Portfolio Management puzzles, solved step by step

Puzzles: 100
Traced to a firm: 31
Topics: 13
Hard: 30

Showing 71–80 of 100

071Over the last 100 trading days, portfolio A's five worst daily losses were Rs 5.2, 5.5, 6.0, 6.3 and 7.0 crore. Portfolio B's were Rs 5.2, 6, 9, 15 and 25 crore. Both report the same one-day 95% value at risk of Rs 5 crore. What is each portfolio's expected shortfall?Portfolio risk mathsCoreRisk managementInstitutional asset management
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How do the two portfolios compare once you look past the value at risk?
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A's expected shortfall is Rs 6.0 crore; B's is about Rs 12.0 crore. With 100 days, the worst 5% are the five worst days, and expected shortfall is their average. A's five add to 30, an average of 6.0. B's add to 60.2, an average of 12.04. Both portfolios cross Rs 5 crore on the same number of days, but when B has a bad day it is, on average, twice as bad.
What does value at risk leave out?
Think of a river's flood mark. Saying the river tops the bank five days a year tells you nothing about whether it rises a hand's width or floods the town. Value at risk tells you the loss that is exceeded on the worst 5% of days, and nothing about how big those losses are. Both portfolios breach Rs 5 crore on five days in a hundred, so their VaR is identical. What happens beyond that line is where they differ, and it is exactly the part the measure does not describe.
Both portfolios have the same Rs 5 crore value at risk, but A's five worst days average Rs 6.0 crore while B's average Rs 12.0 crore, because B's tail stretches out to a Rs 25 crore day.
The relationship
$ES_{95} = \frac{1}{5}\sum_{i=1}^{5} L_{(i)} \qquad A: \frac{30}{5} = 6.0 \qquad B: \frac{60.2}{5} = 12.04$
L_(i) the i-th worst daily loss, Rs crore
5 the number of days in the worst 5% of a 100-day sample
What it says in wordsExpected shortfall is the average loss on the days worse than the value at risk.
Why do risk managers prefer expected shortfall?
Because it cannot be gamed as easily and it adds up sensibly. A trader can sell deep out-of-the-money options, which earn small premiums almost every day and lose heavily now and then. That book can show a low VaR while hiding a large tail. Expected shortfall looks inside the tail, so strategies that pile risk just past the cut-off show up in it. It also behaves well when books are combined: diversification never makes it worse, which VaR cannot promise.
Be honest about the limits. Five observations are a thin sample for estimating anything, and one Rs 25 crore day dominates B's figure. A longer history, or a model of the tail, would be needed before setting limits on it. The comparison is still the right first read: same VaR, and one portfolio's bad days are twice as painful.
Where candidates lose it
The trap is saying the two portfolios carry the same risk because the VaR is the same. The question is built to show that VaR stops at the edge of the tail.
The second miss is quoting B's worst day, Rs 25 crore, as its risk. That is a single observation; expected shortfall averages the whole tail, which is the fair comparison with A.
What the interviewer asks next
Why does VaR sometimes rise when two books are combined, and why can that not happen with expected shortfall?
What kind of strategy produces a tail like portfolio B's?
How would you estimate expected shortfall with only 100 days of data?
072An equity index trades at 22 times forward earnings, pays out 40% of earnings as dividends, and its long-run earnings growth is expected to be 10% a year. The 10-year government bond yields 7%. Which asset is cheaper?Valuation riddlesHardPIMCOSan Diego · 2026
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The earnings yield is 4.5% and the bond yields 7%. What does that comparison tell you?
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On expected return, equities offer about 11.8% against the bond's 7%, a premium of about 4.8 points. The earnings yield, 1 over 22 or 4.5%, looks worse than 7%, but it ignores growth. The dividend yield is 40% of 4.5%, or 1.82%, and adding 10% growth gives about 11.8%. Whether equities are cheaper depends on whether a 4.8-point premium pays enough for equity risk.
Why is 4.5% against 7% the wrong comparison?
Compare a fixed-rent lease with a shop whose profits grow each year. The lease might pay more in year one, but the shop's income keeps rising. A bond's yield is everything it will ever pay, while an earnings yield is only the starting point of a stream expected to grow, so the two cannot be compared directly. The earnings yield of 4.5% sits 2.5 points below the bond, and that gap says almost nothing about which is cheaper.
