Mutual Fund Mastery puzzles, solved step by step

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All topicsCompounding and time value9Statistics, correlation and diversification8Bond maths and duration10Performance measurement and returns8Costs and fee drag8Valuation riddles11Logic and numeracy brainteasers6Estimation and market sizing7Probability and expected value8NAV, units and fund mechanics7Risk, volatility and drawdown8Behavioural traps6Withdrawals and after-tax arithmetic4
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  1. 031A mutual fund distributor's book of Rs 50 crore earns a 0.75% trail commission each year. Markets add 10% a year to the book, and 8% of the book leaves each year as clients redeem or move. At a 12% discount rate, roughly what is the book worth?Costs and fee dragHardDistribution and salesIndian AMCs

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    What growth rate should go into the valuation?

    Show the worked solution

    About Rs 3.5 crore. Year one's trail is 0.75% of Rs 50 crore, Rs 0.375 crore. The book grows 10% from markets and loses 8% to attrition, so it nets 1.10 x 0.92, about 1.2% growth a year, and the trail grows with it. A growing perpetuity at 12% values that at 0.375 divided by (12% minus 1.2%), about Rs 3.47 crore, roughly seven times one year's income.

    Why is the book worth so little next to the Rs 50 crore it holds?

    A distributor does not own the Rs 50 crore; the clients do. What the distributor owns is a stream of income, like the owner of a rented flat owns the rent, not the tenant's savings. The book is worth the present value of its trail income, and that income is only 0.75% of the assets each year. So the right starting point is Rs 37.5 lakh a year, and the question is how that stream grows and how fast it leaks away.

    What a Rs 50 crore trail book is worth, and what moves itThe bookRs 50 crore AUMMarkets+10% a yearAttrition: 8% ofthe book leavesTrail 0.75%Rs 0.375 crore, year 1Net growth: 1.10 x 0.92 = 1.012, so g = 1.2% a yearValue = 0.375 / (12% - 1.2%) = Rs 3.47 croreBook value, Rs crore, one input movedBase case3.47Attrition 4%5.86Market 14%5.27Attrition 12%2.47Market 6%2.59A 4-point swing in attrition movesthe value about as much as a 4-pointswing in market growth
    The Rs 50 crore book grows 10% from markets and loses 8% to attrition, netting about 1.2% a year, while 0.75% flows off as trail. Valued as a growing perpetuity at 12% the book is worth about Rs 3.47 crore, and a 4-point change in attrition moves that value about as much as a 4-point change in market growth.

    How do market growth and attrition combine?

    They multiply. A client who stays sees the book grow 10%; then 8% of the grown book leaves. The net growth is 1.10 times 0.92 less 1, about 1.2%, not 10% minus 8%. That growth feeds a growing perpetuityA stream of payments that continues forever and grows at a constant rate; its value is the first payment divided by the discount rate less the growth rate., which is the standard way to value a stream that neither ends nor stays flat.

    The relationship
    V=C1r−g=0.3750.12−0.012≈Rs 3.47 croreV = \frac{C_1}{r - g} = \frac{0.375}{0.12 - 0.012} \approx \text{Rs } 3.47 \text{ crore}
    C_1year one's trail, 0.75% of Rs 50 crore, Rs 0.375 crore
    rthe discount rate, 12%
    gnet growth of the book, 1.10 x 0.92 less 1, about 1.2%
    What it says in wordsThe book is worth one year's trail divided by the gap between the discount rate and the book's net growth.

    Which lever matters more, markets or client retention?

    About equally, which is the point the interviewer wants. Cutting attrition from 8% to 4% lifts the value to about Rs 5.86 crore; lifting market growth from 10% to 14% lifts it to about Rs 5.27 crore. A distributor cannot control the market but can control service and retention, and retention moves the value as much as the market does. The limits: the formula needs growth below 12%, a trail rate is set by the fund house and can change, and the 10% market growth is an assumption, not a forecast.

    Where candidates lose it

    The first trap is valuing the assets, not the income, and quoting a number near Rs 50 crore. The distributor's claim is a 0.75% slice each year, and the value must start from Rs 37.5 lakh of income.

    The second is subtracting attrition from growth: 10% minus 8% gives 2% and a value of Rs 3.75 crore. The two compound, so the net growth is 1.2%. A small slip in g matters, because g sits in the denominator next to r.

