Mutual Fund Mastery puzzles, solved step by step

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

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012A client needs Rs 2 lakh. He holds fund A, bought for Rs 4 lakh and now worth Rs 5.2 lakh, up 30%, and fund B, bought for Rs 4 lakh and now worth Rs 3 lakh, down 25%. He wants to sell A to lock in the profit. Using an assumed 12.5% tax rate on gains, compare selling A with selling B.Behavioural trapsCoreWealth and advisoryDistribution and sales
Try it first
On tax alone, how far apart are the two choices?
Show the worked solution
Selling B is cheaper on tax by up to about Rs 14,103, and the right question is which fund he would buy today. Rs 2 lakh of A carries a gain of Rs 46,154, so Rs 5,769 of tax at the assumed 12.5%. Rs 2 lakh of B carries a loss of Rs 66,667: no tax, and a loss that can offset other gains. The urge to sell the winner is the disposition effect.
Why does selling the winner feel right?
Picture someone clearing out a wardrobe who gives away the shirts he likes and keeps the ones that never fit, because giving those away would admit the purchase was a mistake. The disposition effect is the habit of selling what has gone up to enjoy the gain and holding what has gone down to avoid the regret, and it decides on the past price rather than on the future. The purchase price of each fund is a fact about the client, not about the funds.
How much does the instinct cost in tax?
Only the gain inside the units sold is taxed. A is worth 1.3 times its cost, so 0.3 over 1.3, about 23%, of any rupee sold is gain: Rs 46,154 on Rs 2 lakh, and Rs 5,769 of tax at the assumed 12.5%. B is worth 0.75 times its cost, so every Rs 2 lakh sold realises a loss of Rs 66,667, pays nothing now and can be set against other gains, worth up to Rs 8,333 at the same rate. The full swing between the two is up to Rs 14,103.
Raising Rs 2 lakh from the winner costs Rs 5,769 of tax at an assumed 12.5%, while raising it from the loser costs nothing and leaves a loss worth up to Rs 8,333 against other gains, a swing of up to Rs 14,103.
The relationship
$\text{Gain in sale} = S\times\frac{V-C}{V} = 2 \times \frac{0.3}{1.3} = 0.4615 \text{ lakh},\qquad \text{Loss} = 2 \times \frac{0.25}{0.75} = 0.6667 \text{ lakh}$
S the amount sold, Rs 2 lakh
V the current value per rupee of cost: 1.3 for A, 0.75 for B
C the cost per rupee of cost, 1
What it says in wordsThe share of a sale that is gain, or loss, equals the share of today's value that sits above, or below, the cost.
Is tax the whole answer?
No, and saying so is what earns the marks. The test that cuts through the feeling is this: if the client held only cash today, would he buy A, B, or neither in these amounts? If B fell because its strategy has stopped working, selling it fixes the portfolio and saves tax. If B fell with its whole category and A has simply had a good run, the portfolio question is about weights and concentration, not about which one he feels good selling.
State the limits. The 12.5% rate is an assumption for the arithmetic; real rules distinguish short and long holding periods, can carry exemption thresholds, and restrict which gains a loss may be set against. Confirm the current rules before using any rate with a client. And this is a framework for a conversation, not an instruction about any real fund.
Where candidates lose it
The common slip is computing tax on the whole Rs 2 lakh, Rs 25,000, as if the sale proceeds were all profit. Only the gain inside the units sold is taxed, and on A that is under a quarter of the proceeds.
The deeper slip is agreeing with the client because locking in profit sounds prudent. The interviewer is checking whether you notice that the decision is being made on purchase prices, and whether you can redirect it to the question of which holding deserves the money today.
What the interviewer asks next
How would the answer change if fund B were down only 2%?
What is the disposition effect's mirror image when markets are rising fast?
How would you raise this with a client who is proud of fund A's gain?
046An investor put Rs 1 lakh into an equity fund at NAV 100. The NAV is now 60 and he adds another Rs 1 lakh. What is his new average cost, what rise does he need to break even, and does averaging down make the fund any better?Behavioural trapsCoreWealth and advisoryDistribution and sales
Try it first
What is his average cost per unit after the second purchase?
Show the worked solution
His average cost is Rs 75 a unit and he needs a 25% rise from 60 to break even, but the fund is no better than before. Rs 1 lakh bought 1,000 units at 100 and 1,667 units at 60, so Rs 2 lakh buys 2,667 units, Rs 75 each. Before the top-up he needed 66.7%. Averaging down moves the break-even point, not the fund's prospects, and it doubles the money exposed to the next move.
Why is the average 75 and not 80?
Spend Rs 100 on mangoes at Rs 100 a kilo and another Rs 100 at Rs 60 a kilo. You have 1 kilo plus 1.67 kilos, 2.67 kilos for Rs 200, which is Rs 75 a kilo. Equal rupees buy more units when the price is low, so the average cost leans towards the lower price; it is the harmonic mean of the two NAVs, not the simple average. That is the same arithmetic that makes rupee-cost averaging in an SIP work, applied here to two purchases.
