Private Wealth Management puzzles, solved step by step

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

Showing 31–40 of 100

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
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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?
033A retiree has Rs 1 crore earning 8% a year. He withdraws Rs 8 lakh, the full 8%, at the end of every year, while inflation runs at 6%. What happens to the real value of his income and his capital over 15 years?Retirement and withdrawalCoreIndian wealth management
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After 15 years, roughly what is his Rs 1 crore worth in today's rupees?
Show the worked solution
His rupees stay flat and their value falls by more than half. Taking the full 8% leaves the capital at Rs 1 crore every year. But prices rise 6% a year, so after 15 years they are 2.40 times higher. His capital is then worth about Rs 41.7 lakh in today's rupees, and his Rs 8 lakh income buys what Rs 3.34 lakh buys now. Only the real return, about 2%, was safe to spend.
Where does the damage come from if he never touches the capital?
A landlord who spends every rupee of rent and never raises it feels fine for a year or two. Fifteen years later the same rent buys half the groceries, and the house has not grown to compensate. Of the 8% return, 6 points are not income at all: they are the amount the capital must grow just to hold its purchasing power. Spending the full nominal return spends that inflation cushion too.
Withdrawing the full 8% keeps the retiree's capital at Rs 1 crore in rupees, but in today's rupees it falls every year to about Rs 41.7 lakh by year 15. His fixed Rs 8 lakh income shrinks to Rs 3.34 lakh of today's purchasing power.
The relationship
$\text{real value}_t = \frac{\text{Rs } 1\text{ crore}}{(1.06)^{t}} \qquad \frac{100}{1.06^{15}} = 41.7 \text{ lakh}$
1.06^t how much prices have risen after t years of 6% inflation
Rs 1 crore the nominal capital, kept flat by withdrawing the full return
What it says in wordsA fixed number of rupees is worth less every year by the amount prices have risen.
What could he safely spend instead?
Only the real return. The capital has to grow 6% a year to stand still, so of the Rs 8 lakh, only about Rs 2 lakh is spendable in the first year, and that withdrawal can rise with inflation each year after. The sustainable withdrawal is the return minus inflation, roughly 1.9% in real terms, not the headline 8%. That is a hard conversation, because the retiree's income drops from Rs 8 lakh to Rs 2 lakh on day one, but it is the honest arithmetic.
The limits: most retirees also spend some capital over a finite lifetime, so the true plan sits between these two extremes. And real portfolios do not earn a smooth 8%; a few bad years early in retirement do far more damage than the same years later.
Where candidates lose it
The trap is saying nothing happens because the capital is untouched. It is untouched in rupees, and the question is deliberately worded in real terms to see whether you notice the difference.
The second loss is saying the capital falls but not by how much. Give the {(1 + P33['inf']) ** 15:.2f} price factor, the Rs {P33['real_cap'][-1]:.0f} lakh real value and the one-line fix: spend the real return, not the nominal one.
What the interviewer asks next
How many years until his real capital halves at 6% inflation?
If he wants his income to keep pace with inflation for 25 years, roughly what first-year withdrawal is sustainable?
How does a bad market in the first three years of retirement change this picture?
034A client is offered a corporate bond yielding 9.5% when government bonds of the same tenor yield 7%. The issuer has roughly a 2% chance of defaulting in any year, and bondholders would recover about 40% if it did. How much of the extra yield is really extra?Fixed income numeracyCorePrivate banking
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Of the 2.5-point spread, roughly how much is left after expected defaults?
Show the worked solution
About 1.3 points of the 2.5-point spread is genuinely extra. Expected loss is the default chance times the share lost: 2% x (100% less 40% recovery) = 1.2 points a year. The spread of 9.5 less 7, or 2.5 points, minus that 1.2 leaves about 1.3 points. That remainder is the pay for bearing uncertainty about defaults and for lower liquidity, not free yield.
Why is a spread not free money?
A moneylender who charges 24% instead of the bank's 12% is not twice as profitable if one borrower in ten never pays. The extra yield on a risky bond is first a charge for the defaults you should expect, and only what is left over is a reward. Clients see 9.5% against 7% and hear 2.5 points of extra income; the adviser's job is to take the expected losses out first.
