Private Wealth Management puzzles, solved step by step

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.

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%.

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.

About Rs 7.2 crore a year. Assume 6 relationship managers, each covering 25 client families: 150 families. At Rs 6 crore of assets each, the branch manages Rs 900 crore. A blended revenue yield of 0.8% across fees, commissions and lending gives Rs 7.2 crore. A top-down check on the client count lands at 160 families, which supports the build.

Where do you start the build?

Think of estimating a local restaurant's takings: tables, covers per table, spend per head. Nobody guesses the total first. Build revenue from counts and rates you can picture, so each assumption can be challenged and fixed without redoing the whole estimate. For a wealth branch the natural chain is relationship managers, families per manager, assets per family and the revenue the bank earns on those assets.

How do you check the estimate a second way?

Rebuild the weakest link from a different direction. The client count is the shakiest number, so check it top down: 8 lakh households, 1 in 1,000 with more than Rs 5 crore to invest, and a 20% share for this branch gives 160 families against 150. Every figure in that chain is an assumption too, stated as one. Then sense-check the output: Rs 1.2 crore of revenue per relationship manager has to cover that manager, the team behind him and the branch, which tells you whether the bank would keep the branch open.

Give the sensitivity before you are asked. The blended yieldTotal revenue from a book divided by the assets in it, mixing fees, commissions, spreads and lending income into one rate. is the most uncertain link: at 0.6% revenue is Rs 5.4 crore, at 1% it is Rs 9 crore. A book heavy in advisory mandates and lending earns more per rupee than one parked in low-fee products, so the product mix moves the answer as much as the client count.

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.

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.

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.

Rs 30 of the remaining Rs 70. After the gap the shares are worth Rs 70 against a Rs 50 loan, a loan-to-value of 71.4%. Selling S of shares repays S of loan, so the lender needs 50 minus S to equal half of 70 minus S, which gives S = 30. The client is left with Rs 40 of shares, a Rs 20 loan and Rs 20 of equity, sold out near the low.

Why does the sale have to be so large?

Think of a bucket with a hole that you are emptying to lower the water to a mark painted halfway up its side, while the bucket itself shrinks as you pour. Every rupee of shares sold repays a rupee of loan but also removes a rupee of collateral, so the sale has to be twice the gap it closes. At a 50% target, each rupee sold lowers the required collateral by only 50 paise, which is why Rs 15 of excess loan needs Rs 30 of sales.

What does the forced sale cost the client if the price recovers?

It locks the loss in. If the stock climbs back to where it started, a rise of 42.9%, his Rs 40 of shares becomes Rs 57.1, and after the Rs 20 loan his equity is Rs 37.1. Had he not been sold out, the same recovery would have put him back at Rs 50 of equity, so the forced sale turned a temporary fall into a permanent loss of about Rs 12.9. A top-up of Rs 15 of cash would have restored the ratio without selling anything.

Say what a private banker does with this. Lending against shares is sized for gaps, not for daily moves: a lender may sell at the open before the client can respond. The cushion before a margin callA demand from the lender to add cash or collateral, or accept a sale, when the loan grows too large relative to the value of the pledged securities. and the cash the client can raise overnight matter more than the interest rate on the loan.

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.

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.

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.

Barely: the risk-adjusted excess, or alpha, is about 0.2%. The market premium was 12 minus 6, or 6 points. A beta of 1.3 earns 1.3 times that, 7.8 points, on top of the 6% risk-free rate, so the fund should have made 13.8% just by holding more market risk. It made 14%. Of the 2-point beat, 1.8 points were paid for by extra risk and 0.2 came from the manager.

Why is beating the index not the same as adding value?

Picture two drivers who both arrive early. One drove carefully and knew a shortcut; the other simply drove 30% faster on the highway. You would not call the second one a better navigator. A fund with a beta of 1.3 is the fast driver: in a rising market it is expected to beat the index simply because it carries more of the market's risk. The client paid for that extra speed with extra drawdown risk, and would have got it from any higher-beta fund.

So the fair yardstick is not the index but what the index would have paid at 1.3 times the risk. That is the capital asset pricing modelA model that says a portfolio should earn the risk-free rate plus its beta times the market premium, the market return less the risk-free rate. expectation, and whatever sits above it is called Jensen's alpha.

What would you tell the client, and what can one year not tell you?

Tell the client the fund did roughly what a higher-risk version of the index would have done, with a sliver on top. One year of 0.2 points of alpha is indistinguishable from noise; it takes several years and a stable beta before anyone can call it skill. Also say the mirror image: in a year the index falls 10%, the same 1.3 beta implies a fall of about 6 + 1.3 x (minus 16), or minus 14.8%, before any skill at all. The client should expect to feel that.

The limitation is the beta itself. It is estimated from past returns, it moves, and a different benchmark gives a different number. Say that you are treating 1.3 as given for the puzzle.

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.

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.

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.

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.

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.

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.

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.

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.