Each Rs 1 lakh is a rectangle of units times NAV: 1,000 units at 100 and 1,667 units at 60. Together they average Rs 75 a unit, so the break-even rise from 60 falls from 66.7% to 25%, while the rupees at stake double to Rs 1.6 lakh.
The relationship
$\bar{c} = \frac{\text{Rs }2{,}00{,}000}{\frac{1{,}00{,}000}{100} + \frac{1{,}00{,}000}{60}} = \frac{2}{\frac{1}{100} + \frac{1}{60}} = 75 \qquad \frac{75}{60} - 1 = 25\%$
\bar{c} average cost per unit
100, 60 the two NAVs paid
What it says in wordsWith equal rupees at each price, the average cost is the harmonic mean of the prices, and the break-even rise is that cost over today's NAV, less one.
Does a lower break-even mean the decision was good?
No, and this is the behavioural point. The break-even number is about his purchase history; the fund's next move does not know or care what he paid. His position today is 2,667 units worth Rs 1.6 lakh, with an unrealised loss of Rs 40,000, the same loss he had before the top-up. A further 10% fall now costs Rs 16,000 instead of Rs 6,000. The question that decides whether to add is whether he would buy this fund today at 60 with fresh money if he had never owned it, given his goal and his allocation.
There are good reasons to add after a fall: a disciplined rebalance back to a target equity weight, or an SIP that keeps running through the dip. There are bad ones: wanting to feel closer to breaking even, or refusing to accept that the first purchase was a mistake. The arithmetic is the same in both cases; only the reason differs, and the adviser's job is to ask which one it is.
Where candidates lose it
The fast wrong answer is 80, the average of the two prices. It treats the purchases as equal units when they were equal rupees. Count the units first and the 75 follows.
The bigger trap is the second half of the question. Candidates who get 75 and 25% often present averaging down as a fix. The interviewer wants to hear that it changes the break-even, not the quality of the fund, and that it raises the money at risk.
What the interviewer asks next
If he had added Rs 2 lakh at 60 instead of Rs 1 lakh, what would his average cost be?
When is adding to a falling fund a sound decision?
How is this different from an SIP buying through the same fall?
062Choice 1: a sure Rs 50,000, or a 50% chance of Rs 1.2 lakh. Choice 2: a sure loss of Rs 50,000, or a 50% chance of losing Rs 1.2 lakh. Most people take the sure gain and gamble on the loss. Which choices maximise expected value, and what does that common pattern do to a portfolio?Behavioural trapsCoreWealth and advisoryDistribution and sales
Try it first
Which pair of choices has the higher expected value?
Show the worked solution
Expected value says take the coin toss on the gain and the sure loss, the opposite of what most people do. The toss is worth Rs 60,000 against a sure Rs 50,000; on losses it costs Rs 60,000 against Rs 50,000. Combined, the popular pair gives +Rs 50,000 or -Rs 70,000, which is worse in every outcome than +Rs 70,000 or -Rs 50,000. In a portfolio the same pattern sells winners early and holds losers.
What does expected value say for each choice?
Weight each outcome by its probability and add. In choice 1 the coin toss is worth 0.5 x Rs 1,20,000 = Rs 60,000, Rs 10,000 more than the sure thing. In choice 2 the toss costs 0.5 x Rs 1,20,000 = Rs 60,000, Rs 10,000 worse than the sure loss. So a person who maximises expected value gambles on the gain and accepts the loss, and most people do the reverse. Taking a sure Rs 50,000 is defensible on its own if the person cannot afford to walk away with nothing; the oddity is the switch to gambling the moment the frame becomes a loss.
Most people take the sure gain and gamble on the loss, which combines into +Rs 50,000 or -Rs 70,000, while the expected value choices combine into +Rs 70,000 or -Rs 50,000, better in both outcomes.
Why is the popular pair worse in every outcome, not just on average?
Put the two choices together, because in real life they arrive together. The popular pair, sure +50,000 plus the loss gamble, ends at +50,000 if the toss goes well and -70,000 if it goes badly. The expected value pair, the gain gamble plus the sure loss, ends at +70,000 or -50,000. The second pair beats the first by Rs 20,000 whichever way the coin falls, so the popular choice is not a matter of taste; it is a mistake caused by judging each choice in its own frame. This is the pattern Kahneman and Tversky described in prospect theoryA description of how people actually choose under risk: they judge outcomes as gains or losses from a reference point and feel losses more sharply than equal gains..
Now the portfolio. A stock up 30% is a gain, so the investor wants the sure thing and sells. A stock down 30% is a loss, so the investor prefers to gamble on a recovery and holds. This is the disposition effectThe habit of selling investments that have risen too early and holding investments that have fallen too long., and it leaves a portfolio full of its weakest holdings while the strongest have been cashed out. The same pull shows up in fund redemptions: investors exit a fund that has done well to lock in the gain and stay in one that has done badly to avoid booking a loss. The limit of the lesson: expected value ignores how much a person can bear to lose, and for a large loss relative to wealth a sure thing can be the right choice.
