Debt Capital Markets puzzles, solved step by step

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  1. 093A Rs 1,000 crore fund charges a 2% management fee and a 20% performance fee on returns above fees, and earns a 10% gross return. Investors push the management fee down to 1.5%. What performance fee rate keeps the manager's revenue the same?Compounding, PIK and feesCoreTwo SigmaNew York · 2026

    Try it first

    Roughly what performance fee replaces the lost 0.5%?

    Show the worked solution

    A performance fee of about 24.7%. Today the manager earns Rs 20 crore of management fee plus 20% of the Rs 80 crore return after fees, Rs 16 crore, for Rs 36 crore. At 1.5% the fixed fee is Rs 15 crore and the return after fees rises to Rs 85 crore, so the performance fee must bring Rs 21 crore: 21 / 85 = 24.7%. The swap is exact only at a 10% gross return.

    Why does the performance fee base change?

    Think of a salesperson paid a fixed salary plus a share of profit after salary. Cut the salary and the profit after salary goes up, so the share needed to make up the difference is smaller than a straight swap would suggest. The performance fee is charged on the return left after the management fee, so lowering the management fee enlarges the base the performance fee is charged on. That is why the answer is 24.7%, not 25%.

    Same revenue at 10%, different revenue anywhere elsefixed 20perf 16362% and 20%fixed 15perf 21361.5% and 24.7%5% gross10% gross15% grossold 26.0new 23.6new 48.4old 46.0equal at 36Revenue, Rs crore, by gross return
    At a 10% gross return both fee terms pay the manager Rs 36 crore, but at 5% the old terms pay 26.0 against 23.6 and at 15% the new terms pay 48.4 against 46.0, so the trade shifts revenue from weak years to strong ones.
    The relationship
    15+x (100−15)=20+0.20 (100−20)  ⇒  x=36−1585=24.7%15 + x\,(100 - 15) = 20 + 0.20\,(100 - 20) \;\Rightarrow\; x = \frac{36 - 15}{85} = 24.7\%
    100the 10% gross return on Rs 1,000 crore, in Rs crore
    15, 20the new and old management fees, Rs crore
    xthe new performance fee rate
    What it says in wordsSet the new fixed fee plus the new share of the bigger base equal to today's total.

    Is the manager really indifferent?

    Only at a 10% gross return. At 5% gross, the old terms pay Rs 26.0 crore and the new pay Rs 23.6 crore; at 15%, the old pay Rs 46.0 crore and the new Rs 48.4 crore. Swapping fixed fee for performance fee moves the manager's revenue out of weak years and into strong ones, so the trade depends on the return you assume. Investors who push for it pay less when things go badly and more when they go well, which is often exactly what they want. A real fund would also have a hurdle rate, a high-water mark and fees charged on average rather than opening assets; each changes the arithmetic, not the logic.

    Where candidates lose it

    The common answer is 25% or 22.5%, from treating the two fees as if they sat on the same base. The management fee is on assets and the performance fee is on return after fees, so moving one changes the base of the other.

    The second loss is saying the new terms are equivalent. They are equal at one assumed return only; say so, and give the 5% and 15% cases to show which way the risk moved.

    What the interviewer asks next

    • What performance fee keeps revenue the same if the assumed gross return is 15%?
    • The fund adds a 5% hurdle, with performance fee only on returns above it. How does that change the answer at 10%?
    • From the investor's side, which fee terms would you prefer in a year you expect to be weak, and why?

    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