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.

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.

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.

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.