Private Wealth Management puzzles, solved step by step

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

Showing 11–20 of 50 · filtered from 100Clear filters

021A fund house's factsheet shows its 10 open equity schemes averaging 14% a year since launch. It actually launched 16; the 6 it closed or merged averaged minus 2% a year. What was the average across all 16 schemes it launched?Behavioural trapsCoreMutual fund distributionIndian wealth management
Try it first
Pick the average across all 16 schemes.
Show the worked solution
8%, not 14%. Weight each group by how many schemes it holds: 10 schemes at 14% contribute 140, and 6 at minus 2% contribute minus 12. The total, 128, over 16 schemes is 8%. The factsheet's 14% describes only the schemes that survived, which is why the full launch record is the honest measure of the fund house.
Why does the factsheet overstate the record?
Think of a coaching centre that advertises the average score of the students who finished the course, after the weaker ones dropped out. The average is true of the finishers and misleading about the centre. A record that only shows what survived is flattered, because the failures were removed for being failures. That is survivorship biasThe distortion that comes from judging a group only by the members still around, when the ones that failed have dropped out of the data.: the closed schemes did not vanish at random, they closed because they did badly.
The factsheet's 10 open schemes average 14%, but the 6 closed schemes averaged minus 2%, so across all 16 schemes the fund house launched the record is 8%.
Why not take the midpoint of 14% and minus 2%?
Because the groups are different sizes. An average of averages is only right when each group holds the same number of items; otherwise each average has to be weighted by its count. The midpoint, 6%, gives the 6 closed schemes as much weight as the 10 open ones and understates the record. Ten at 14 and six at minus 2 gives 8%.
The relationship
$\bar r = \frac{10 \times 14\% + 6 \times (-2\%)}{16} = \frac{140 - 12}{16} = 8\%$
10, 6 the number of open and closed schemes
14%, -2% each group's average yearly return
16 all schemes the fund house launched
What it says in wordsThe average across all schemes is each group's average weighted by how many schemes it holds.
Take it to the client conversation. A factsheet does not have to show closed or merged schemes, so the question to ask a fund house is how many schemes it has launched and what happened to the ones that are gone. The same bias sits inside category averages that drop merged funds; the numbers here are an illustration of the method.
Where candidates lose it
The trap is accepting 14% because it is printed on an official document. The candidate who does not ask what is missing has shown the exact blind spot an adviser is paid to cover.
The second loss is the midpoint, 6%. It notices the closed schemes but forgets to weight by count, so it ends up wrong in the other direction.
What the interviewer asks next
If the closed schemes had been merged into the survivors, how would the reported record change?
How would you check a fund house's record for survivorship before recommending it?
Where else in wealth management does survivorship bias show up?
023An at-the-money option's value rises roughly with the square root of its time to expiry. If a one-year at-the-money call is worth Rs 100, what is a three-month at-the-money call on the same stock worth?Options and structured productsCorePrivate banking
Try it first
Pick the three-month call's value.
Show the worked solution
About Rs 50. Three months is a quarter of a year, and the square root of one quarter is one half, so the option keeps half its one-year value. The flip side matters as much: the one-year option loses Rs 50 over its first nine months and the other Rs 50 in its last three, so time decay speeds up sharply as expiry approaches.
Why the square root of time?
Think of a person taking random steps left or right. After four steps they are typically about two steps from the start, not four, because steps partly cancel. After sixteen steps, about four. Price uncertainty spreads with the square root of time, and an at-the-money option's value is roughly proportional to that spread. The standard rule of thumb for an at-the-money call is 0.4 times volatility times price times the square root of time: at 25% volatility on a Rs 1,000 stock over one year that gives Rs 100.
An at-the-money option worth Rs 100 at one year is still worth Rs 50 at three months because value follows the square root of time, so it loses 13.4, 15.9 and 20.7 in the first three quarters and 50 in the last.
What does the curve mean for a client who sells options?