The earnings yield of 4.5% looks worse than the bond's 7%, but the index's expected return, a 1.8% dividend yield plus 10% growth, is about 11.8%, a premium of about 4.8 points over the bond.
How do you put them on the same footing?
Estimate the equity's expected return the way you would a bond's. For a stock or an index, that is roughly the dividend yield plus long-run growth, the logic of the Gordon growth model. The dividend yield is the payout ratio times the earnings yield, and the growth rate does the rest. Here 40% of 4.55% is 1.82%, and 10% growth takes the total to 11.82%. Against 7% on the bond, equities offer 4.82 extra points a year.
The relationship
$E[R] \approx \frac{D}{P} + g = 0.40 \times \frac{1}{22} + 10\% = 1.82\% + 10\% = 11.82\%$
D/P the dividend yield, the payout ratio times earnings over price
g long-run growth in earnings and dividends, 10%
What it says in wordsAn equity's expected return is roughly its dividend yield plus the rate at which its dividends grow.
Then test the growth number, because the answer rests on it. Growing earnings 10% while paying out 40% means reinvesting 60% at a return on equity of about 16.7%, which is demanding for a whole market. If growth were 8%, the premium would shrink to about 2.8 points. A view on which asset is cheaper is really a view on whether that premium, after testing growth, pays enough for the extra risk of equities. That is the judgement to state, with the numbers that drive it.
Where candidates lose it
The trap is comparing the earnings yield with the bond yield and declaring bonds cheaper. That comparison ignores growth and treats a rising income stream as if it were fixed.
The second loss is taking the 10% growth at face value. Check it against the payout ratio: growth needs reinvestment, and the implied return on equity tells you whether the number is plausible.
What the interviewer asks next
What equity risk premium would you need to call equities and bonds fairly valued here?
How does inflation change the comparison between an earnings yield and a nominal bond yield?
What growth rate makes the index's expected return exactly equal to 7%?
Asked at PIMCO, Debt Capital Markets, San Diego, 2026 (Wall Street Oasis): Which is cheaper us bonds or us equities
073Estimate how many individuals in India hold a direct equity portfolio worth more than Rs 50 lakh, the minimum ticket for a portfolio management service.Market sizing and estimationHardIndian wealth managementIndian asset management
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Which step decides the answer most?
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Roughly 5 lakh people, within a range of about 3 to 10 lakh. Start from about 18 crore demat accounts, an assumption to confirm, and divide by 1.5 accounts per person: 12 crore individuals. Perhaps 40% hold a meaningful portfolio, 4.8 crore. Wealth is heavily skewed, so assume about 1 in 100 of those hold more than Rs 50 lakh: about 4.8 lakh. A Pareto-tail check gives the same order of magnitude.
Why is the headline account count a trap?
Think of a cricket academy with thousands of registered players. Asking how many could play first-class cricket is not a question about registrations; it is about the very top of the talent curve. Portfolio sizes are highly skewed, so the count above a high threshold is a small slice of the total, and the size of that slice, not the headline, decides the answer. Crores of accounts become a few lakh people above Rs 50 lakh.
About 18 crore demat accounts shrink to 12 crore individuals and 4.8 crore with meaningful portfolios, and only about 1 in 100 of those holds more than Rs 50 lakh, which is roughly 4.8 lakh people.
How do you defend the 1 in 100?
With a second route. Suppose 20% of the 4.8 crore holders have more than Rs 5 lakh. Wealth tails often thin out like a Pareto distributionA skewed distribution in which the share above any level falls by a fixed power as the level rises, often used for wealth and city sizes.: raise the threshold tenfold and the share falls by a factor of 10 to about 20. Two independent routes landing in the same range is what turns a guess into an estimate. From Rs 5 lakh to Rs 50 lakh is a tenfold rise, so between 4.8 and 9.6 lakh people sit above Rs 50 lakh, which brackets the first answer.
The relationship
$N = \frac{18}{1.5} \times 0.40 \times 0.01 \text{ crore} = 4.8 \text{ lakh}$
18 demat accounts, crore, a round assumption
1.5 accounts per individual
0.40 share holding a meaningful portfolio
0.01 share of those above Rs 50 lakh
What it says in wordsAccounts to people, people to active holders, then the thin top slice above the threshold.
