illustrative 30% slab, the taxable bond's 7.5% leaves the client 5.25% after tax, while the tax-free bond keeps its full 5.4%. The taxable bond would need to yield at least 7.71% to match.
For which clients does the answer flip?
Solve for the tax rate at which the two are equal: 1 minus 5.4 / 7.5, which is 28%. Any client whose marginal rate is below 28% keeps more from the taxable bond; any client above it keeps more from the tax-free one. That is why the same product can be right for a senior partner and wrong for his retired mother, and why an adviser asks about the slab before quoting yields.
Limits worth saying: tax-free bonds are often thinly traded, so the exit price matters; surcharge and cess change the effective rate; and tax treatment depends on current law, so confirm the client's actual rate and the bond's status before you rely on the comparison.
Where candidates lose it
The trap is answering 7.5% because it is the bigger number, without asking about tax at all. For a wealth desk that is the one question you must never skip, because nearly every client comparison is an after-tax comparison.
The second slip is dividing when you should multiply, and grossing 7.5 up instead of 5.4. Name which yield you are converting, and why, before you touch the numbers.
What the interviewer asks next
What is the taxable-equivalent yield for a client at a 20% slab?
Why might a tax-free bond trade below its issue price in the secondary market?
How would the comparison change if the client expected his slab to fall after retirement?
032Suppose every fund manager is pure luck: each fund has a 50% chance of beating its benchmark in any year, independently. Out of 1,000 funds, how many will beat the benchmark five years in a row?Probability and risk of lossWarm upMutual fund distributionIndian wealth management
Try it first
Quick: how many of the 1,000 funds show a five-year streak by luck alone?
Show the worked solution
About 31 funds. The chance of beating the benchmark five years running by luck is one half multiplied by itself five times, 1 in 32. Out of 1,000 funds that is 1,000 divided by 32, or about 31.25. So a large field of funds throws up dozens of perfect five-year records even if nobody has any skill, and a streak on its own is weak evidence.
Why does a large field guarantee some long streaks?
Put 1,000 people in a hall and ask each to toss a coin five times. Nobody would be surprised that about 31 of them get five heads, and nobody would ask them for coin-tossing lessons. A rare event for one participant becomes a near certainty somewhere in a big enough crowd. Funds are the same crowd, and the ones with perfect records are the ones that get advertised.
If each fund beats its benchmark with a coin-flip chance each year, 1,000 funds shrink to 500, 250, 125, 62.5 and finally about 31 with perfect five-year records. Those 31 streaks appear with no skill anywhere in the field.
The relationship
$E[\text{streaks}] = N \cdot p^{\,k} = 1000 \times 0.5^5 = 31.25$
N the number of funds, 1,000
p the chance of beating the benchmark in one year, 0.5
k the length of the streak, 5 years
What it says in wordsThe expected number of lucky streaks is the size of the field times the chance that any one fund strings the wins together.
What should an adviser take from this when screening funds?
That a track record needs a comparison against luck, not just a count of good years. Even ten straight years of beating the index would be expected from about 0.98 fund out of 1,000 by chance, so one such fund in a large category is not proof of skill. What helps more: a consistent process, returns that survive a fair risk adjustment, and results after costs over several market conditions.
The limitation of the puzzle is the 50% and the independence. In reality, after costs the average fund beats its benchmark less than half the time, and good and bad years may be correlated with a manager's style. Both change the count, but not the lesson.
Where candidates lose it
The first trap is saying zero or a handful, because five in a row feels rare. It is rare for one fund; it is common in a field of 1,000. The interviewer is testing whether you think about the size of the crowd.
The second trap is getting 31 and stopping. Add the adviser's conclusion in one line: streaks are what luck produces in a large field, so screen on process and risk-adjusted results, not on the streak.
What the interviewer asks next
If the true chance of beating the benchmark after costs is 40%, how many five-year streaks do you expect?
How many funds would you need for one ten-year streak by luck?
What evidence would make you believe a streak is skill?
038A client borrows Rs 50 lakh against Rs 1 crore of shares. The lender makes a margin call when the loan reaches 60% of the collateral's value. How far can the shares fall before the call arrives?Leverage and borrowingWarm upPrivate banking
Try it first
How big a fall triggers the margin call?
Show the worked solution
About 16.7%. The loan stays at Rs 50 lakh, so the call comes when 50 is 60% of the collateral, which means collateral of 50 / 0.6 = Rs 83.3 lakh. Falling from Rs 1 crore to Rs 83.3 lakh is a drop of 16.7%. A 50% loan-to-value sounds like a large cushion, but the lender's trigger sits well inside it.
Why is the buffer smaller than the loan-to-value suggests?
A family pledges gold worth Rs 1 lakh for a Rs 50,000 loan and feels safe because the loan is half the gold. But the jeweller will call for more gold well before the gold is worth Rs 50,000. The margin call is set on the ratio of loan to collateral, and only the collateral moves, so the question is how far the denominator can shrink before the ratio hits the trigger. Going from 50% to 60% needs the collateral to lose one sixth of its value, not a tenth and not a half.
The Rs 50 lakh loan stays fixed while the collateral shrinks around it, so loan-to-value climbs from 50% to 60% when the shares fall only 16.7%, to Rs 83.3 lakh. After a 40% fall the loan is 83.3% of the collateral.
The relationship
$C^{*} = \frac{L}{m} = \frac{50}{0.60} = 83.3 \qquad \text{fall} = 1 - \frac{83.3}{100} = 16.7\%$
L the loan, Rs 50 lakh, fixed
m the loan-to-value at which the lender calls, 60%
C* the collateral value that triggers the call
What it says in wordsThe call comes when the collateral has shrunk to the loan divided by the trigger ratio.
What happens when the call arrives?
The client must bring the ratio back, usually to where it started. At the trigger, restoring a 50% loan-to-value needs either Rs 8.3 lakh of repayment or Rs 16.7 lakh of extra shares pledged, within days. If he has neither, the lender sells shares at the low price, which locks in the loss. In a sharp market fall, many borrowers face the same call at once, which is why the forced selling tends to arrive at the worst prices.
One limit worth saying: interest that is added to the loan rather than paid pushes the loan up over time, so the real buffer is a little smaller than 16.7%. And a single volatile stock can move 16.7% in a week.
Where candidates lose it
The fast wrong answer is 10%, from subtracting 50 from 60. It treats loan-to-value as if it moved one for one with the share price, when the ratio's denominator is the thing falling.
The other slip is answering 50%, the fall that wipes out the client's equity, which ignores that the lender acts long before that. Solve for the collateral at the trigger and state the fall; then say what the client must do when it arrives.
What the interviewer asks next
What fall triggers the call if the client borrowed Rs 40 lakh instead?
How much must he repay at the trigger to restore a 50% loan-to-value?
Why do lenders apply bigger haircuts to mid-cap shares than to large-cap ones?
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 business economicsWarm upWealth management
Try it first
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 relationship
$N^{*} = \frac{\text{new per year}}{a} \qquad \frac{12}{0.15} = 80, \quad \frac{8}{0.15} = 53.3$
N* 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?

