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Portfolio Management puzzles, solved step by step

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  1. 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?
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