Then say what the number is for, and what it misses. A portfolio management service can also be funded from bank deposits, mutual fund units or property sales, so the true addressable pool is wider than direct equity holders. The Rs 50 lakh minimum and every count used here are figures to confirm against current SEBI rules and depository data; the structure of the estimate is the part to trust.
Where candidates lose it
The trap is quoting the demat account count, or some large share of it, as the answer. It confuses accounts with people and the whole distribution with its top slice, and it lands a hundred times too high.
The second loss is presenting assumptions as facts. Say each number as a round assumption, show the skew check, and give a range, not a single figure said with false precision.
What the interviewer asks next
How would the answer change if the threshold rose to Rs 1 crore?
What data would you use to test the 1 in 100 assumption?
Why might the addressable market for this service be larger than the count of direct equity holders?
074An analyst takes ten years of monthly data, builds rolling 12-month fund and market returns sampled every month, regresses one on the other, and reports an alpha with a t-statistic of 3.6 from ordinary least squares. Why is that overstated, and roughly what is an honest t-statistic?Statistics and forecastingHardAQR Capital ManagementGreenwich · 2022AQR Capital ManagementGreenwich · 2022
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Roughly how large is the honest t-statistic?
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Because the observations overlap, the honest t-statistic is close to 1, about 1.04. Ten years of monthly data give 109 rolling 12-month windows, but each shares 11 months with its neighbour. OLS assumes independent errors, so it treats 109 observations as 109 pieces of information. With the overlap, the variance of the estimate is understated about twelvefold, and 3.6 over the square root of 12 is about 1.0.
Which OLS assumption breaks?
Picture asking the same twelve people for their opinion, then swapping one person each month and asking again. You would not claim 109 independent surveys. OLS standard errors assume the regression errors are uncorrelated with each other, and overlapping windows make them strongly correlated, so the standard errors come out far too small. The alpha estimate itself is not biased; what is wrong is the claim about how precisely it is known, which is exactly what the t-statistic reports.
Two 12-month windows one month apart share 11 months, so their correlation is 11 over 12 and falls in equal steps to 1 over 12 at an 11-month gap, which inflates the true variance of the estimate about 12-fold.
How do you get to about 1?
Add up the overlap. If monthly returns are independent, two 12-month windows k months apart have a correlation of 12 minus k over 12. The variance of an average of such overlapping sums is inflated by one plus twice the sum of those correlations, which here is 1 plus 2 times 5.5, or 12. The t-statistic shrinks by the square root of the inflation factor, 3.6 divided by the square root of 12. That gives about 1.04: nowhere near significant, and consistent with having only about ten independent years.
The relationship
$\text{VIF} = 1 + 2\sum_{k=1}^{11}\frac{12-k}{12} = 12 \qquad t^* = \frac{3.6}{\sqrt{12}} = 1.04$
VIF variance inflation from the overlap
(12-k)/12 the correlation of two windows k months apart
t* the corrected t-statistic
What it says in wordsOverlap inflates the true variance about twelvefold, so divide the naive t-statistic by the square root of twelve.
How would you fix it? Three answers, in order of simplicity. Run the regression on non-overlapping monthly returns, which uses all the data with independent errors. Or keep the overlap and use standard errors that allow for autocorrelation, such as Newey-West or Hansen-Hodrick with 11 lags. Or sample the 12-month returns once a year, which leaves only ten points but honest ones. The interviewer wants to hear that the fix is about the standard errors, not the coefficient.
Where candidates lose it
The trap is defending 3.6 because the sample has over a hundred observations. The count of rows is not the count of independent pieces of information, and that is the whole point of the question.
The second loss is saying the alpha estimate itself is biased. It is not; the problem is its precision. Name the broken assumption, uncorrelated errors, and the fix, corrected standard errors or non-overlapping data.
What the interviewer asks next
What other OLS assumptions matter most for return regressions, and how would you check them?
Why do overlapping returns make long-horizon predictability look stronger than it is?
How many lags would you use in Newey-West standard errors here, and why?
Asked at AQR Capital Management, Investments, Greenwich, 2022 (Wall Street Oasis): they asked about how to fix ols assumptions
Asked at AQR Capital Management, Investments, Greenwich, 2022 (Wall Street Oasis): How would you fix violations of the OLS assumptions?