The corporate bond's 2.5-point spread over the 7% government bond shrinks to 1.3 points once 1.2 points of expected loss are taken out, leaving an expected return of about 8.3%. The spread only covers defaults up to a 4.2% annual default chance.
The relationship
$\text{spread left} = s - PD \times (1-R) = 2.5\% - 2\% \times 0.6 = 1.3\%$
s the spread over the government bond, 2.5 points
PD the yearly probability of default, 2%
R the recovery rate, 40%
What it says in wordsWhat the spread really pays is the spread minus the losses you should expect every year on average.
What does the 1.3 points actually pay for?
Two things the average hides. Defaults cluster in bad years, exactly when the client also has equity losses, so the bond fails when he can least afford it. And a corporate bond is harder to sell than a government bond. If the true default chance is 4.2% rather than 2%, the whole spread is eaten and the client is holding extra risk for nothing. So the useful question is how confident anyone can be in the 2%.
The puzzle simplifies: a default also stops future coupons, recoveries take time to arrive, and the default chance is not constant over a bond's life. Treat 1.3 points as the order of magnitude, and read the issuer's actual rating history and covenants before any real comparison.
Where candidates lose it
The first trap is subtracting the full 2% default chance, forgetting that bondholders recover 40%. That gives 0.5 points left and makes the bond look worse than it is. The opposite error ignores defaults and calls the whole 2.5 points extra income.
Say the formula out loud, default chance times loss given default, then add the one sentence on why the remaining 1.3 points exists. That second part is what separates an adviser from a yield quoter.
What the interviewer asks next
What default chance would make the client indifferent between the two bonds?
If recovery falls to 20%, how much spread is left?
Why do spreads widen sharply in a recession even if default rates have not yet risen?
035A client needs Rs 80,000 in cash. He owns two lots of 1,000 shares each of the same stock, now at Rs 80. He bought one lot at Rs 100 and the other at Rs 60. Which lot should he sell to raise the money, and why?Behavioural trapsCoreWealth management
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What should decide which lot he sells?
Show the worked solution
Sell the lot bought at Rs 100; the only thing the purchase price changes is tax. Both lots are the same stock at Rs 80, and he keeps 1,000 identical shares either way, so the future is the same. Selling the Rs 60 lot books a Rs 20,000 gain and, at an illustrative 20% rate, Rs 4,000 of tax now. Selling the Rs 100 lot books a Rs 20,000 loss, pays nothing, and can shelter other gains.
Why does the price he paid not matter to the stock?
Two people own identical Rs 80 notes, one found on the road and one earned after a hard week. The notes buy exactly the same things. A share at Rs 80 has one future, and it is the same whether its owner paid Rs 60 or Rs 100. The urge to sell the winner to lock in a profit and to hold the loser until it gets back to cost is called the disposition effect, and it comes from anchoring on a number the market has forgotten.
Selling either lot raises Rs 80,000 and leaves the client holding 1,000 identical shares at Rs 80. Selling the Rs 60 lot triggers Rs 4,000 of illustrative tax now; selling the Rs 100 lot books a Rs 20,000 loss that pays no tax and can shelter other gains.
How big is the tax difference, and is it permanent?
At an illustrative 20% on short-term gains, selling lot B costs Rs 4,000 today. Selling lot A costs nothing and books a Rs 20,000 loss; if he has other gains this year, that loss can reduce their tax by up to Rs 4,000. The swing between the two choices is up to Rs 8,000 for the same stock and the same cash. Part of it is timing rather than a permanent saving: the gain inside lot B is still there, and will be taxed if he sells it later.
Frame it for the client without judging the instinct, because nearly everyone has it. The current tax rates, the holding periods that decide short or long term, and the rules on which losses can be set off against which gains all change over time, so confirm the current ones before acting on the numbers.
Where candidates lose it
Candidates say sell the winner and bank the profit, which is the exact bias the interviewer is probing. Others say it makes no difference at all, which misses the one thing that genuinely differs.
Give both halves: the purchase price is irrelevant to the stock's future, and relevant only through tax. Then quantify the tax, and say that part of the saving is a deferral, not a gift.
What the interviewer asks next
