Mutual Fund Mastery puzzles, solved step by step

Waiting saves Rs 5,000, and it puts the whole Rs 5 lakh at five more weeks of market risk, about Rs 27,900 either way at one standard deviation. The load is 1% of the redemption value. At an assumed 18% annual volatility, a five-week move has a standard deviation of 5.6%. With no drift assumed, there is about a 43% chance of falling more than the 1% saved. The load is a known cost to weigh, not an automatic reason to wait.

What exactly does waiting buy?

Think of a train ticket with a cancellation fee that disappears if you wait until tomorrow. If you were going to travel anyway, waiting costs nothing. If you need the money for something else tonight, waiting has a cost the fee schedule does not show. An exit load is a certain cost on one side; staying invested for the waiting period is an uncertain gain or loss on the other, and the two have to be sized against each other. The certain side here is 1% of Rs 5 lakh, Rs 5,000.

How big is the uncertain side?

Scale annual volatility to five weeks with the square root of time. Eighteen per cent times the square root of 5 over 52 is 5.58%, about Rs 27,900 on Rs 5 lakh: the possible swing is several times the load. If the market has no drift over those weeks, the chance of losing more than 1% is the chance of a move below -1%, which is 43%. Waiting is close to a coin toss with a small Rs 5,000 tilt in its favour.

The right answer depends on why the money is leaving. If the investor would stay invested anyway, waiting is close to free and the Rs 5,000 is worth having. If the money is needed for a fixed purpose, or he has decided he no longer wants this exposure, five weeks of risk on the full amount is a real cost. Check one more thing: holding periods can also change how a gain is taxed, so confirm whether the same date crosses a tax threshold under current rules. The 18% volatility is an assumption for the arithmetic.

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.

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.

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.

About 0.48% a year, roughly half a percent. Turnover of 120% means the fund sells and rebuys 1.2 times its portfolio in a year. Each rupee replaced costs one sale and one purchase, 0.4% together, so the drag is 1.2 x 0.4%. That cost shows up as a lower NAV, never as a line in the expense ratio, so the investor pays it without seeing it.

Why does a cost this size not appear on the factsheet?

Think of a shopkeeper who keeps rearranging the stock. The rent is printed on the lease, but every time he returns goods and reorders, the supplier keeps a small handling margin, and that never appears on any bill he shows you. The expense ratioThe annual charge for running a fund: management fee, administration, distribution and similar costs, shown as a percentage of assets. is the rent. Trading costs are the handling margin: brokerage, taxes on trades and the impact costThe amount a price moves against a large buyer or seller while the order is being filled. It is paid through a worse price, never through a bill. of moving prices, all paid through the prices the fund gets, so they land in the NAV and not in the expense ratio. Which explicit trading charges may be loaded inside the expense ratio is set by regulation and should be checked for the market you are in; impact cost is never there.

How do you turn turnover into a cost without double counting?

Portfolio turnoverThe share of a portfolio replaced in a year, usually measured as the smaller of purchases or sales divided by average assets. counts how much of the book is replaced. At 120%, every rupee of assets is sold and rebought 1.2 times in the year. Because the 0.4% already covers both legs of a replacement, the cost is simply turnover times the round-trip cost: 1.2 x 0.4% = 0.48%. The common slip is to say a replacement has a buy and a sell and double it to 0.96%, counting each leg twice. A fund turning over 20% of its book pays only 0.08%.

Put rupees on it, because half a percent sounds small. Rs 10 lakh compounding for 20 years at 11.3% grows to about Rs 85.1 lakh; at 10.82% it grows to about Rs 78.0 lakh. The gap is about Rs 7.0 lakh, paid quietly. The limit of the estimate: impact cost depends on how liquid the stocks are and how large the fund is, so the same turnover costs a small-cap fund of Rs 20,000 crore far more than a large-cap fund of Rs 2,000 crore.

The equity fund's fee takes 15% of its expected return; the liquid fund's takes about 3.8%. A fee is charged on the money invested, but it comes out of the return, so it should be measured against the return. 1.5 / 10 is 15%; 0.25 / 6.5 is 3.85%. Measured against the 3.5% extra that equity is expected to earn over cash, the 1.5% fee takes 43%.

Why does 1.5% sound smaller than it is?

An agent who charges you 1.5% of your house price to sell it sounds cheap until you remember you only made Rs 10 lakh of profit on a Rs 1 crore house: the Rs 1.5 lakh fee takes 15% of the profit. Fund fees are quoted on the money invested, but they are paid out of the return, so the honest size of a fee is the fee divided by the return it takes from. For the equity fund, 1.5 / 10 = 15%: almost one rupee in every seven the fund is expected to earn goes to costs. For the liquid fund, 0.25 / 6.5 = 3.85%.

What is the sharper way to measure the equity fee?

An investor holds equity instead of cash to earn the extra return, the equity risk premiumThe return equities are expected to earn above cash or short government bills, as pay for their extra risk.. If cash pays 6.5% and equity is expected to make 10%, the extra is 3.5%. A 1.5% fee takes 1.5 / 3.5 = 43% of that extra, so close to half of the reason for owning equity goes in costs. That is why low-cost index funds draw so much money: the fee matters most where the expected extra return is thin.

Two limits keep this honest. Expected returns are assumptions, not promises, and in a year when the fund falls the fee takes more than all of the return. And a higher fee can still be worth paying if the manager adds more than the fee in return after costs, which is rare enough that the evidence for it should be asked for, not assumed.

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.

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.

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.

About 0.56% a year when stocks return 13%, and the cash pays for itself only when stocks return less than 6%. The cash earns 6% instead of 13% on 8% of the fund: 0.08 x 7 points is 0.56%, so the fund returns 12.44%. If stocks fall 20%, the same cash means the fund loses 17.92%, a cushion of 2.08 points. Cash is a cost whenever stocks beat cash and a cushion when they do not.

Why is the cost the gap and not the whole return?

Keeping some money in a savings account rather than a share portfolio does not cost you the shares' return; it costs the difference between the shares' return and the interest the account pays. Cash drag is the cash weight multiplied by the gap between what the stocks earned and what the cash earned, not by the stocks' whole return. With 8% in cash, 13% on stocks and 6% on cash, the fund loses 0.08 x 7, or 0.56 points, against a fully invested version of itself.

When does the cash earn its keep?

Whenever stocks return less than cash. The breakeven is exactly the cash rate, 6% here: above it the cash costs, below it the cash helps. In a year when stocks fall 20%, the fund falls only 17.92%, because 8% of it earned plus 6% instead of minus 20%. Over ten years of 13% stock returns, though, the drag compounds: Rs 1 lakh grows to about Rs 3.39 lakh fully invested and about Rs 3.23 lakh with the cash, a difference of about Rs 16,500.

Say why funds hold cash at all before judging it. Some is needed to pay redeeming investors without forced selling; some is new money not yet invested; some is a deliberate call that prices are high. The first two are a cost of running an open-ended fund; only the third is a market view, and it should be judged like any other bet, by whether it paid over a full cycle. A fund that holds a lot of cash and calls it caution is making a market-timing bet, whatever it calls it.