Mutual Fund Mastery puzzles, solved step by step

About Rs 4.1 lakh a day, taken inside the NAV. 1.5% of Rs 1,000 crore is Rs 15 crore a year; divided by 365 it is about Rs 4.11 lakh a day. The fund books that as a liability before striking the NAV, so each unit is worth a little less, about 0.21 paise a day at an NAV of 50. The investor never sees a deduction because the cost is already in the price.

If nothing is deducted, how is the fee paid?

Think of a restaurant that folds the service charge into the menu price instead of adding it to the bill. You pay it with every dish; you just never see a line saying so. A fund's expenses are charged to the scheme itself every day, so they reduce net assets and the NAV, and the investor pays through a slightly lower price per unit rather than a visible deduction. The number of units you hold never changes because of the fee.

How small is it per unit, and why does that matter?

At an NAV of 50, one day's share is 50 times 1.5% over 365, about Rs 0.0021, or 0.21 paise. Nobody notices a fifth of a paise a day, which is exactly why the expense ratio has to be read off the factsheet rather than felt in the account. Across a year it is 1.5% of the money, and it compounds as a drag like any other cost.

Two practical points complete the answer. Because assets change every day, the accrual is recomputed on each day's net assets rather than fixed at Rs 4.1 lakh. And the published returns of a fund are already after this cost, so a fair comparison with an index must use the fund's NAV returns against the index's total return. Expense ratio limits are set by regulation and change; confirm the current SEBI framework before quoting one.

1,968.406 units. Stamp duty of 0.005% on Rs 50,000 is Rs 2.50, so Rs 49,997.50 is actually invested. Divided by the NAV of 25.40, that is 1,968.4055, rounded to 1,968.406. The figure 1,968.504 divides the full Rs 50,000 by the NAV and ignores the duty; the 0.098 extra units are worth about Rs 2.49, the duty give or take rounding.

Why does the charge come off before the units are counted?

Think of buying petrol with a Rs 500 note when the pump adds a Rs 5 card fee: you get Rs 495 worth of litres, not Rs 500 worth. A purchase is converted to units only after any charge on the transaction is deducted, so the units equal the net amount divided by the NAV, not the gross amount. Here the charge is a stamp duty of 0.005%, as stated in the question; the rate is set by law and can change, so confirm the current rate before using it.

How do you do the division cleanly?

Work in two steps and check the gap. Fifty thousand over 25.40 is 1968.5039; the duty removes Rs 2.50, which at 25.40 is about 0.0984 of a unit, so the answer is 1,968.4055, shown as 1,968.406. Checking it that way tells you the difference between the two answers is exactly the duty converted into units, which is a useful sense check in any operations role.

Two practical points complete the answer. Which NAV applies depends on when the application and the money reach the fund relative to the cut-off time, so 25.40 is the NAV for the day the purchase qualifies, not necessarily the day it was submitted. And units are shown to three decimals on the statement; the exact rounding convention is set out in the scheme's documents, which is where an operations team would check it.

About Rs 95,000 before costs, and the trade itself pushes the premium down. The participant buys the underlying basket at Rs 245.60 a unit, swaps it for 50,000 new ETF units, and sells them at Rs 247.50, keeping Rs 1.90 a unit. That is a 0.77% premium on Rs 1.23 crore. Selling the new units adds supply, so the price falls towards NAV until the premium no longer covers costs.

Where does the profit come from?

Picture a sweet shop that sells a box of twelve laddoos for more than the twelve laddoos cost loose. Someone will buy loose laddoos, box them, and sell the boxes until the gap closes. An ETF unit is a box of shares, and when the box trades above the value of what is in it, the participant who can make new boxes earns the gap. Only authorised participantsLarge brokers or market makers allowed by the fund house to create and redeem ETF units in bulk, by exchanging baskets of the underlying shares. can make boxes, and only in creation-unit sizes, here 50,000 units.

Why does the premium shrink rather than persist?