Would your answer change if the lot bought at Rs 60 had been held long enough to qualify as long term?
The client says he cannot bear to realise a loss. How do you handle that conversation?
What if he has no other capital gains this year to use the loss against?
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?Estimation and sizingCoreIndian wealth management
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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 relationship
$PV = C\sum_{t=0}^{n-1}\left(\frac{1+g}{1+r}\right)^{t} = 18 \times 20.16 = 362.9 \text{ lakh}$
C 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?
037Explain Black-Scholes through one number. What is an at-the-money one-year call on a Rs 1,000 stock with 25% volatility worth, roughly, and what happens to that price if volatility doubles?Options and structured productsCoreGoldman SachsZurich · 2025
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Volatility doubles from 25% to 50%, everything else fixed. What happens to the call's price?
Show the worked solution
About Rs 100, and doubling volatility roughly doubles it to about Rs 200. With no interest or dividends, Black-Scholes prices an at-the-money call at very nearly 0.4 x stock price x volatility x the square root of time: 0.4 x 1,000 x 0.25 x 1 = Rs 100. The exact formula gives Rs 99.5. At 50% volatility the exact price is Rs 197.4. The option is priced as the expected value of its payoff, and that expectation grows with how far the stock can move.
What is Black-Scholes actually doing?
Imagine a rain insurance policy for an outdoor wedding that pays only if it pours. Its fair price depends on how uncertain the weather is: in a steady dry season it is nearly worthless, in a volatile monsoon it is dear. Black-Scholes prices an option as the average payoff over every path the stock could take, where the spread of those paths is set by volatility. The owner of a call keeps the upside of big moves and loses at most the premium on the downside, so a wider spread of paths is worth more.
At the money, with rates set to zero, the formula collapses to a clean shortcut. The standard normal distributionThe bell curve with mean zero and standard deviation one, used to describe the spread of possible stock returns in the model. has height 1 over the square root of 2 pi at its centre, which is 0.399, and that is where the 0.4 comes from.
The relationship
$C_{\text{ATM}} \approx \frac{1}{\sqrt{2\pi}}\,S\,\sigma\sqrt{T} \approx 0.4 \times 1000 \times 0.25 \times 1 = 100$
S the stock price, Rs 1,000, equal to the strike
\sigma the stock's annual volatility, 25%
T time to expiry in years, 1
1/\sqrt{2\pi} about 0.399, the height of the bell curve at its centre
What it says in wordsAn at-the-money call is worth about 40% of one standard deviation of the stock's move over the option's life.
For an at-the-money one-year call on a Rs 1,000 stock, the exact Black-Scholes price is Rs 99.5 at 25% volatility and Rs 197.4 at 50%, almost a straight line. The 0.4 shortcut tracks it closely, so doubling volatility roughly doubles the price.
Why would a wealth interviewer care about this?
Because structured products sold to private clients are bundles of options, and the client is often the seller of volatility without knowing it. A note that pays a high coupon while volatility is high is usually paying for an option the client has written, and the coupon rises with volatility for exactly the reason on this chart. The same shortcut shows time matters by its square root: a three-month option on the same stock costs about half the one-year option, Rs 49.8, not a quarter.
The limits: the shortcut is only good at the money and for short maturities with low rates. The model assumes constant volatility and smooth prices, which real markets break, and that is why traders quote different volatilities for different strikes.
Where candidates lose it
Candidates recite the formula, N of d1 and N of d2, and cannot say what any of it means or produce a number. A wealth interviewer wants the intuition and one sanity check, not the algebra.
The other slip is guessing that doubling volatility quadruples the price because variance quadruples. At the money the price moves with volatility, not its square. Give Rs 100, then Rs 200, then say why the client selling that volatility in a structured note should care.
What the interviewer asks next
What is the same option worth with three months to expiry?
How does the shortcut change for an at-the-money put?
Why does a reverse convertible pay a higher coupon when volatility rises?
Asked at Goldman Sachs, 2026 | EMEA | Zurich | Wealth Management | Summer Analyst Interview, Zurich, 2025 (Wall Street Oasis): Moreover, I was asked to explain Black and Scholes.
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?