It means time decayThe fall in an option value as expiry approaches with nothing else changing, often called theta. is not even. Half of a one-year option's value is lost in its final quarter, so a seller collects decay fastest close to expiry, which is also when a sudden move hurts most. For a client selling covered calls every month, this is why short-dated options are the usual choice, and why the income comes with gap risk.
The relationship
$C_{3m} \approx C_{1y} \sqrt{\frac{3}{12}} = 100 \times 0.5 = 50$
C_1y the one-year at-the-money call, Rs 100
3/12 three months as a fraction of the year
C_3m the three-month call, same stock and volatility
What it says in wordsScale an at-the-money option's value by the square root of the ratio of the times to expiry.
State where the rule breaks. It holds for at-the-money options with low interest rates; deep in or out of the money options do not scale this way, and volatility for three months need not equal volatility for a year. It is a desk estimate, not a pricing model.
Where candidates lose it
The trap is Rs 25: scaling value in a straight line with time. It is the natural first answer and it is off by half, which tells the interviewer the candidate has not met the idea that uncertainty grows with the square root of time.
The second loss is stopping at Rs 50 without the decay point. The follow-up is almost always about when the option loses its value, and the curve answers it.
What the interviewer asks next
What is a one-month at-the-money call worth on the same basis?
If volatility doubles, what happens to the one-year call's value?
Why do many option sellers prefer to sell one-month options rather than one-year options?
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?Wealth business economicsCorePrivate 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 relationship
$\text{Blend} = \frac{0.01 \times 10 + 0.006 \times 20 + 0.004 \times 15}{45} = \frac{0.28}{45} = 0.622\%$
10, 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?
027A client runs a Rs 10,000 monthly SIP for 20 years and earns 1% a month. Roughly how big is the corpus at the end, and what share of it is his own money against growth?Compounding and doublingCoreMutual fund distributionIndian wealth management
Try it first
Quick instinct: roughly what share of the final corpus is growth rather than his own contributions?
Show the worked solution
About Rs 1 crore, of which only Rs 24 lakh is his own money. 240 instalments of Rs 10,000 make Rs 24 lakh. At 1% a month, invested at the start of each month, the corpus is Rs 99,91,479, about Rs 99.9 lakh. Growth is Rs 75.9 lakh, roughly 76% of the final pile. In a long SIP the compounding, not the saving, builds most of the corpus.
How do you get close to Rs 1 crore without a calculator?
Start with the growth factor. At 1% a month money doubles in about 70 months, the rule of 70. Twenty years is 240 months, about 3.4 doublings, so each rupee put in on day one grows roughly ten to eleven times; the exact figure is 10.89. The corpus of a level SIP is the instalment times (growth factor minus 1) divided by the monthly rate. That is 10,000 x (10.89 minus 1) / 0.01, close to Rs 99 lakh, and a little more if each instalment goes in at the start of the month.
The relationship
$FV = P \cdot \frac{(1+i)^n - 1}{i}\cdot(1+i) = 10{,}000 \times \frac{1.01^{240}-1}{0.01} \times 1.01$
P the monthly instalment, Rs 10,000
i the monthly return, 1%
n the number of instalments, 240
(1+i) the extra month of growth because each instalment is invested at the start of the month
What it says in wordsEvery instalment grows for the months it has left, and the corpus is the sum of all those grown instalments.
Rs 24 lakh of contributions becomes a corpus of about Rs 99.9 lakh, so growth supplies Rs 75.9 lakh. The growth share of the pile climbs from 27% at year 5 to 48% at year 10 and 76% at year 20, because the compounding arrives late.
Why does most of the growth arrive in the last few years?
Think of a mango tree planted every month. The saplings from the last year bear nothing yet; the trees from year one are fully grown. At year 10 the pile is about Rs 23.2 lakh; the next ten years add Rs 76.7 lakh, 3.3 times as much, although the client saves exactly the same amount in each decade. That is why stopping a SIP in year 12 to fund a car costs far more than the instalments skipped.
The limitation: 1% every month is a smooth assumption. Real equity returns arrive unevenly, and the order in which good and bad years land changes the final number. Say the corpus is an illustration of the mechanism, not a projection for the client.
Where candidates lose it
