Mutual Fund Mastery puzzles, solved step by step

Puzzles: 100
Traced to a firm: 29
Topics: 13
Hard: 30

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019A fund charges a 1% exit load on redemptions within 12 months of purchase. An investor wants to redeem Rs 5 lakh in month 11. What does waiting five weeks save, and what does the wait put at risk?Costs and fee dragWarm upIndian AMCsDistribution and sales
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How does the Rs 5,000 saving compare with a typical five-week market move on Rs 5 lakh?
Show the worked solution
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.
Waiting from month 11 past the month-12 load cliff saves a certain Rs 5,000, while a one standard deviation five-week move on Rs 5 lakh at an assumed 18% volatility is about Rs 27,900 either way, more than five times the saving.
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 relationship
$\sigma_{5w} = 18\% \times \sqrt{5/52} = 5.58\%,\qquad P(\text{fall} > 1\%) = \Phi\!\left(-\frac{1\%}{5.58\%}\right) \approx 43\%$
18% the assumed annual volatility of the fund
5/52 five weeks as a fraction of a year
\Phi the normal cumulative probability
What it says in wordsShrink the yearly swing to five weeks, then ask how often a move that size falls by more than the load saved.
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.
Where candidates lose it
The common slip is treating the load as the only number and saying always wait. That ignores that the investor is choosing to keep Rs 5 lakh exposed for five more weeks, which can cost or earn several times the load.
The opposite slip is saying the load is trivial so never wait. Rs 5,000 is certain; if the money would otherwise stay invested, there is little reason to give it away. The interviewer wants the two sides weighed, not a rule.
What the interviewer asks next
How would the answer change for a liquid fund with a much lower volatility?
Why do funds charge exit loads at all?
If the investor redeems in two halves, one now and one after month 12, what does that do to the load and the risk?
069A 1.5% expense ratio sounds small. If an equity fund's expected return before fees is 10%, what fraction of the return goes in fees? For a liquid fund returning 6.5% before a 0.25% expense ratio, what fraction?Costs and fee dragWarm upIndian AMCsDistribution and sales
Try it first
What share of the equity fund's expected return does the fee take?
Show the worked solution
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%.
The equity fund's 1.5% fee takes 15% of a 10% expected return, the liquid fund's 0.25% fee takes 3.8% of 6.5%, and against the 3.5% extra return that equity is held for, the same 1.5% takes 43%.
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.
The relationship
$\frac{\text{fee}}{\text{expected return}} = \frac{1.5}{10} = 15\% \qquad \frac{0.25}{6.5} = 3.8\% \qquad \frac{1.5}{10 - 6.5} = 43\%$
fee the expense ratio, % of assets a year
expected return what the fund is expected to earn before fees, % a year
6.5 the cash rate, used to find the extra return
What it says in wordsA fee's real size is its share of the return, and sharper still, its share of the extra return you took risk for.
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.
Where candidates lose it
The trap is comparing the fee with the investment, the way it is quoted, and calling it small. The interviewer wants the fee compared with the return, which makes 1.5% look ten times larger.
The second miss is treating all fees alike. A 0.25% fee on a liquid fund and a 1.5% fee on an equity fund take very different shares of what each is expected to earn; say both shares and the comparison makes itself.
What the interviewer asks next
Inflation is 5%. What share of the equity fund's real return does the fee take?
A fund charges 2% and its manager is expected to beat the index by 1% before fees. What is the investor's expected result against the index?
Why do fee differences matter more in debt funds than they first appear to?

18%	the assumed annual volatility of the fund
5/52	five weeks as a fraction of a year
\Phi	the normal cumulative probability

fee	the expense ratio, % of assets a year
expected return	what the fund is expected to earn before fees, % a year
6.5	the cash rate, used to find the extra return

Try it first

What exactly does waiting buy?

How big is the uncertain side?

Where candidates lose it

What the interviewer asks next

Try it first

Why does 1.5% sound smaller than it is?

What is the sharper way to measure the equity fee?

Where candidates lose it

What the interviewer asks next