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  1. 087A fund charges 2 and 20 and earns a gross return of 12% on Rs 1,000 crore. Investors push the management fee down to 1%. What performance fee keeps the manager's total fee income unchanged at that return?Returns, compounding and feesCoreTwo SigmaNew York · 2026

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    What performance fee keeps the manager whole?

    Show the worked solution

    About 27.3%. At 2 and 20 the manager earns Rs 20 crore of management fee and 20% of the remaining Rs 100 crore gain, Rs 20 crore: Rs 40 crore in all. At 1%, the management fee is Rs 10 crore and the gain after it is Rs 110 crore. To keep Rs 40 crore the performance fee must bring in Rs 30 crore, which is 30/110, or 27.3%. The two deals match only at a 12% gross return.

    What does the manager earn today?

    Think of a tailor who charges a fixed stitching fee plus a share of whatever the finished suit sells for above cost. Cut the fixed fee and the share must rise to keep the same income, but the share now applies to a slightly larger base. At 2 and 20 on Rs 1,000 crore earning 12%, the manager takes Rs 20 crore of management fee plus 20% of the Rs 100 crore gain left after it, Rs 40 crore in total. Investors keep Rs 80 crore, a net return of 8%.

    Cutting the fixed fee enlarges the base the performance fee works onfee 20100 leftfor the share2 and 20fee 10110 leftfor the share1% and ?Gross gain: Rs 120 crore, 12% of 1,000fixed 20share 2020% x 10040Old: 2 and 20fixed 10share 3027.3% x 11040New: 1% and 27.3%Manager's income,Rs croreNew share = 30 / 110 = 27.3%
    Under 2 and 20 the manager's Rs 40 crore is Rs 20 crore fixed plus 20% of Rs 100 crore; under a 1% fixed fee it is Rs 10 crore plus 27.3% of Rs 110 crore, because the smaller fixed fee leaves a larger gain for the performance fee.

    How do you find the new performance fee?

    Keep the total at Rs 40 crore. The management fee falls to Rs 10 crore, so the performance fee must bring in Rs 30 crore, and it is charged on a gain of Rs 110 crore, not Rs 100 crore. 30 divided by 110 is 27.3%. The base grows because less has been taken off the top before the performance fee is worked out. State the assumptions as you go: no hurdle rate, and no earlier losses to recover below a high-water markThe highest value an investor has paid a performance fee on; no new performance fee is charged until the fund climbs back above it..

    The relationship
    f=40−10120−10=30110=27.3%f = \frac{40 - 10}{120 - 10} = \frac{30}{110} = 27.3\%
    40the manager's total fee income under 2 and 20, Rs crore
    10the new 1% management fee, Rs crore
    120the gross gain, 12% of Rs 1,000 crore
    What it says in wordsThe new performance fee is the income still needed, divided by the gain left after the new management fee.

    Is the new deal really the same for investors?

    Only at a 12% gross return. The new deal pays the manager less in poor years and more in good ones, so it moves risk from the investors to the manager. At a 4% gross return the old deal pays Rs 24 crore and the new one Rs 18.2 crore; at 20% the old pays Rs 56 crore and the new one Rs 61.8 crore. That is why allocators push for a lower fixed fee even at the price of a higher share: they would rather pay for performance than for size.

    Gross return2 and 20, Rs crore1 and 27.3, Rs croreWho gains from the switch
    4%24.018.2Investors
    12%40.040.0Neither
    20%56.061.8Manager
    Manager's fee income on Rs 1,000 crore under each deal: the two match at a 12% gross return, the new deal pays Rs 5.8 crore less at 4% and Rs 5.8 crore more at 20%.

    Where candidates lose it

    The common slip is 30%: dividing the Rs 30 crore needed by the old Rs 100 crore base, forgetting that a smaller management fee leaves a larger gain for the performance fee to work on. The other is 25%, dividing by the gross Rs 120 crore.

    The second loss is stopping at 27.3% as though the two deals were identical. They match only at a 12% return, and the interviewer wants to hear who comes out ahead in good years and in bad ones.

    What the interviewer asks next

    • At what gross return does the manager prefer the new deal?
    • Add a 5% hurdle to the new deal. What performance fee keeps the manager whole now?
    • How does a high-water mark change what the performance fee is worth to the manager?

    Asked at Two Sigma, Equity Capital Markets, New York, 2026 (Wall Street Oasis): the 2/20 rule, and if one part of this equation changed, how would the other variable make up for it