Mutual Fund Mastery puzzles, solved step by step

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

Showing 31–40 of 71 · filtered from 100Clear filters

045A target maturity debt fund has a portfolio yield to maturity of 7.4% and an expense ratio of 0.2%. What return should an investor who holds to maturity expect, and why will it not be exactly that?Bond maths and durationCoreFixed income desksIndian AMCs
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What is the best single estimate of the hold-to-maturity return, per year?
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About 7.2% a year: the portfolio's yield to maturity less the expense ratio. Holding to the fund's maturity removes most of the price risk, so the bonds earn roughly their 7.4% yield and the fund keeps 0.2% a year. It will not be exactly 7.2% because coupons are reinvested at future yields nobody knows, the fund tracks its index imperfectly, and the yield you lock in is the one on the day you invest. On these numbers the drift is about plus or minus 0.13% a year.
Why is yield to maturity a fair starting point?
A fixed deposit tells you its rate because the bank promises to hold it to maturity for you. A bond does the same if you hold it to maturity: price swings along the way wash out, and what remains is the yield to maturityThe single discount rate that makes the present value of a bond coupons and principal equal its price today; the return earned if the bond is held to maturity and coupons are reinvested at that same rate.. A target maturity fund holds bonds that mature near one date and then pays out, so an investor who stays to that date earns close to the portfolio's yield to maturity, less the fund's costs. 7.4% less 0.2% is about 7.2% a year.
The portfolio's 7.40% yield to maturity less the 0.20% expense ratio gives a best estimate of 7.20% a year, and reinvesting coupons at 6.4% to 8.4% instead of 7.4% would move the realised return to between 7.07% and 7.33% after costs, with tracking effects of a few basis points on top.
Why will the realised return not be exactly 7.2%?
Yield to maturity quietly assumes every coupon is reinvested at the same yield, and the future reinvestment rate is unknown. Take a 5-year bond bought at par with a 7.4% coupon. If its coupons can only be reinvested at 6.4%, the realised return is about 7.27% a year; at 8.4% it is about 7.53%. After the 0.2% fee that is 7.07% to 7.33%. The fund also holds bonds that do not mature on exactly one date, keeps some cash, and replicates its index imperfectly, each worth a few basis points either way.
The relationship
$r_{\text{hold}} \approx \text{YTM} - \text{TER} = 7.4\% - 0.2\% = 7.2\%$
YTM the portfolio's yield to maturity on the day you invest, 7.4%
TER the total expense ratio, 0.2% a year
r_hold the return a hold-to-maturity investor can reasonably expect
What it says in wordsFor an investor who stays to maturity, the best estimate of the return is today's portfolio yield less the yearly cost.
What else should the investor be told?
Three things. The estimate holds only to maturity: an investor who exits after two years takes the market price then, which can be well above or below the path to 7.2%. The yield locked in is the one on the day of investment, not the one quoted at launch. And the figure is before tax; how a debt fund's gains are taxed has changed in recent years, so confirm the current treatment before turning 7.2% into an after-tax number. The estimate is the honest best guess, not a promise.
Where candidates lose it
The trap is quoting 7.4% as the return, forgetting that the expense ratio is taken out of the NAV every day. The fund's yield is the bonds' yield; the investor's return is that less the cost.
The second loss is treating 7.2% as a promise because the fund holds to maturity. It is an estimate: reinvestment, tracking and timing all move it, and an exit before maturity exposes the investor to price risk.
What the interviewer asks next
Yields rise 1% the day after you invest. What happens to your NAV and to your return if you hold to maturity?
Why do coupon reinvestment effects matter less for a 2-year fund than a 10-year fund?
How would you compare this fund with a 5-year bank deposit at 7.1%?
046An investor put Rs 1 lakh into an equity fund at NAV 100. The NAV is now 60 and he adds another Rs 1 lakh. What is his new average cost, what rise does he need to break even, and does averaging down make the fund any better?Behavioural trapsCoreWealth and advisoryDistribution and sales
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What is his average cost per unit after the second purchase?
Show the worked solution
His average cost is Rs 75 a unit and he needs a 25% rise from 60 to break even, but the fund is no better than before. Rs 1 lakh bought 1,000 units at 100 and 1,667 units at 60, so Rs 2 lakh buys 2,667 units, Rs 75 each. Before the top-up he needed 66.7%. Averaging down moves the break-even point, not the fund's prospects, and it doubles the money exposed to the next move.
Why is the average 75 and not 80?
Spend Rs 100 on mangoes at Rs 100 a kilo and another Rs 100 at Rs 60 a kilo. You have 1 kilo plus 1.67 kilos, 2.67 kilos for Rs 200, which is Rs 75 a kilo. Equal rupees buy more units when the price is low, so the average cost leans towards the lower price; it is the harmonic mean of the two NAVs, not the simple average. That is the same arithmetic that makes rupee-cost averaging in an SIP work, applied here to two purchases.