Candidates either multiply 24 lakh by a rough growth factor, treating every rupee as if it compounded for 20 years, or they give up and say the answer needs a spreadsheet. The first overstates the corpus several times over; the second fails the numeracy the question is testing.
Say the contributions first, then the growth factor from the rule of 70, then the annuity formula. Ending with the growth share is what turns the arithmetic into an adviser's point.
What the interviewer asks next
How much bigger is the corpus if the SIP runs 25 years instead of 20?
What monthly SIP gives Rs 1 crore in 15 years at the same rate?
Why is 1% a month slightly more than 12% a year?
029Product X takes a 3% commission upfront and nothing after. Product Y takes no upfront fee but a 1% trail every year on the value of the investment. Ignoring compounding, after how many years has Y cost the client more? And where does compounding move that break-even?Fee and cost dragCoreMutual fund distributionIndian wealth management
Try it first
Once you let the fees compound, what happens to the 3-year break-even?
Show the worked solution
Simple addition says 3 years; with compounding it is 3.03 years, almost unchanged. Three years of 1% equals the 3% upfront. Compounded, the trail leaves the client 0.99 to the power t of his no-fee wealth and the upfront leaves 0.97 of it forever. They meet where 0.99^t = 0.97, at 3.03 years. The market return cancels out, because both fees are a share of the same growing balance.
Why does the market return drop out?
A shopkeeper can take his cut as one slice of the cake at the start or as a thin slice every year. However much the cake rises, each fee is a fraction of whatever cake there is. An upfront fee leaves the client 97% of the wealth he would otherwise have had, for ever; a 1% trail leaves him 99% after one year, 98.01% after two, and 0.99^t after t years. The growth rate multiplies both sides equally, so it cancels when you compare them.
The relationship
$0.99^{\,t} = 0.97 \;\Rightarrow\; t = \frac{\ln 0.97}{\ln 0.99} = 3.03 \text{ years}$
0.99^t the share of no-fee wealth left after t years of a 1% trail
0.97 the share left after a one-time 3% upfront fee
What it says in wordsThe trail costs more once its compounded bite exceeds the one-time bite of the upfront fee.
The upfront fee costs a flat 3% of the client's no-fee wealth for ever, while the trail's cost rises from 1% after one year to 2.97% after three and crosses the flat line at 3.03 years. Counting rupees of trail paid instead, the dashed line, crosses early at about 2.5 years, which is the misleading version.
Where do candidates go wrong when they try to add compounding?
They count rupees. On Rs 100 in a market rising 10% a year, the trail rupees add up to Rs 3 after only about 2.5 years, because 1% of a growing balance is more rupees each year. Rupees paid at different dates are not comparable; the right yardstick is how much wealth the client ends with. On that yardstick the upfront fee also cost him the growth on the 3% that never got invested, and the two effects cancel almost exactly.
The practical reading for a distributor conversation: for a holding period under about three years the trail is cheaper; beyond it, the upfront structure is. The limit is that real products often combine both, and exit loads, switch costs and the quality of ongoing service are not in this sum.
Where candidates lose it
The first trap is stopping at 3 years when the interviewer explicitly asks about compounding. The second, more common, is claiming compounding makes the trail much more expensive much sooner, which comes from adding rupees paid in different years as if they were the same money.
Frame both fees as a share of the no-fee outcome. Then the answer is one line of logarithms, and saying that the market return cancels is the insight the question is fishing for.
What the interviewer asks next
What is the break-even if the upfront fee is 5% and the trail is 1%?
How does an exit load in year 1 change the comparison?
Why might a client rationally prefer the trail even for a long holding?
030A client's monthly spending is 40% on food and household items rising at 4% a year, 30% on rent and services rising at 8%, and 30% on school fees and healthcare rising at 12%. What is his personal inflation rate, and why might it differ from the headline index?Inflation and real returnCoreWealth management
Try it first
Before you calculate: what is his personal inflation rate?
Show the worked solution
His personal inflation rate is 7.6%. Weight each category's price rise by its share of his spending: 40% of 4 is 1.6, 30% of 8 is 2.4 and 30% of 12 is 3.6, which add to 7.6%. It differs from the headline index because the index weights a national average basket, heavy in food, while this household spends much more on schooling and healthcare, whose prices rise faster.