Every round of the trade adds new units to the market, and that extra supply pushes the ETF price down towards the value of its basket. Buying the basket nudges the shares up a little too. The participant stops when the gap no longer pays for brokerage, taxes, impact and the risk of prices moving mid-trade. If those costs are 0.25% of the basket, about Rs 30,700, the net gain is about Rs 64,300, and the trade stops once the price is within about Rs 0.61 of NAV. The reverse trade works on a discount: buy units cheap, redeem them for the basket, sell the shares.

When does the mechanism fail to hold the price?

The arbitrage is only as good as the participants' ability to trade the basket. If the underlying shares are illiquid, or a market is shut while the ETF trades, or participants step back in a stressed market, premiums and discounts can stay wide for days. The iNAV is itself an estimate, refreshed every few seconds, so a small gap may be noise. The 0.25% cost is an assumption for the arithmetic; real costs depend on the basket.

She holds 10,000 main units at Rs 23.75, worth Rs 2,37,500, plus 10,000 segregated units valued at zero. The fund has 32 crore units; Rs 760 crore of healthy bonds over those units gives Rs 23.75. If 60% of the bond comes back, Rs 24 crore is spread over 32 crore segregated units, Rs 0.75 each, so she receives Rs 7,500. Her total is Rs 2,45,000 against Rs 2,50,000 before.

Why split the fund instead of simply marking the bond to zero?

Picture a housing society that lends money to a builder who then stops paying. If the society writes the loan off and lets members leave with their share of what is left, the members who leave first give up their slice of any money later recovered, and the ones who stay collect it all. A plain write-down hands the value of a future recovery to whoever is still in the fund when the cash arrives, not to whoever owned the fund when the loss happened. A segregated portfolioA separate pool, created on a credit event, that holds only the troubled bond. Everyone who held the fund that day gets matching units in it. fixes that by giving every holder on the day a separate, frozen claim on the bad bond.

Here the fund has Rs 800 crore at a NAV of Rs 25, so it has 32 crore units. The bond of Rs 40 crore moves out; Rs 760 crore of healthy bonds stays behind. Divide by the same 32 crore units and the main NAV is Rs 23.75. Her 10,000 units there are worth Rs 2,37,500, and she also receives 10,000 segregated units, valued at nothing today.

What does the recovery pay, and who would have got it without segregation?

A 60% recovery brings back Rs 24 crore. Spread across 32 crore segregated units it is Rs 0.75 a unit, so she receives Rs 7,500 whether or not she has since redeemed her main units. Without segregation, the same Rs 24 crore would land on whoever held the single fund on recovery day. Suppose half the units redeem at Rs 23.75 after the write-down: the recovery then lands on only 16 crore units, Rs 1.50 each. The holders who stayed collect Rs 15,000 per 10,000 units, double their fair share, and the holders who left get nothing.

Say the limit too. Segregation does not reduce the loss; she is still Rs 5,000 down on Rs 2,50,000. It only makes sure the loss and any recovery fall on the same people. Indian rules allow it only after a defined credit event such as a rating downgrade, with conditions set in SEBI circulars that should be checked before quoting them.

About Rs 1.68 lakh from the liquid fund, against about Rs 1.58 lakh from the overnight fund. Short-term fund income accrues daily, so it is amount x yield x days / 365: Rs 10 crore x 6.8% x 9 / 365 = Rs 1,67,671. At 6.4% it is Rs 1,57,808. The gap of about Rs 9,863 is what the treasurer is paid for accepting the liquid fund's small extra rate and credit risk.

How do you turn an annual yield into nine days of income?

A shopkeeper who rents a room for Rs 36,500 a year earns Rs 100 a day, and nobody would charge a guest for a nine-day stay by quoting the year. Yields are quoted per year, but liquid and overnight funds accrue income every calendar day, so the money earned is the yearly yield scaled by days over 365. Rs 10 crore at 6.8% earns Rs 18,630 a day; nine days is Rs 1,67,671. The overnight fund, at 6.4%, earns Rs 17,534 a day and Rs 1,57,808 over the same nine days.

Is the extra Rs 9,863 worth taking?