Each Rs 1 lakh is a rectangle of units times NAV: 1,000 units at 100 and 1,667 units at 60. Together they average Rs 75 a unit, so the break-even rise from 60 falls from 66.7% to 25%, while the rupees at stake double to Rs 1.6 lakh.
The relationship
$\bar{c} = \frac{\text{Rs }2{,}00{,}000}{\frac{1{,}00{,}000}{100} + \frac{1{,}00{,}000}{60}} = \frac{2}{\frac{1}{100} + \frac{1}{60}} = 75 \qquad \frac{75}{60} - 1 = 25\%$
\bar{c} average cost per unit
100, 60 the two NAVs paid
What it says in wordsWith equal rupees at each price, the average cost is the harmonic mean of the prices, and the break-even rise is that cost over today's NAV, less one.
Does a lower break-even mean the decision was good?
No, and this is the behavioural point. The break-even number is about his purchase history; the fund's next move does not know or care what he paid. His position today is 2,667 units worth Rs 1.6 lakh, with an unrealised loss of Rs 40,000, the same loss he had before the top-up. A further 10% fall now costs Rs 16,000 instead of Rs 6,000. The question that decides whether to add is whether he would buy this fund today at 60 with fresh money if he had never owned it, given his goal and his allocation.
There are good reasons to add after a fall: a disciplined rebalance back to a target equity weight, or an SIP that keeps running through the dip. There are bad ones: wanting to feel closer to breaking even, or refusing to accept that the first purchase was a mistake. The arithmetic is the same in both cases; only the reason differs, and the adviser's job is to ask which one it is.
Where candidates lose it
The fast wrong answer is 80, the average of the two prices. It treats the purchases as equal units when they were equal rupees. Count the units first and the 75 follows.
The bigger trap is the second half of the question. Candidates who get 75 and 25% often present averaging down as a fix. The interviewer wants to hear that it changes the break-even, not the quality of the fund, and that it raises the money at risk.
What the interviewer asks next
If he had added Rs 2 lakh at 60 instead of Rs 1 lakh, what would his average cost be?
When is adding to a falling fund a sound decision?
How is this different from an SIP buying through the same fall?
047An equity fund has a 25% chance of a negative year, independently each year. What is the chance that an investor who holds it for five years sees at least one losing year?Probability and expected valueWarm upFund research and ratingsIndian AMCs
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Your first guess: the chance of at least one losing year in five?
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About 76%. The easy route is the opposite event. Five positive years in a row needs a 75% chance to come up five times: 0.75 to the fifth is about 23.7%. Every other outcome includes at least one losing year, so the chance is 1 minus 0.237, about 76.3%. A small yearly chance of loss becomes close to a sure thing over an ordinary holding period.
Why work with the opposite event?
Ask a cricket fan the chance that a bowler concedes at least one boundary in an over, and the quick way is to ask the chance he concedes none. At least one is messy to count directly, because it covers one loss, two losses and every combination; none is a single clean path, so compute none and subtract from one. Here none means five positive years, each with a 75% chance, independent of the others: 0.75 times itself five times is 23.7%.
The chance that every year so far has been positive falls by a quarter each year, from 75% after one year to 23.7% after five, so the chance of at least one losing year in five is about 76.3%.
The relationship
$P(\text{at least one loss}) = 1 - (1-p)^n = 1 - 0.75^5 \approx 0.763$
p the chance of a losing year, 25%
n years held, 5
What it says in wordsThe chance of at least one losing year is one minus the chance that every year is positive.
Why does an adviser care about this number?
Because it sets the client's expectation before the first bad year arrives. Over five years a losing year is the likely case, not the unlucky one, so a client who has not been told this reads the first negative year as something gone wrong. On the same assumptions the expected number of losing years in five is 1.25, the chance of exactly one is about 40%, and over ten years the chance of at least one rises to about 94%. A losing year is a calendar-year label; it says nothing about whether the five-year return was positive.
State the two assumptions. The 25% is an illustration, not a measured figure for any market, and real yearly returns are not fully independent: bad years cluster in some periods. Clustering lowers the chance of at least one losing year slightly while making the losing stretches longer. The method survives both caveats; the exact figure does not.
Where candidates lose it
The trap is answering 25%, as if holding longer did not create more chances to see a loss, or adding 25% five times and reaching 125%. Both come from treating at least one as a simple sum.