    What the interviewer asks next

    • What attrition rate would make the book worth Rs 5 crore?
    • Trail is cut to 0.5%. What is the book worth, and what does the distributor's business depend on now?
    • Why might a buyer of this book use a higher discount rate than 12%?
  2. 083A fund charges 1.5% a year but has an active share of only 20%: the other 80% of the portfolio effectively is the index. If index exposure is worth 0.2% a year, what are you really paying for the active 20%?Costs and fee dragHardFund research and ratingsIndian AMCs

    Try it first

    What is the effective fee on the active slice?

    Show the worked solution

    About 6.7% a year for each rupee of genuine active management. The 80% that tracks the index is worth 0.2%, so it accounts for 0.8 x 0.2%, or 0.16 points, of the fee. The remaining 1.34 points pay for the 20% that differs from the index, and 1.34 divided by 0.20 is 6.7%. The active slice must beat the index by 6.7 points a year just to earn its fee.

    What is active share, and why does it change the price?

    Suppose a caterer charges a premium price per plate, but four of the five dishes are the same ones any local dhaba serves. You are paying the premium almost entirely for the fifth dish. Active shareThe share of a fund portfolio, by weight, that differs from its benchmark index. Zero means an exact copy of the index; 100% means no overlap at all. is the part of a fund's portfolio that differs from its benchmark; the rest is the index in disguise, and you could buy that part for an index fund's price. An active share of 20% means only a fifth of the money is doing anything the index would not.

    Most of the fee is paying for a small part of the portfolioThe portfolio, by what it does80% moves with the index20% activeThe 1.5% fee, split by what each part is worth0.161.34 points pay for the active 20%The index-like 80% of the money needs only 0.8 x 0.2% = 0.16 points of the feePrice per rupee of exposure, a yearIndex exposure0.2%The active slice1.34 / 0.20 = 6.7%A fund with 80% active share and the same 1.5% fee: about 1.8% per rupee of active management
    Priced at 0.2%, the index-like 80% of the portfolio accounts for only 0.16 points of the 1.5% fee, so the remaining 1.34 points pay for the 20% active slice, an effective 6.7% a year per rupee of active management.

    How do you split the fee between the two parts?

    Price each part at what it would cost on its own. The index-like 80% could be held through an index fund at 0.2%, so it deserves 0.8 x 0.2%, or 0.16 points of the fee. Everything left, 1.34 points, is the price of the active 20%, and expressed per rupee of active exposure that is 6.7% a year.

    The relationship
    factive=F−(1−AS) findexAS=1.5−0.8×0.20.2=6.7%f_{active} = \frac{F - (1 - AS)\,f_{index}}{AS} = \frac{1.5 - 0.8 \times 0.2}{0.2} = 6.7\%
    Fthe fund's total fee, 1.5%
    ASactive share, 20%
    f_{index}the price of index exposure, 0.2%
    f_{active}the effective price of each rupee of active management
    What it says in wordsTake the index part's fair cost out of the fee, then spread what is left over the active slice only.

    What would the active slice have to deliver?

    To merely match a cheap index fund after costs, the active 20% must beat the index by 6.7 points a year on its own money. Beating an index by that margin year after year is rare, which is why a high fee on a low active share is the first combination fund researchers flag. Compare a genuinely active fund with 80% active share charging the same 1.5%: its index part uses 0.04 points, and its active part costs about 1.8% per rupee. Same headline fee, well under a third of the effective price.

    Say the limitation too. Active share measures difference, not skill: a fund can be very different from its index and still lose. The point is narrower and firmer. A fund that is barely different from its index cannot justify an active fee, because most of what you pay for is available for a fraction of the price.

    Where candidates lose it

    Most candidates take 1.5% as the price, compare it with the index fund's 0.2%, and conclude the fund costs 1.3 points more. That understates the problem, because it spreads the extra cost over money that is not being actively managed at all.

    The second loss is reaching 6.7% and not saying what it means. Turn it into a hurdle: the active slice must beat the index by 6.7 points a year just to break even with the cheap alternative.

    What the interviewer asks next

    • At what active share would the effective active fee fall to 2%?
    • Why might a fund's active share drift down as its assets grow?
    • What else would you check before calling a fund a closet indexer?