Private Wealth Management puzzles, solved step by step

Puzzles
100
Traced to a firm
3
Topics
13
Hard
30
Topic
All topicsCompounding and doubling8Returns arithmetic9Fee and cost drag8Inflation and real return7Tax arithmetic7Probability and risk of loss9Retirement and withdrawal8Fixed income numeracy8Behavioural traps8Estimation and sizing8Options and structured products6Leverage and borrowing6Wealth business economics8
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Showing 1–2 of 2 · filtered from 100Clear filters
  1. 016A portfolio management service charges a 2% fixed fee plus 20% of returns above an 8% hurdle. In a year when the gross return is 15% on Rs 1 crore, what is the client's net return, and what share of the gross gain went in fees?Fee and cost dragHardIndian wealth management

    Try it first

    Pick the client's net return, with the performance fee charged on the return after the fixed fee.

    Show the worked solution

    The client nets 12%, and fees take 20% of the gross gain. The 2% fixed fee brings 15% down to 13%. That is 5 points above the 8% hurdle, and 20% of 5 points is a 1% performance fee. Net return is 12%, Rs 12 lakh on Rs 1 crore. Fees are Rs 3 lakh of the Rs 15 lakh gross gain. The exact order of fees is set by the agreement.

    Why do the two fees stack rather than sit side by side?

    Think of a restaurant bill with a fixed cover charge and then a service charge worked out on what is left. Each charge is modest on its own, but together they take a real share of the meal. The fixed fee is paid in every year, good or bad, and the performance fee then takes a slice of whatever is left above the hurdle, so in a good year the two stack. Here 2 points and 1 point together take a fifth of a 15% year.

    A 15% gross year on Rs 1 crore, after a fixed and a performance fee15.0%Gross-2.0%Fixed fee13.0%After fixed-1.0%Performance12.0%Net to client8% hurdle13 - 8 = 5 pointsx 20% = 1.0% feeOn Rs 1 croreGross Rs 15 lakhFees Rs 3 lakhNet Rs 12 lakhFees take 20%of the gross gain
    On Rs 1 crore a 15% gross year loses 2 points to the fixed fee and 1 point to the performance fee on the 5 points above the 8% hurdle, leaving the client 12%, so fees take Rs 3 lakh of the Rs 15 lakh gain.

    What changes if the agreement charges the performance fee on the gross return?

    Then the hurdle is measured before the fixed fee. The performance fee becomes 20% of 7 points, 1.4%, the net return falls to 11.6%, and fees take 22.7% of the gain instead of 20%. The same headline terms give two answers, which is why the order of calculation, the high-water markA rule that performance fees are only paid on gains above the highest value the account has previously reached, so the client does not pay twice for recovering a loss. and the basis for the fixed fee all have to be read in the agreement.

    On Rs 1 croreFee after fixed feeFee on gross
    Gross gain, Rs lakh15.015.0
    Fixed fee, 2%(2.0)(2.0)
    Performance fee, 20% above 8%(1.0)(1.4)
    Net gain, Rs lakh12.011.6
    Share of gross gain paid in fees20.0%22.7%
    Charging the performance fee after the fixed fee leaves the client Rs 12.0 lakh; charging it on the gross return leaves Rs 11.6 lakh, so the same headline terms differ by Rs 40,000 on Rs 1 crore.

    One more layer is worth a sentence: fees usually attract GST in India, charged on top, which widens the gap further. Confirm the current rate and treatment before quoting a client a net figure.

    Where candidates lose it

    The trap is taking the performance fee as 20% of the whole 15% gross return, or forgetting the fixed fee comes out first. Both give a wrong net figure with total confidence.

    The quieter loss is quoting 12% without the convention. Say that you have assumed the performance fee is charged after the fixed fee, and give the other answer, 11.6%, in the same breath.

    What the interviewer asks next

    • What is the net return in a year when the gross return is 8%?
    • At what gross return do fees take exactly a quarter of the gain?
    • How does a high-water mark change the fee in the year after a loss?
  2. 042A portfolio manager takes 20% of each year's gains as a performance fee, with no high-water mark. The portfolio returns plus 30%, minus 30%, then plus 30%. How much fee is paid on Rs 100, where does the client end, and what would a high-water mark have changed?Fee and cost dragHardPrivate banking

    Try it first

    Without a high-water mark, how do the total fees compare with the client's own three-year gain?

    Show the worked solution

    Fees total Rs 11.21 and the client ends at Rs 107.63; a high-water mark would have cut fees to Rs 6 and left him Rs 112.84. Year 1 takes 130 to 124 after a fee of 6. Year 2 falls to 86.8. Year 3 rises to 112.84, and without a mark the manager takes 20% of that 26.04 rise, 5.21. With a mark at 124, the year-3 rise only recovers old ground, so no fee is due.

    Why is the client charged twice?

    A painter paid per wall painted repaints the same wall after the rain washes it off and bills you again. You have one painted wall and two invoices. Without a high-water mark, the manager is paid on every rise, including rises that only recover ground the client already paid a fee on. The client paid for the climb from 100 to 124 in year 1, lost it in year 2, and paid again for climbing from 86.8 to 112.84, most of which is the same ground.

    Without a high-water mark, the manager is paid twice for the same ground80100120140StartYear 1: +30%Year 2: -30%Year 3: +30%high-water mark 124fee -6.00fee -5.2186.8, no fee130112.84107.63No mark: fees 11.21, client ends 107.63With mark: fees 6.00, client 112.84No fees: 118.3
    The fund's NAV rises to 130, pays a fee of 6, falls to 86.8, then rises to 112.84 and pays a second fee of 5.21, ending at 107.63. With a high-water mark at 124 the year-3 rise earns no fee and the client keeps 112.84.
    YearReturnNAV before feeFee, no markNAV after, no markFee, with mark
    1+30%130.006.00124.006.00
    2-30%86.800.0086.800.00
    3+30%112.845.21107.630.00
    Total11.21107.636.00
    Fees on Rs 100 at 20% of gains. With a high-water mark the year-3 NAV of 112.84 stays below the 124 mark, so no fee is due and the client ends at 112.84.

    What does the high-water mark fix, and what does it not?

    It fixes double charging: a fee is due only on value above the highest level on which a fee was already paid. Here the mark saves the client 5.21 on Rs 100 and turns a gain of 7.63 into 12.84. It does not stop the manager being paid for a lucky year, and a mark can be reset when money is withdrawn or a new series is opened, so the terms matter. Hurdle rates and fee crystallisation periods are the other clauses worth reading.

    Notice also that three years of plus 30, minus 30, plus 30 would compound to only 118.3 even with no fees, because a 30% loss needs a 42.9% gain to recover. The fees then take a large share of a small result.

    Where candidates lose it

    The common error is computing the fee on the three-year gain, 20% of 18.3, and missing that it is charged each year on each rise. The other is forgetting that the year-1 fee changes the base for years 2 and 3.

    Walk the three years in order, state the NAV after each fee, and then run the high-water case. The sentence the interviewer wants is that without a mark the client pays twice for the same ground.

    What the interviewer asks next

    • What if the fee carried a 6% hurdle as well as a high-water mark?
    • How does a high-water mark change the manager's incentive after a bad year?
    • The client withdraws half his money after year 2. What happens to his high-water mark?