Where candidates lose it
The trap is defending the popular answer as risk aversion. Risk aversion would mean taking the sure thing in both choices; switching to the gamble on losses is a different thing, and the interviewer wants you to name the switch.
The second miss is stopping at expected value. Join the two choices into one set of outcomes and show that the popular pair loses in every state; that is what turns a preference into an error.
What the interviewer asks next
How would you explain the disposition effect to a client who refuses to sell a fund down 40%?
Change the gamble to a 50% chance of Rs 1 lakh. Does the expected value answer change?
What portfolio rule would stop an investor from holding losers too long?
097A client keeps Rs 5 lakh in a fixed deposit at 7% as an emergency fund while carrying Rs 2 lakh of credit card debt at 36% a year. What does this arrangement cost her each year, and why do so many people do it?Behavioural trapsCoreWealth and advisoryDistribution and sales
Try it first
Roughly what does holding both cost her a year, before tax?
Show the worked solution
About Rs 58,000 a year before tax, and more after it. On the matching Rs 2 lakh she pays 36%, Rs 72,000, while that slice of the deposit earns 7%, Rs 14,000. Clearing the card from the deposit saves the difference, and leaves Rs 3 lakh in the emergency fund. People keep both because they treat the deposit and the debt as separate pots with separate jobs, when money is interchangeable.
Why does holding both cost money?
Imagine filling a bucket at 7 litres a minute while a hole at the bottom drains 36. Keeping the tap on does not save the water; plugging the hole does. Savings and debt in the same household net against each other: Rs 2 lakh in the deposit and Rs 2 lakh owed on the card leave her net worth exactly where it would be with neither, except that one pays her 7% and the other charges her 36%. Her net worth is Rs 3 lakh whichever way she arranges it; the only thing the arrangement changes is the interest bill.
On the matching Rs 2 lakh she pays Rs 72,000 a year on the card and earns Rs 14,000 on the deposit, so keeping both costs about Rs 58,000 a year before tax and about Rs 62,200 after an assumed 30% tax on the deposit interest.
The relationship
$\text{Cost} = D \times (r_{card} - r_{FD}) = 2{,}00{,}000 \times (36\% - 7\%) = 58{,}000$
D the debt that the deposit could repay, Rs 2 lakh
r_{card} the card's interest rate, 36% a year
r_{FD} the deposit rate, 7% a year
What it says in wordsThe yearly cost is the overlap between savings and debt times the gap between the two rates.
Why do sensible people do it anyway?
Because people keep money in mental pots with labels, an idea behavioural economists call mental accounting. The deposit is labelled 'emergency', and spending it feels like breaking a promise; the card is labelled 'monthly spending', and its balance feels like a bill to be dealt with later. There is a real worry underneath too: if she empties the deposit, where does the money come from in a crisis? The answer is that once the card is cleared, its unused limit is itself an emergency line, and she still has Rs 3 lakh in the deposit.
Say what the simple figure leaves out. Deposit interest is taxed, so at an assumed 30% slab she keeps only Rs 9,800 of the Rs 14,000, and the cost rises to about Rs 62,200. Card interest is usually charged monthly, which makes 36% a year closer to 43% when compounded. Every refinement makes holding both more expensive, not less, which is why this is among the cheapest wins an adviser can find. Confirm the client's actual tax slab and card terms before quoting her a figure.
Where candidates lose it
Candidates quote Rs 72,000, the card interest alone, which forgets that clearing the card means giving up the deposit's interest on the same money. The true saving is the gap between the two rates.
The other loss is answering only the arithmetic. The question asks why people do it, and the interviewer wants mental accounting named, along with the real concern about emergencies and how to address it.
What the interviewer asks next
She worries she will run up the card again after clearing it. How would you respond?
What if the debt were a home loan at 8.5% rather than a card at 36%?
How would you explain this to a client without making her feel foolish?

S	the amount sold, Rs 2 lakh
V	the current value per rupee of cost: 1.3 for A, 0.75 for B
C	the cost per rupee of cost, 1

\bar{c}	average cost per unit
100, 60	the two NAVs paid

D	the debt that the deposit could repay, Rs 2 lakh
r_{card}	the card's interest rate, 36% a year
r_{FD}	the deposit rate, 7% a year

Try it first

Why does selling the winner feel right?

How much does the instinct cost in tax?

Is tax the whole answer?

Where candidates lose it

What the interviewer asks next

Try it first

Why is the average 75 and not 80?

Does a lower break-even mean the decision was good?

Where candidates lose it

What the interviewer asks next

Try it first

What does expected value say for each choice?

Why is the popular pair worse in every outcome, not just on average?

Where candidates lose it

What the interviewer asks next

Try it first

Why does holding both cost money?

Why do sensible people do it anyway?

Where candidates lose it

What the interviewer asks next