R	the absolute return over the whole period, here 150% or 1.5
n	the number of years, here 10
r	the compounded annual rate, often called CAGR

(1.06)^12	how much prices grow in 12 years at 6% a year
PV	the future Rs 1 lakh expressed in today's buying power

2, 5, 13	the number of stocks that doubled, halved and stayed flat
20	the whole watchlist, equally weighted

S_T	the stock price at expiry
110	the strike price of the call sold
3	the premium received up front
V_T	the value of the stock plus the short call, per share

Try it first

Why is 15% the wrong annual figure?

How do you get 9.6% without a calculator?

Where candidates lose it

What the interviewer asks next

Try it first

Why divide by the price rise instead of subtracting the inflation?

How do you say this to a client with most of his money in a savings account?

Where candidates lose it

What the interviewer asks next

Try it first

Why does the regret feel bigger than the numbers?

How do you use the number with the client?

Where candidates lose it

What the interviewer asks next

Try it first

What exactly has the client sold?

When does the trade help and when does it hurt?

Where candidates lose it

What the interviewer asks next

Try it first

Why does the higher rate give the smaller bill?

What else should the comparison include?

Where candidates lose it

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Why does the simple average mislead?

Why does this matter in a wealth review?

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What is the fair way to compare the two yields?

For which clients does the answer flip?

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Why does a large field guarantee some long streaks?

What should an adviser take from this when screening funds?

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Why is the buffer smaller than the loan-to-value suggests?

What happens when the call arrives?

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Why does attrition set the minimum pace?

What does the number tell a wealth business?

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