Mutual Fund Mastery puzzles, solved step by step

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.

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.

They gain exactly the same: Rs 20,000 each. Rs 1 lakh buys 10,000 units at Rs 10 or about 555.6 units at Rs 180. The same portfolio rising 20% lifts the NAVs to Rs 12 and Rs 216. Both holdings are worth Rs 1.2 lakh. A low NAV is not cheap and a high NAV is not expensive: what you earn is a percentage of the money you put in.

Why does a Rs 10 unit feel cheaper than a Rs 180 unit?

A pizza cut into twelve slices is not more pizza than the same pizza cut into four. Each slice is smaller, that is all. An NAV is the fund's portfolio value divided by the number of units in issue, so a lower NAV means the same money is cut into more, smaller slices. The instinct that Rs 10 is cheap comes from shares, where a low price is also misleading, and from shopping, where a lower price usually buys the same thing for less. Here it buys a smaller slice of the same thing.

What actually decides the gain?

Only the portfolio. A fund's return is the percentage change in its NAV, and the NAV moves by exactly the percentage the portfolio moves, less costs, whatever level it starts from. An NAV of 180 means the older fund has grown eighteen-fold since its own launch at 10; it tells you about the past and nothing about the next move. Two funds holding the same portfolio at the same cost will deliver the same return from here.

Is there any real difference between the two funds?

Yes, but none of it is about the NAV level. A new fund has no track record, may take weeks to deploy the money it raises, and may carry a different expense ratio. An older fund may be larger, which matters in small caps. Those are real reasons to prefer one or the other. A lower NAV is not one of them, and saying so plainly is what the interviewer is listening for.

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.

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.

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.

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.

52%, the same as on any other day. If each day's move is independent, the five falls carry no information about tomorrow. A run of five falls was unlikely before it began, 0.48 to the fifth power or about 2.5%, but that probability belonged to days that are now finished. Believing a rise is due is the gambler's fallacy.

Why does the streak not make a rise more likely?

A captain who has lost five tosses in a row walks out for the sixth feeling owed a win. The coin has no record of the first five and no sense of fairness to restore; it is still 50:50. Independence means past outcomes do not enter the calculation for the next one, so tomorrow's chance of a rise is the 52% it always was. The feeling that things must even out is real, and it has a name: the gambler's fallacy. It is strongest exactly when a streak is long, which is when it does the most damage to decisions.

Where does the tiny probability come from, and why is it the wrong number?

It answers a different question. Standing on Monday morning, the chance of five falls in a row was 0.48 multiplied by itself five times, about 2.5%, and the chance of six in a row was about 1.2%, roughly one in 82. Once five falls have happened, the only uncertainty left is tomorrow, and for independent days the chance of a rise given the streak equals the chance of a rise on any day. Six falls in a row is rare only when viewed from the start; viewed from Friday evening, it needs just one more fall.

Is the independence assumption true for real markets?

Not exactly, and saying so earns credit. Day-to-day direction in a broad index is very hard to predict from the previous days, but the size of moves does cluster: a run of falls often comes with bigger swings, so tomorrow's move may be larger even if its direction is a near coin toss. For an adviser the danger is not the arithmetic but the conversation: a client who believes a bounce is due will add money for the wrong reason, or hold out for a rebound the odds do not promise. A streak on its own is not a reason to act; any case for investing has to rest on the client's plan and horizon, not on the last five days.

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.

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.