The quieter loss is forgetting the independence assumption. Say it in one breath with the answer; it is what makes 0.75 to the fifth valid.
What the interviewer asks next
What is the chance of exactly two losing years in five?
How many years would you have to hold for the chance of at least one losing year to pass 90%?
Why might the chance of a losing five-year period be far lower than the chance of a losing year?
048A fund's NAV at the end of each quarter runs 100, 130, 110, 140, 91, 120. What is its maximum drawdown, and why is it not measured from the starting NAV of 100?Risk, volatility and drawdownWarm upRisk and complianceIndian AMCs
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What is the maximum drawdown?
Show the worked solution
The maximum drawdown is 35%, from the peak of 140 to the trough of 91. Drawdown is always measured from the highest value reached before the fall, because that is the value an investor held and then lost. Measured from the start, 91 looks like a mild 9% dip, which hides how much was lost on the way. The fund later climbs to 120, still 14.3% below its peak.
Why measure from the peak and not from the start?
A house bought for Rs 1 crore, valued at Rs 1.4 crore at the top of a boom and then sold for Rs 91 lakh, did not lose 9%. Its owner watched Rs 49 lakh disappear. A drawdown measures the pain of falling from the best point reached, so it runs from the running peak, which keeps rising whenever the NAV sets a new high. Anyone who invested at 140, or held through it, lost 35%, and that is the risk the measure is built to show.
The NAV path touches 140 and then falls to 91, a 35% drawdown from the running peak, while the earlier dip from 130 to 110 is only 15.4%; measured from the starting 100, the low of 91 would look like just a 9% fall.
How do you compute it step by step?
Walk along the path and keep two numbers: the highest NAV so far and the current NAV. At each point the drawdown is current over peak, less one. The maximum drawdown is the worst of those readings, here 91 over 140 less one, minus 35%. The dip from 130 to 110 gives minus 15.4%, a smaller drawdown. The final 120 against a peak of 140 is a drawdown of minus 14.3% still open.
The relationship
$DD_t = \frac{NAV_t}{\max_{s \le t} NAV_s} - 1, \qquad MDD = \min_t DD_t = \frac{91}{140} - 1 = -35\%$
NAV_t the NAV at time t
max NAV_s the running peak up to time t
MDD the maximum drawdown, the worst reading
What it says in wordsEach drawdown compares today's NAV with the best NAV so far; the maximum drawdown is the deepest of them.
Add the recovery maths: from 91 the fund needs a 53.8% rise just to get back to 140. And the measure depends on how often you look. These are quarter-end NAVs; a daily series could show a deeper trough between the quarter ends, so a maximum drawdown should always be quoted with its data frequency and period.
Where candidates lose it
The trap is measuring from the starting NAV and answering 9%, because the question opens with 100. The interviewer is checking that you know the reference point moves up with every new high.
The second slip is dividing by the trough, 49 over 91, and answering 54%. That is the gain needed to recover, not the drawdown. Say both numbers and label them.
What the interviewer asks next
What gain does the fund need from 120 to set a new high?
Why might a daily NAV series show a larger maximum drawdown than quarter-end NAVs?
Two funds have the same volatility; one has a much larger maximum drawdown. What could explain it?
049A Rs 10,000 monthly SIP runs for 20 years at 12% a year, taken as 1% a month. What share of the final corpus appears only in the last five years? Most people guess about a quarter.Compounding and time valueHardIndian AMCsDistribution and sales
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What share of the 20-year corpus is added in years 16 to 20?
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About half: 49.5%. At 1% a month the corpus is about Rs 50.5 lakh after 15 years and Rs 99.9 lakh after 20, so the final five years add Rs 49.5 lakh. Only Rs 6 lakh of that is new instalments; about Rs 41.2 lakh is growth on the pot already built. An SIP's corpus is back-loaded, which is why stopping early costs far more than the missed instalments.
Why is the guess of a quarter so far off?
A quarter assumes the corpus grows by the same amount each year, like a piggy bank filled with the same coins every month. Compounding is not a piggy bank. Each year's growth is a percentage of a pot that is already larger than the year before, so the rupee gains get bigger every year and the corpus is heavily back-loaded. After 15 years of Rs 10,000 a month the pot holds about Rs 50.5 lakh, and five more years at 1% a month multiply that by 1.01 to the 60th, about 1.82, before a single new instalment is counted.
The SIP corpus reaches Rs 23.2 lakh at year 10 and Rs 50.5 lakh at year 15, then adds Rs 49.5 lakh in the last five years to end at Rs 99.9 lakh; of that addition, Rs 41.2 lakh is growth on the year-15 pot and only Rs 6 lakh is new instalments.
Where exactly does the last five years' money come from?
