Portfolio Management puzzles, solved step by step

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  1. 055An open-ended fund holds Rs 500 crore of assets across 20 crore units, a NAV of Rs 25. Investors redeem Rs 50 crore. What happens to the NAV and to the number of units?Funds, ETFs and implementationWarm upMorningstarMumbai · 2025

    Try it first

    Straight after the redemption, what is the NAV?

    Show the worked solution

    The NAV stays at Rs 25; the units fall from 20 crore to 18 crore. Redemptions are paid at NAV, so Rs 50 crore buys back 2 crore units at Rs 25 each and those units are cancelled. The fund is left with Rs 450 crore of assets across 18 crore units, which is still Rs 25 a unit. A redemption shrinks the fund, not the value of each unit.

    Why does money leaving not lower the NAV?

    Think of a pizza cut into 20 equal slices. If two friends leave and take their slices with them, 18 slices remain, and each one is exactly as big as before. An open-ended fund cancels the units that are redeemed and pays out exactly what they were worth, so assets and units fall in the same proportion and the NAV per unit does not move. Rs 50 crore at Rs 25 a unit is 2 crore units cancelled, leaving Rs 450 crore across 18 crore units.

    Redemptions cancel units at NAV: the fund shrinks, the NAV does notBefore the redemptionAssets Rs 500 croreUnits 20 croreNAV = 500 / 20 =Rs 25After Rs 50 crore is redeemedAssets Rs 450 croreUnits 18 croreNAV = 450 / 18 =Rs 251 crore units, worth Rs 25 croreunits cancelled; Rs 50 crore paid out of the fund's assetsThe leaving investors take exactly what their units were worth, so the ones who stayare left with the same Rs 25 of assets behind each unit.
    Rs 50 crore of redemptions cancels 2 of the fund's 20 crore units at Rs 25 each, so assets fall to Rs 450 crore and units to 18 crore, and the NAV is still Rs 25 a unit.
    The relationship
    NAV=assets−liabilitiesunits=500−5020−2=25\text{NAV} = \frac{\text{assets} - \text{liabilities}}{\text{units}} = \frac{500 - 50}{20 - 2} = 25
    assetsthe market value of everything the fund holds, Rs crore
    unitsunits outstanding, crore
    2units cancelled, 50 divided by the NAV of 25
    What it says in wordsTake the same amount off the top and the bottom in the same proportion, and the ratio does not change.

    So what does a redemption change?

    Two things, both real. First, the manager must raise the Rs 50 crore, usually by selling holdings, and the transaction costsBrokerage, taxes and the price impact of selling, paid out of the fund when it trades. of those sales are paid by the whole fund, including the investors who stayed. Large redemptions dilute the remaining investors through trading costs, not through the NAV arithmetic. Exit loads, where a scheme charges them and credits them back to the scheme, go the other way and cushion those who stay. Second, a fund that has to sell in a hurry may sell what is easiest to sell, which leaves the remaining portfolio less liquid than before.

    The day's NAV is the one used, struck after the market closes, which is why a redeeming investor cannot know the exact price when placing the request. The precise cut-off times and load rules are set by the regulator and the scheme documents, so confirm the current ones rather than quoting them from memory.

    Where candidates lose it

    The trap is answering Rs 22.50: dividing the smaller Rs 450 crore by the old 20 crore units. Candidates who think of NAV as a share price picture money leaving as bad news for the price. In a fund, the leavers take their units with them.

    The opposite miss, Rs 27.78, divides the old assets by the new unit count. Say it as one sentence: units are cancelled at NAV, so both halves of the ratio fall together.

    What the interviewer asks next

    • Who bears the cost when a large redemption forces the fund to sell illiquid holdings?
    • What happens to the NAV when new money comes in instead?
    • How does an ETF handle outflows differently from an open-ended fund?

    Asked at Morningstar, Private Markets, Mumbai, 2025 (Wall Street Oasis): They asked questions such as: What are derivatives? Can you explain NAV? What are ETFs?

  2. 080A fund turns over 120% of its portfolio a year, and each round trip, selling a holding and buying its replacement, costs 40 basis points. What is the annual drag on returns from trading?Funds, ETFs and implementationWarm upPortfolio implementationMutual funds

    Try it first

    What is the annual trading drag?

    Show the worked solution

    About 0.48% a year. Turnover of 120% means the fund sells and replaces the equivalent of its whole portfolio 1.2 times a year. At 40 basis points per round trip, the drag is 1.2 x 40, or 48 basis points. On a Rs 1,000 crore fund that is Rs 4.8 crore a year, taken from returns rather than charged as a fee.

    What exactly is a round trip, and why count it that way?

    Trading in a car costs you twice: the dealer pays less than it is worth when you sell, and charges more than it is worth when you buy the next one. A fund switching one stock for another pays the same two-sided cost, so the natural unit is the round trip: one sale and one purchase together. Reported turnover is usually the lesser of purchases and sales over average assets, which counts each switch once, so 120% maps to 1.2 round trips.

    Turnover becomes round trips, and round trips become basis points of returnTurnover a year1 full round trip+0.2 = 1.2 round tripsCost per round trip40 bp: spread, impact, brokerage and taxes on one sale plus one purchaseDrag a year40 bp+8 bp = 48 bp, or 0.48% a yearWhat the investor sees against what the investor pays, basis points a yearExpense ratio, say100 bp: on the factsheetTotal cost of ownership+48148 bp
    Turnover of 120% is 1.2 round trips a year at 40 basis points each, a 48 basis point drag; beside an assumed 1.00% expense ratio, the investor's true cost is 148 basis points, and the trading part never appears on the factsheet.
    The relationship
    drag=turnover×cost per round trip=1.2×40=48 bp\text{drag} = \text{turnover} \times \text{cost per round trip} = 1.2 \times 40 = 48 \text{ bp}
    turnoverportfolio replaced per year, 120%
    cost per round tripspread, market impact, brokerage and taxes on a sale and a purchase, 40 bp
    What it says in wordsMultiply how many times the portfolio is replaced by what one replacement costs.

    Why does this matter if the expense ratio looks fine?

    The expense ratio covers the manager's fee and running costs. Trading costs are paid inside the portfolio, through worse prices and brokerage, so they reduce the return without ever appearing in the expense ratio. A fund with a modest fee and high turnover can cost more in total than a pricier fund that trades little. For a Rs 1,000 crore fund, 48 basis points is Rs 4.8 crore a year.

    Say the limitation too. The 40 basis points is an average; impact rises with trade size, so a fund that grows while keeping the same turnover usually pays more per round trip, not less.

    Where candidates lose it

    The common slip is doubling the answer to 96 basis points on the grounds that turnover counts both the buy and the sell. The usual definition already counts each switch once, and the cost per round trip already includes both legs.

    The second slip is saying the cost is already in the expense ratio. It is not, and the interviewer asks precisely to see if you know where trading costs hide.

    What the interviewer asks next

    • The fund doubles in size and keeps the same turnover. What happens to cost per round trip?
    • How would you estimate a fund's trading costs from its published numbers?
    • Why do index funds usually have far lower turnover than active funds?