Mutual Fund Mastery puzzles, solved step by step

Puzzles: 100
Traced to a firm: 29
Topics: 13
Hard: 30

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063Estimate how many full-time mutual fund distributors a district town of 5 lakh people can support. Build it from households, the share that invests, average fund assets and the trail income a distributor needs to make a living.Estimation and market sizingHardIndian AMCsDistribution and sales
Try it first
Which is the right place to start the estimate?
Show the worked solution
About 20 full-time distributors. Five lakh people in households of four is 1,25,000 households. If 12% invest Rs 3 lakh each, the town holds Rs 450 crore. Suppose half comes through distributors: Rs 225 crore, which at an assumed 0.8% trail pays Rs 180 lakh a year. A distributor needing Rs 9 lakh a year in gross trail means about 20 can live on it.
What actually limits the number of distributors?
Ask how many tailors a colony can support and you do not count the people; you count the stitching work and divide by what keeps one tailor going. A distributor is paid from trail commissionA yearly commission paid to a distributor as a percentage of the client assets they hold in a fund, for as long as the money stays invested., so the town's capacity is the trail pool divided by one livelihood, not the population divided by some ratio of advisers to people. That tells you the order of the chain before you guess a single number: people, then households, then investors, then assets, then the share that pays a distributor, then the trail.
Five lakh people become 1,25,000 households, 15,000 investing households and Rs 450 crore of fund assets, of which Rs 225 crore through distributors pays a trail pool of Rs 180 lakh a year, enough for about 20 full-time distributors at Rs 9 lakh each.
How do you defend each guess, and which one moves the answer most?
Say each assumption with a reason. Four people to a household is a fair Indian average. Twelve percent of households holding funds is a cautious guess for a district town. Rs 3 lakh is a modest balance once systematic plans have run a few years. Half through distributors leaves the rest to direct plans, apps and bank branches. Trail rates vary by scheme and over time, so 0.8% is an assumption to confirm. The answer is a product of guesses, so a change in any one moves it in proportion: halve the trail and the town supports half as many.
Change one input Distributors supported
Base case 20
Trail 0.5% instead of 0.8% 12.5
20% of households invest instead of 12% 33.3
Each needs Rs 18 lakh instead of Rs 9 lakh 10
Each row changes one assumption from the base case and leaves the rest alone.
Close with the sanity check and the limit. Twenty distributors for 15,000 investing households is about 750 families each, which is a full book for one person with a small office. In reality many towns have far more registered distributors than this, because most are part-time, also sell insurance or deposits, or work for a bank, so their fund trail is only part of their income. The estimate sizes the full-time capacity, not the head count on a register.
Where candidates lose it
The common loss is starting from the population and dividing by an invented ratio of advisers to people. That produces a number with no economics behind it, and the interviewer cannot check any step.
The second is giving one number with no sensitivity. Say which assumption you are least sure of, usually the trail rate or the share that invests, and show how the answer moves when it changes.
What the interviewer asks next
How would the answer change if the town's investors move steadily to direct plans?
Estimate the same town's total yearly flow into systematic investment plans.
Why might an AMC still want a branch in a town that supports only 20 full-time distributors?
093Passive funds tracking an index hold an assumed Rs 50,000 crore. A stock is added to the index at a weight of 1.2%, and it trades about Rs 250 crore a day. How much must the passive funds buy, and how many days of the stock's trading is that?Estimation and market sizingHardPassive and index teamsIndian AMCs
Try it first
How many days of the stock's normal trading does the passive buying equal?
Show the worked solution
About Rs 600 crore, or 2.4 days of the stock's entire trading. Passive funds must hold the stock at its index weight: 1.2% of Rs 50,000 crore is Rs 600 crore. Against Rs 250 crore of daily trading, that is 2.4 days of every share traded, and they want to own it by the day the change takes effect. If they took only a quarter of each day's volume, the buying would take about 9.6 days.
Why is index buying forced rather than optional?
Picture a school that announces every student must own a particular textbook by Monday, and the only shop stocks a few dozen copies a day. The shopkeeper knows exactly how many will be needed and by when. An index fund has no view on the stock; its job is to hold every stock at its index weight, so when a stock enters the index, every passive fund tracking it must buy, in a known amount, by a known date. That predictability is what makes inclusion a trading event, not just a news item.
Passive funds holding Rs 50,000 crore must buy Rs 600 crore of a stock entering at a 1.2% weight, which is 2.4 days of all its trading at Rs 250 crore a day, and about 9.6 days if they take only a quarter of each day's volume.
How do you size it, and why measure it in days?
The rupee amount is just the weight times the passive money: 0.012 x Rs 50,000 crore is Rs 600 crore. On its own that number means little, because Rs 600 crore is trivial in one stock and enormous in another. Dividing by daily traded value turns it into a measure of difficulty: 2.4 days means the funds must buy every share traded for more than two full days, which nobody can do without pushing the price up. A desk usually assumes a buyer can take only a fraction of the day's volume quietly; at a quarter, the job takes about 9.6 days.
The relationship
$\text{Days} = \frac{w \times AUM}{ADV} = \frac{0.012 \times 50{,}000}{250} = 2.4$
w the stock's weight in the index, 1.2%
AUM money in funds tracking the index, Rs 50,000 crore, an assumption
ADV average daily traded value of the stock, Rs 250 crore
What it says in wordsForced buying in rupees, divided by what trades in a day, gives the number of days of all trading the funds need.
Who positions for it, and what does the estimate leave out?
Traders who expect the inclusion buy ahead of the effective date and sell to the index funds on it, so part of the price move usually happens before the passive funds trade at all. The passive funds also pay for the purchase by selling a slice of every other stock, about Rs 600 crore spread across the rest of the index, which barely registers in each. The estimate leaves out active funds that hug the same benchmark and buy for similar reasons, which makes the real demand larger, and it assumes the weight is set by the stock's full market value; index providers commonly weight by the shares freely available for trading, so check the actual weight before relying on the size.
Where candidates lose it
Candidates compute Rs 600 crore and stop. The rupee figure is the easy half; the interviewer wants it set against liquidity, because Rs 600 crore tells you nothing until you know whether the stock trades Rs 25 crore a day or Rs 2,500 crore.
The second slip is assuming the funds can simply take all the volume. Say that a buyer can only take part of each day's trading without moving the price, and that traders front-run the known demand.
What the interviewer asks next
The stock is removed from the index instead. Who is on the other side of the passive selling?
Passive assets double over five years. What happens to the days-of-volume figure for the same stock?
Why might a stock rise after the inclusion is announced but fall back after the effective date?

Change one input	Distributors supported
Base case	20
Trail 0.5% instead of 0.8%	12.5
20% of households invest instead of 12%	33.3
Each needs Rs 18 lakh instead of Rs 9 lakh	10

w	the stock's weight in the index, 1.2%
AUM	money in funds tracking the index, Rs 50,000 crore, an assumption
ADV	average daily traded value of the stock, Rs 250 crore

Try it first

What actually limits the number of distributors?

How do you defend each guess, and which one moves the answer most?

Where candidates lose it

What the interviewer asks next

Try it first

Why is index buying forced rather than optional?

How do you size it, and why measure it in days?

Who positions for it, and what does the estimate leave out?

Where candidates lose it

What the interviewer asks next