Split the Rs 49.5 lakh three ways. The 60 new instalments put in Rs 6 lakh. Those instalments earn about Rs 2.2 lakh of growth by year 20. The year-15 pot of Rs 50.5 lakh earns about Rs 41.2 lakh. The engine of the final years is the money already invested, not the money still to come. For contrast, the first ten years build only about Rs 23.2 lakh, 23% of the final corpus, though half the instalments are paid in them.
The relationship
$\text{share}_{16\text{-}20} = 1 - \frac{FV_{180}}{FV_{240}}, \qquad FV_n = m\,\frac{(1.01)^n - 1}{0.01}\,(1.01)$
m the monthly instalment, Rs 10,000
FV_n the corpus after n monthly instalments paid at the start of each month
1.01 one plus the 1% monthly return
What it says in wordsThe last five years' share is one minus the year-15 corpus divided by the year-20 corpus.
What does this mean for an investor thinking of stopping at year 15?
It depends what stopping means. Redeeming at year 15 gives up about Rs 49.5 lakh, half the eventual corpus, to save Rs 6 lakh of instalments. Pausing the instalments but staying invested is far cheaper: the year-15 pot alone grows to about Rs 91.7 lakh, so the cost is about Rs 8.2 lakh. The 12% is an assumption for the arithmetic; real returns vary year to year, and a bad last five years would cut the back-loaded gain sharply, which is the sequence risk of an SIP.
Where candidates lose it
The trap is answering a quarter because five years is a quarter of twenty. It treats the corpus as if it grew in a straight line. Name the compounding before you name a number.
The second loss is crediting the last five years' gain to the last five years' instalments. Only Rs 6 lakh of the roughly Rs 49 lakh is new money; most of it is growth on the pot built in the first fifteen years.
What the interviewer asks next
What share of the corpus appears in the last five years of a 30-year SIP at the same return?
At 8% a year instead of 12%, is the corpus more or less back-loaded?
Why does starting an SIP five years earlier matter more than adding five years at the end?
051A Rs 800 crore debt fund writes a Rs 40 crore bond down to zero and segregates it into a separate portfolio. An investor holds 10,000 units bought at a NAV of Rs 25. What does she hold after segregation, at what NAVs, and what does she receive if 60% of the bond is later recovered?NAV, units and fund mechanicsHardFund operationsFixed income desks
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Right after segregation, what does her holding look like?
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She holds 10,000 main units at Rs 23.75, worth Rs 2,37,500, plus 10,000 segregated units valued at zero. The fund has 32 crore units; Rs 760 crore of healthy bonds over those units gives Rs 23.75. If 60% of the bond comes back, Rs 24 crore is spread over 32 crore segregated units, Rs 0.75 each, so she receives Rs 7,500. Her total is Rs 2,45,000 against Rs 2,50,000 before.
Why split the fund instead of simply marking the bond to zero?
Picture a housing society that lends money to a builder who then stops paying. If the society writes the loan off and lets members leave with their share of what is left, the members who leave first give up their slice of any money later recovered, and the ones who stay collect it all. A plain write-down hands the value of a future recovery to whoever is still in the fund when the cash arrives, not to whoever owned the fund when the loss happened. A segregated portfolioA separate pool, created on a credit event, that holds only the troubled bond. Everyone who held the fund that day gets matching units in it. fixes that by giving every holder on the day a separate, frozen claim on the bad bond.
Here the fund has Rs 800 crore at a NAV of Rs 25, so it has 32 crore units. The bond of Rs 40 crore moves out; Rs 760 crore of healthy bonds stays behind. Divide by the same 32 crore units and the main NAV is Rs 23.75. Her 10,000 units there are worth Rs 2,37,500, and she also receives 10,000 segregated units, valued at nothing today.
On the credit event the fund splits: the main portfolio keeps Rs 760 crore at a NAV of Rs 23.75, the defaulted bond moves into a segregated portfolio at zero with matching units, and a 60% recovery later pays Rs 0.75 a unit, taking her total to Rs 2,45,000 against Rs 2,50,000 before.
What does the recovery pay, and who would have got it without segregation?
A 60% recovery brings back Rs 24 crore. Spread across 32 crore segregated units it is Rs 0.75 a unit, so she receives Rs 7,500 whether or not she has since redeemed her main units. Without segregation, the same Rs 24 crore would land on whoever held the single fund on recovery day. Suppose half the units redeem at Rs 23.75 after the write-down: the recovery then lands on only 16 crore units, Rs 1.50 each. The holders who stayed collect Rs 15,000 per 10,000 units, double their fair share, and the holders who left get nothing.
The relationship
$\text{NAV}_{\text{main}} = \frac{800 - 40}{32} = 23.75 \qquad \text{recovery per unit} = \frac{0.6 \times 40}{32} = 0.75$
800 fund assets before the default, Rs crore
40 the defaulted bond, Rs crore
32 units outstanding, crore, fixed on the day of segregation
0.6 the share of the bond later recovered
What it says in wordsBoth portfolios divide by the same unit count, because every holder on the day gets one segregated unit per main unit.
