Mutual Fund Mastery puzzles, solved step by step

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100
Traced to a firm
29
Topics
13
Hard
30
Topic
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. 007Tarvela AMC's assets under management rose from Rs 40,000 crore to Rs 52,000 crore over a period in which the industry grew from Rs 5 lakh crore to Rs 7 lakh crore. Did Tarvela's market share rise?Logic and numeracy brainteasersWarm upIndian AMCsGlobal asset managers

    Try it first

    Quick call: what happened to Tarvela's share?

    Show the worked solution

    No. Tarvela's share fell from 8.0% to about 7.4%. Its AUM grew 30% while the industry grew 40%. Share is 40,000 over 5,00,000 before and 52,000 over 7,00,000 after. To hold 8% Tarvela needed Rs 56,000 crore, so it is Rs 4,000 crore short of standing still. Growing slower than your market means losing share while growing.

    Why can a business grow and still shrink?

    A child who grows 3 cm in a year while every classmate grows 5 cm is taller than last year and lower in the line-up. Market share is a ratio, so it rises only when your growth beats the market's, and a large rupee gain means nothing on its own. Tarvela's Rs 12,000 crore gain sounds big until you set it next to the industry's Rs 2 lakh crore.

    Growing 30% in a market growing 40% loses share+30%Tarvela AMC40,000 to 52,000+40%Industry5 to 7 lakh croreGrowth in AUM over the period, Rs croreMarket share8.0%7.4%8.0% would need Rs 56,000 croreBeforeAfterShare falls although AUM rose Rs 12,000 crore
    Tarvela AMC grew its assets 30% while the industry grew 40%, so its market share fell from 8.0% to 7.4%, and holding 8% would have needed Rs 56,000 crore rather than Rs 52,000 crore.

    What is the fastest way to answer without dividing big numbers?

    Compare growth factors. New share equals old share times Tarvela's growth factor over the industry's: 8% times 1.30 over 1.40. 1.3 over 1.4 is about 0.93, so the share falls by about 7% of itself, from 8.0% to 7.43%. You never need to divide 52,000 by 7,00,000 unless asked for the decimal.

    The relationship
    s1=s0×1+gAMC1+gind=8.0%×1.301.40=7.43%s_1 = s_0 \times \frac{1 + g_{AMC}}{1 + g_{ind}} = 8.0\% \times \frac{1.30}{1.40} = 7.43\%
    s_0, s_1market share before and after
    g_{AMC}Tarvela's AUM growth, 30%
    g_{ind}the industry's AUM growth, 40%
    What it says in wordsShare moves by the ratio of your growth factor to the market's.

    Add the analyst's question. AUM growth has two parts, market movement and net flows. If Tarvela is heavier in a segment that rose less, it could lose share with no problem in its sales. Splitting growth into the part the market gave and the part investors gave is the next thing an interviewer will ask for.

    Where candidates lose it

    The trap is answering yes because Rs 12,000 crore of growth sounds impressive. The interviewer has deliberately given a big absolute gain in a market growing faster, to see whether you reach for the ratio.

    The second slip is subtracting growth rates, 30 minus 40, and saying share fell by 10 points. Share fell by about 0.57 points, from 8.0% to 7.43%; it is the ratio 1.3 over 1.4 that matters.

    What the interviewer asks next

    • What growth did Tarvela need to gain half a point of share?
    • How would you split Tarvela's growth into market movement and net inflows?
    • Why might an AMC accept losing share in one category?
  2. 057A fund cuts its expense ratio from 1.5% to 1.2%. Is that a 0.3% cut, a 30 basis point cut or a 20% cut, and which description will a client misunderstand?Logic and numeracy brainteasersWarm upIndian AMCsGlobal asset managers

    Try it first

    Which descriptions of the change are correct?

    Show the worked solution

    It is a 0.3 percentage point cut, which is 30 basis points, and a 20% relative cut in the fee; "a 0.3% cut" is the sloppy one. Basis points remove the ambiguity. The 20% is true but invites a client to imagine returns rising 20%; on Rs 10 lakh the saving is Rs 3,000 a year, and a net return of 8.5% becomes 8.8%.

    Why are there two different answers that are both right?

    A shop raises the price of milk from Rs 50 to Rs 60. It went up by Rs 10, and it went up by 20%. Nobody confuses those, because rupees and percent look different. With rates, the change and the base are both percentages, so "percent" can mean the gap between two rates or the change relative to the old rate, and you must say which. The gap between 1.5% and 1.2% is 0.3 percentage pointsThe plain difference between two percentages. From 1.5% to 1.2% is a fall of 0.3 percentage points.. Relative to the old fee, 0.3 is a fifth of 1.5, a 20% cut.

    One fee cut, three honest names, one misleading onePercentage points0.3 pp1.5% minus 1.2%The difference of two ratesBasis points30 bps1 bp = 0.01 pointThe desk's unit; no ambiguityRelative change-20%0.3 / 1.5Of the fee, not of returnsSaid as "a 0.3% cut"Heard as 0.3% of the fee:1.5% x 0.997 = 1.4955%A cut 100 times too smallWhat it means on Rs 10 lakhFee Rs 15,000 falls to Rs 12,000: Rs 3,000 savedNet return at a 10% gross: 8.5% to 8.8%Return up 3.5% in relative terms, not 20%
    The same fee cut from 1.5% to 1.2% is 0.3 percentage points, 30 basis points or a 20% relative cut, and on Rs 10 lakh it saves Rs 3,000 a year while lifting a net return from 8.5% to 8.8%.

    Which description will a client get wrong, and what should you say instead?

    "A 0.3% cut" fails one way: a careful reader can take it as 0.3% of the fee, which would leave 1.5% x 0.997 = 1.4955%, a cut a hundred times too small. "A 20% cut" fails the other way: it is true of the fee, but a client hears 20% and imagines the investment doing 20% better. The fee is a slice of a slice; a 20% smaller slice lifts a net return of 8.5% to 8.8%, only 3.5% better in relative terms. The clean form for a desk is basis pointsHundredths of a percentage point. 30 basis points equal 0.30 percentage points.; the clean form for a client is rupees: Rs 15,000 a year on Rs 10 lakh becomes Rs 12,000.

    The relationship
    1.5%−1.2%=0.3 pp=30 bps1.5−1.21.5=20%1.5\% - 1.2\% = 0.3\text{ pp} = 30\text{ bps} \qquad \frac{1.5 - 1.2}{1.5} = 20\%
    pppercentage points, the plain gap between two rates
    bpsbasis points, one hundredth of a percentage point
    1.5the old fee, the base for the relative change
    What it says in wordsSubtract for points, divide by the old rate for percent change, and name which one you mean.

    The same confusion runs through everything a fund desk reports: a yield moving from 7.0% to 7.5% is 50 basis points, not 0.5%, and a fund outperforming by 2% might mean two points or a fiftieth more. The limit worth stating: neither unit tells the client the money, so pair any rate change with the rupee effect on their actual holding.

    Where candidates lose it

    The trap is picking one answer and defending it. The interviewer is not after 0.3 or 20; they want to hear that these are two different quantities and that the unit must be named every time.

    The second miss is not taking the client's view. Saying 20% to a client is legally true and practically misleading, because it invites them to apply the 20% to their returns. Translate into rupees on their holding.

    What the interviewer asks next

    • A bond yield rises from 6.8% to 7.2%. Describe the change in three correct ways.
    • A fund's return beat the index's 10% by 2%. List the two things this could mean.
    • Why do desks quote spreads in basis points rather than percent?