040A client can run a Rs 10,000 monthly SIP that rises 10% every year, or a flat Rs 15,000 monthly SIP. Both run 15 years at 12% a year, treated as 1% a month. Which ends bigger, and in which year does the step-up overtake on the monthly instalment?Compounding and doublingHardMutual fund distributionIndian wealth management

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The step-up ends bigger. Where does most of its advantage come from?

Show the worked solution

The step-up ends bigger, Rs 86.8 lakh against Rs 75.7 lakh, but it wins late and by saving more. Its instalment first beats Rs 15,000 in year 6, at Rs 16,105, and its corpus overtakes only in year 11. Over 15 years it puts in Rs 38.1 lakh against Rs 27.0 lakh; the growth on each is almost identical, about Rs 48.7 lakh.

Why does the step-up lag for so long?

Two students save for a trip: one puts in Rs 150 a week from the start, the other begins at Rs 100 and adds 10% every term. The steady saver is ahead for most of the year because her money arrived first. The step-up pays in less than the flat SIP for the first five years, and money put in early is the money that compounds longest, so its corpus trails until year 11. Its year-5 instalment is still only Rs 14,641.

The step-up instalment passes the flat Rs 15,000 in year 6 and reaches Rs 37,975 by year 15, but its corpus overtakes only in year 11. At year 15 it holds Rs 86.8 lakh against Rs 75.7 lakh, with almost identical growth of about Rs 48.7 lakh on each.

	Flat Rs 15,000	Step-up from Rs 10,000
Total put in	Rs 27.0 lakh	Rs 38.1 lakh
Corpus at year 5	Rs 12.4 lakh	Rs 9.8 lakh
Corpus at year 10	Rs 34.9 lakh	Rs 33.7 lakh
Corpus at year 15	Rs 75.7 lakh	Rs 86.8 lakh
Growth at year 15	Rs 48.7 lakh	Rs 48.7 lakh

Both SIPs invested at the start of each month at 1% a month; the step-up rises 10% at the start of each year.

So is the step-up the better plan?

It is a different plan, not a smarter one. The step-up ends ahead because it asks the client to save Rs 11.1 lakh more; per rupee saved, the flat SIP compounds better because its money arrives earlier. Where the step-up earns its place is fit: it matches a salary that rises each year, so the client can afford it without strain in year one. The honest comparison for a client is between what each plan asks of his budget in each year, not between two final numbers.

Limits: 1% every month is smooth, real returns are not, and the step-up puts its biggest instalments in the last years, so a bad market late in the plan hurts it more. The 10% step-up also assumes the client's income actually rises that fast.

Where candidates lose it

Most candidates say the step-up wins and credit compounding. The step-up does win, but compounding favours the flat SIP rupee for rupee; the extra corpus is almost exactly the extra saving. That is the insight the interviewer is fishing for.

The other loss is the crossover year. The instalment crosses in year {P40['cross_contrib']}, when 10,000 x 1.1 to the power 5 first tops 15,000, but the corpus takes until year {P40['cross_corpus']}. Say both, and say why they differ.

What the interviewer asks next

What flat SIP would match the step-up's corpus at year 15?
How does the answer change over 25 years instead of 15?
The client's salary rises 5% a year, not 10%. Which plan fits him better, and why?

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%

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

1.06^t	how much prices have risen after t years of 6% inflation
Rs 1 crore	the nominal capital, kept flat by withdrawing the full return

s	the spread over the government bond, 2.5 points
PD	the yearly probability of default, 2%
R	the recovery rate, 40%

Try it first

What is the fair way to compare the two yields?

For which clients does the answer flip?

Where candidates lose it

What the interviewer asks next

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Why does a large field guarantee some long streaks?

What should an adviser take from this when screening funds?

Where candidates lose it

What the interviewer asks next

Try it first

Where does the damage come from if he never touches the capital?

What could he safely spend instead?

Where candidates lose it

What the interviewer asks next

Try it first

Why is a spread not free money?

What does the 1.3 points actually pay for?

Where candidates lose it

What the interviewer asks next

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Why does the price he paid not matter to the stock?

How big is the tax difference, and is it permanent?

Where candidates lose it

What the interviewer asks next

Try it first

What exactly is the cover replacing?

Which assumptions move the answer most?

Where candidates lose it

What the interviewer asks next

Try it first

What is Black-Scholes actually doing?

Why would a wealth interviewer care about this?

Where candidates lose it

What the interviewer asks next

Try it first

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

What happens when the call arrives?

Where candidates lose it

What the interviewer asks next

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Why does attrition set the minimum pace?

What does the number tell a wealth business?

Where candidates lose it

What the interviewer asks next

Try it first

Why does the step-up lag for so long?

So is the step-up the better plan?

Where candidates lose it

What the interviewer asks next