Say the limit too. Segregation does not reduce the loss; she is still Rs 5,000 down on Rs 2,50,000. It only makes sure the loss and any recovery fall on the same people. Indian rules allow it only after a defined credit event such as a rating downgrade, with conditions set in SEBI circulars that should be checked before quoting them.
Where candidates lose it
Most candidates stop at the main NAV of Rs 23.75 and forget the second set of units. The interviewer is testing whether you know the investor keeps a claim on the bad bond, which is the whole reason segregation exists.
The second loss is dividing the recovery by the wrong number. The segregated units match the units outstanding on the day of the event, 32 crore, not the units left in the main portfolio after later redemptions or new purchases.
What the interviewer asks next
A new investor buys the main portfolio the day after segregation. Does she get any segregated units?
Why might a fund manager prefer to hold a defaulted bond at a small positive value instead of zero?
The recovery arrives in three instalments over two years. How is it paid out?
053You backtest 20 fund-selection rules, none of which has any real skill. Each rule's measured alpha is pure noise with a standard deviation of 2% a year. What alpha does the best rule show in the backtest, and what should you expect from it out of sample?Statistics, correlation and diversificationHardFund research and ratingsGlobal asset managers
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Roughly what alpha does the best of the 20 rules show in the backtest?
Show the worked solution
The best rule shows about 3.7% of alpha in the backtest, and you should expect about zero from it afterwards. The largest of 20 normal draws sits about 1.87 standard deviations above the mean, and 2% noise times 1.87 is 3.7%. Picking the winner selects the luckiest draw, and luck does not repeat, so its expected alpha out of sample is the true alpha of every rule: zero.
Why does the best rule look good when none of them is?
Ask twenty people to toss a coin ten times and one of them will probably get eight heads. Nobody concludes that person has a talent for heads. When you choose the best of many attempts, you are choosing the luckiest draw, and the more attempts you make, the luckier the winner looks. One rule on its own shows more than 2% alpha only about one time in six. Among 20 rules, the best one shows more than 3% about 75% of the time.
Twenty rules with no skill scatter around zero with a 2% spread, the best of them shows about 3.7% in the backtest, and the same rule's expected alpha in the years after selection is zero.
The relationship
$E\left[\max_{i \le 20} \alpha_i\right] \approx 1.87 \times 2\% \approx 3.7\% \qquad E[\alpha_{\text{next}}] = 0$
alpha_i the backtest alpha of rule i, pure noise
1.87 how many standard deviations the largest of 20 normal draws sits above the mean, on average
2% the spread of the noise in each rule's alpha
What it says in wordsThe winner's backtest alpha measures how many rules you tried, not how good the winner is.
What should you expect out of sample, and how would you check a real rule?
Out of sample the noise is drawn again, fresh, and the rule has no skill, so its expected alpha is zero. The gap between 3.7% and zero is the price of searching, sometimes called selection biasThe distortion that comes from reporting the best of many tries as if it were the only try. The winner looks better than its true quality.. The honest checks follow from that. Hold back data the rules never saw and test only the winner on it. Raise the bar with the number of rules tried: a one-rule test might accept 2 standard deviations, but after 20 tries the best result is expected to reach 1.87 on luck alone. Ask whether the rule has an economic reason to work.
This is also why fund ranking tables are a weak guide on their own. A category with 20 funds and no skill still produces a fund that beat its peers by about 3.7% a year over the backtest window, and the marketing for that fund writes itself. The limit of the arithmetic: real rules are correlated, which shrinks the effective number of tries and the size of the winner's luck.
Where candidates lose it
The trap is answering zero to the first half. Every rule averages zero, but the question asks about the best one, and the maximum of 20 draws is far from the average draw. Candidates who say zero have not noticed the selection step.
The mirror trap is answering 3.7% to the second half and believing the winner will keep it. The interviewer wants both halves: a large number in the backtest and zero afterwards, with the reason.
What the interviewer asks next
How would the best backtest alpha change if you tested 200 rules instead of 20?
Your rules are strongly correlated with each other. Does the winner look more or less lucky?
How many years of out-of-sample data would you need to tell a true 2% alpha from zero at this noise level?
054At an 8% yield, which has the highest duration: a 10-year zero-coupon bond, a 10-year 9% coupon bond, or a 15-year 12% coupon bond?Bond maths and durationHardFixed income desksIndian AMCs
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Gut call first: which bond carries the most interest rate risk?
Show the worked solution