An overnight fundA debt fund that lends only for one business day at a time, mostly through overnight repo-style borrowing, so it carries almost no rate or credit risk. lends for one day at a time; a liquid fundA debt fund holding money market paper and short bonds that mature within about three months, so its NAV moves only slightly with rates and credit events. holds paper running out to about three months. The 0.4% yield gap is pay for that extra term and credit exposure, and over nine days it comes to Rs 9,863 on Rs 10 crore, about 0.01% of the money. A treasurer weighs that against the small chance of a mark-down in the liquid fund during the same nine days. For a company that needs every rupee back on day nine, the overnight fund's certainty can be worth more than Rs 9,863.

Two practical limits. Liquid funds in India can charge an exit load on very short holdings, and the cut-off times for same-day NAV decide which day's NAV applies, so check the scheme's current terms before working out a short stay. And the quoted yield is the portfolio's yield; the realised return depends on what happens to that paper over the nine days, so the figures above are estimates, not quotes.

2,333.333 units, and nobody gains or loses on the day. The holding is worth 1,000 x Rs 42, or Rs 42,000. Divided by B's NAV of Rs 18, that is 2,333.333 units, and 2,333.333 x Rs 18 is Rs 42,000 again. The swap ratio, 42 over 18, is 2.333 units of B per unit of A. A merger changes the unit count and the scheme, not the value held.

Why does a lower NAV not make scheme B cheaper?

Change a Rs 500 note into Rs 100 notes and you get five of them. You now hold more notes, but you are no richer. A NAV is the value of one unit, so the number of units you hold only means something when multiplied by the NAV; a merger at NAV swaps notes of one size for notes of another. Scheme B's Rs 18 NAV only says its units started at a lower price or have grown less since launch. It says nothing about whether B is cheap, good or bad.

So can a merger leave an investor worse off?

Not on the day of the swap, when both schemes are valued at their closing NAVs. What a merger can change is everything after the swap: a different portfolio, a different expense ratio, a different level of risk, and possibly a tax event. If scheme B charges more, holds riskier bonds or follows another strategy, the investor's future returns change even though the swap itself was fair. That is why investors in a scheme being merged are generally offered a window to exit without an exit load; confirm the current rules on how that window works before relying on it.

The three decimals are not decoration. Registrars in India commonly allot units to three decimal places, so the answer is 2,333.333 and not a rounded 2,333. Rounding down to whole units would take about Rs 6 from this investor, and across lakhs of folios that adds up, so fractional units exist precisely to keep the swap exact.

Rs 16,000: the redemption uses all 1,000 January units and 200 June units. The January units gain Rs 15 each, Rs 15,000; the 200 June units gain Rs 5 each, Rs 1,000. An average cost of Rs 25 gives Rs 12,000, because it spreads the cheap January units across units still held. It also loses the purchase dates, which decide each lot's holding period.

Which units does a redemption actually sell?

Think of a shop's milk shelf: staff push the oldest cartons to the front so they sell first. Under first-in-first-out, a redemption is matched against the oldest units still held, lot by lot, so each unit sold carries the price and the date of the purchase it came from. That is the convention commonly used for mutual fund units in India; confirm how it applies to the investor's own folio. Here the January lot of 1,000 goes first, and only then 200 from June.

Why does the average-cost figure mislead?

Because it pretends every unit cost Rs 25. The units actually sold were mostly the cheap January ones, so the true gain is higher now, Rs 16,000 against Rs 12,000. The total gain over the whole holding does not change, Rs 20,000 once all 2,000 units are sold at Rs 35; what changes is how much of it is counted now and how much later. The 800 units left have a cost of Rs 30 under first-in-first-out, Rs 24,000, not the Rs 20,000 an average-cost view would record.

The dates matter as much as the amounts. Suppose she redeems the following March and the line between short and long term is twelve months, an assumption here; confirm the current rule for the fund type. Then the January units are long term and the 200 June units short term, so the Rs 15,000 and the Rs 1,000 may be taxed differently. An average-cost view cannot even ask the question, because it has thrown away the dates. Registrars track every purchase as a separate lot for exactly this reason.