How is a personal inflation rate built?
Think of a monthly bill as a thali. If dal gets 4% dearer but dal is only a small part of the plate, it barely moves the bill; if the costliest item on the plate jumps, the whole bill jumps. An inflation rate is a weighted average: each item's price rise counts in proportion to its share of what you actually spend. The same rule builds the national index, only with national weights.
The client's 40, 30 and 30 split contributes 1.6, 2.4 and 3.6 points of inflation, adding to 7.6%, well above an illustrative 5% headline print. Over 20 years that gap turns a Rs 1 lakh monthly spend into Rs 4.33 lakh rather than Rs 2.65 lakh.
The relationship
$\pi_{\text{personal}} = \sum_i w_i\,\pi_i = 0.4(4) + 0.3(8) + 0.3(12) = 7.6\%$
w_i the category's share of monthly spending
\pi_i the category's own yearly price rise
What it says in wordsPersonal inflation is each category's price rise weighted by how much of the budget it takes.
Why does the gap matter for a financial plan?
Because the plan's target corpus is built from future spending. At 7.6% a year, today's Rs 1 lakh of monthly spending needs Rs 4.33 lakh in 20 years; at an illustrative 5% headline rate it would need only Rs 2.65 lakh. A retirement plan built on the headline number would come up about 39% short on the spending side. Affluent households tend to spend more on education, healthcare and services, which is why advisers often assume a higher inflation rate than the index for them.
The limitations are real. Weights shift as life changes: school fees end, healthcare grows in retirement. The category rates here are illustrative, and the current headline figure should be read from the official release, not assumed.
Where candidates lose it
The common slip is averaging 4, 8 and 12 to get 8%, ignoring that the categories are not equal shares of spending. A smaller group then fails the second half by saying the headline index is simply wrong.
The index is not wrong; it measures a different basket. Say that the difference comes from weights, then show what the gap does to a 20-year spending target.
What the interviewer asks next
When the children finish school, his basket becomes 55% food, 35% services and 10% healthcare. What is his inflation rate now?
What real return does his portfolio need to hold its purchasing power if it earns 10% nominal?
Which categories would you expect to dominate a retired couple's basket?
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
Try it first
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
Try it first
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
Try it first
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
Try it first
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?

10, 6	the number of open and closed schemes
14%, -2%	each group's average yearly return
16	all schemes the fund house launched

C_1y	the one-year at-the-money call, Rs 100
3/12	three months as a fraction of the year
C_3m	the three-month call, same stock and volatility

10, 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

P	the monthly instalment, Rs 10,000
i	the monthly return, 1%
n	the number of instalments, 240
(1+i)	the extra month of growth because each instalment is invested at the start of the month

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Why does the factsheet overstate the record?

Why not take the midpoint of 14% and minus 2%?

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Why the square root of time?

What does the curve mean for a client who sells options?

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Why is the answer not 0.4%?

What does the blend do as the client grows?

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How do you get close to Rs 1 crore without a calculator?

Why does most of the growth arrive in the last few years?

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Why does the market return drop out?

Where do candidates go wrong when they try to add compounding?

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How is a personal inflation rate built?

Why does the gap matter for a financial plan?

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

What could he safely spend instead?

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Why is a spread not free money?

What does the 1.3 points actually pay for?

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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?

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What exactly is the cover replacing?

Which assumptions move the answer most?

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