The 10-year zero, with a duration of 10.0 years. A zero pays everything at maturity, so its duration equals its maturity. The 15-year 12% bond has a duration of about 8.6 years, because its large coupons bring value forward, and the 10-year 9% bond is about 7.1. The zero moves most when rates move, even though it is not the longest bond.
Why is maturity the wrong ruler?
Think of two loans to a friend. One friend repays everything in one go after ten years. The other repays a large slice every year for fifteen years. Most of the second loan is back in your hands long before the first friend pays a rupee. Duration measures when, on average, a bond's value comes back to you, weighted by the present value of each payment, and rate risk follows that average, not the final date. A zero returns all of its value at one date, so its duration is exactly its maturity.
At an 8% yield the 10-year zero balances at 10.0 years, the 10-year 9% bond at 7.1 years and the 15-year 12% bond at 8.6 years, because the large coupons of the longest bond pull its balance point inside that of the zero.
How do you rank them without a calculator?
Use two rules and one check. A zero's duration is its maturity. A coupon bond's duration is always below its maturity, and the higher the coupon, the further below. So the only real contest is between the zero at 10 and the 15-year bond, and a 12% coupon pulls hard: about 60% of that bond's present value arrives in the first ten years. The 10-year 9% bond cannot beat the 10-year zero, because it has the same final date and pays some value earlier.
The relationship
$D = \frac{\sum_t t \cdot \frac{CF_t}{(1+y)^t}}{\sum_t \frac{CF_t}{(1+y)^t}}$
t the year a cash flow arrives
CF_t the cash flow in year t, coupon plus face at maturity
y the yield, 8% here
What it says in wordsDuration is the average arrival time of a bond's cash flows, each weighted by what it is worth today.
Add the sizing, because desks price risk in rupees. Modified durationMacaulay duration divided by one plus the yield. It gives the approximate percentage price change for a one point move in yield. is Macaulay duration over 1.08, so the zero loses about 9.3% of its price for a one point rise in yield and the 15-year bond about 7.9%. The limit: this is a small-move estimate, and it ignores the curve changing shape. Even a 30-year 12% bond only reaches about 11.5 years, because a coupon bond's duration can never exceed that of a perpetuity, 13.5 years at 8%.
Where candidates lose it
The instinct is to pick the 15-year bond because it is the longest. That confuses the last payment date with the average one, and on a desk it means hedging the wrong book.
The quieter miss is treating coupon size as a detail. At 12% the coupons are large enough to pull the duration down to 8.6 years; at a 2% coupon the same 15-year bond would have a duration well above 10.
What the interviewer asks next
What coupon on the 15-year bond would make its duration equal to the zero's?
Why does a floating-rate bond have a duration close to its next reset date?
Yields rise from 8% to 10%. Which of the three loses the most in rupees per Rs 100 of face?
056An equity fund has 120% annual portfolio turnover and pays about 0.4% round trip in impact cost and brokerage every time it replaces a holding. Roughly how much return does it lose each year that never appears in the expense ratio?Costs and fee dragCoreFund research and ratingsIndian AMCs
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How much does the trading cost take from the return each year?
Show the worked solution
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.
A fund earning 12.5% gross loses 1.2% to its expense ratio and a further 0.48% to trading, so the investor receives 10.82% and about 29% of the total cost never appears in the expense ratio.
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%.
The relationship
$\text{hidden drag} = \text{turnover} \times \text{round-trip cost} = 1.2 \times 0.4\% = 0.48\%$
turnover the fraction of the portfolio replaced in a year, 1.2 here
round-trip cost brokerage, taxes and impact cost for one sale plus one purchase, 0.4% here
What it says in wordsMultiply how often the book is replaced by what one replacement costs, and you have the yearly drag that the expense ratio does not show.
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.
Where candidates lose it
The first lost answer is zero, from a candidate who assumes the expense ratio is the whole cost of owning a fund. The interviewer is checking whether you know that trading costs travel through the NAV, out of sight.
The second is 0.96%, from doubling a cost that was already quoted round trip. Ask, or state, whether the 0.4% is per side or per round trip before you multiply.
What the interviewer asks next
Why would a larger fund with the same turnover usually pay a higher round-trip cost?
How could you estimate a fund's trading cost from its disclosed returns and its index?
An index fund has 8% turnover. Roughly what is its hidden drag at the same cost per trade?
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.
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
$1.5\% - 1.2\% = 0.3\text{ pp} = 30\text{ bps} \qquad \frac{1.5 - 1.2}{1.5} = 20\%$
pp percentage points, the plain gap between two rates
bps basis points, one hundredth of a percentage point
1.5 the 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?

YTM	the portfolio's yield to maturity on the day you invest, 7.4%
TER	the total expense ratio, 0.2% a year
r_hold	the return a hold-to-maturity investor can reasonably expect

\bar{c}	average cost per unit
100, 60	the two NAVs paid

p	the chance of a losing year, 25%
n	years held, 5

NAV_t	the NAV at time t
max NAV_s	the running peak up to time t
MDD	the maximum drawdown, the worst reading

Try it first

Why is yield to maturity a fair starting point?

Why will the realised return not be exactly 7.2%?

What else should the investor be told?

Where candidates lose it

What the interviewer asks next

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Why is the average 75 and not 80?

Does a lower break-even mean the decision was good?

Where candidates lose it

What the interviewer asks next

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Why work with the opposite event?

Why does an adviser care about this number?

Where candidates lose it

What the interviewer asks next

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Why measure from the peak and not from the start?

How do you compute it step by step?

Where candidates lose it

What the interviewer asks next

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Why is the guess of a quarter so far off?

Where exactly does the last five years' money come from?

What does this mean for an investor thinking of stopping at year 15?

Where candidates lose it

What the interviewer asks next

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Why split the fund instead of simply marking the bond to zero?

What does the recovery pay, and who would have got it without segregation?

Where candidates lose it

What the interviewer asks next

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Why does the best rule look good when none of them is?

What should you expect out of sample, and how would you check a real rule?

Where candidates lose it

What the interviewer asks next

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Why is maturity the wrong ruler?

How do you rank them without a calculator?

Where candidates lose it

What the interviewer asks next

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

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

Where candidates lose it

What the interviewer asks next

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Why are there two different answers that are both right?

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

Where candidates lose it

What the interviewer asks next