075A callable bond is priced at 100.0. If yields rise 50 basis points its price falls to 98.9; if yields fall 50 basis points it rises only to 100.6. What are its effective duration and effective convexity?Bond mathsHardAmundiLondon · 2018
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What sign does the convexity take?
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Effective duration is about 1.7 and effective convexity about -200. Duration is the price difference across the two shocks over twice the price times the shock: 1.7 over 1.0, which is 1.7. Convexity is the sum of the shocked prices less twice the base, over the price times the shock squared: minus 0.5 over 0.0025, which is -200. The call caps the price, so it gains less than it loses.
Why effective duration rather than the usual formula?
Think of renting out a flat on a lease the tenant can cancel whenever cheaper flats appear. When rents fall, the tenant leaves and you do not keep the high rent; when rents rise, you are stuck. A callable bond's cash flows change with yields, because the issuer calls it when rates fall, so you measure its duration from how its price actually moves, not from a fixed schedule of coupons. That is effective duration: shock the yield both ways, reprice, and read the slope.
The relationship
$D_{eff} = \frac{P_- - P_+}{2P_0\Delta y} = \frac{100.6 - 98.9}{2 \times 100 \times 0.005} = 1.7 \qquad C_{eff} = \frac{P_- + P_+ - 2P_0}{P_0 \Delta y^2} = \frac{-0.5}{0.0025} = -200$
P_- price when yields fall 50 bp, 100.6
P_+ price when yields rise 50 bp, 98.9
P_0 the starting price, 100.0
Delta y the shock, 0.005
What it says in wordsDuration is the average slope across the two shocks; convexity is how much the two moved prices bend away from a straight line.
The callable bond rises only to 100.6 when yields fall 50 basis points, because the call caps it below 101, but falls to 98.9 when yields rise, so its effective duration is 1.7 and its convexity is negative, about -200.
What does negative convexity cost the holder?
It means the bond loses more when yields rise than it gains when they fall. The holder has sold the issuer an option to refinance, and the price of that option is the upside given up when rates fall. A straight bond with a duration of about 4 would gain about 2.0 points for a 50 basis point fall; this one gains 0.6. The holder is paid for this through a higher yield than an equivalent straight bond, and the question for a portfolio manager is whether that extra yield covers the option given away.
Two more things are worth saying. The duration of 1.7 is not fixed: as yields fall towards the level where a call becomes likely, duration shrinks further, and as they rise, it lengthens towards the bond's straight duration. That shifting is why callable bonds, and mortgage securities with the same feature, need effective measures rather than the textbook formulas. The curve in the figure is a stylised fit around the three prices given; a real one would come from an option pricing model.
Where candidates lose it
The trap is computing a positive convexity by habit, or dividing by the shock rather than the shock squared and getting minus 1. Write the formula, put the sign of 100.6 plus 98.9 minus 200 on the page, and the negative number is obvious.
The second loss is giving the numbers without the story. Say that the call caps the upside, which is why duration is short and convexity negative.
What the interviewer asks next
Estimate the price change for a 100 basis point fall using this duration and convexity. Why might it be wrong?
Why does a callable bond's effective duration lengthen when yields rise?
What would the price-yield curve of a putable bond look like?
Asked at Amundi, Rates, London, 2018 (Wall Street Oasis): What would your allocation be in today's market? What is effective duration?
076A Rs 100 crore bond portfolio has a modified duration of 5. What is its DV01, and roughly what does a 25 basis point rise in yields cost?Bond mathsWarm upFixed incomeRisk management
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Say the DV01 before you work it through.
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DV01 is Rs 5 lakh, so a 25 basis point rise costs about Rs 1.25 crore. Modified duration of 5 means the value moves about 5% for each percentage point of yield, or 0.05% per basis point. 0.05% of Rs 100 crore is Rs 5 lakh, and 25 basis points is 25 times that.
Why turn duration into rupees at all?
A shopkeeper who says the rent went up 4% has told you something; one who says it went up Rs 2,000 a month has told you what to do about it. Duration is the percentage version. DV01, the rupee change for a one basis point move, is the version a desk can add across positions, compare with a limit and put in a risk report. Two portfolios with the same duration but different sizes carry very different rupee risk, and only DV01 shows it.
Rs 100 crore times a modified duration of 5 times 0.0001 is Rs 5 lakh per basis point, so a 25 basis point rise in yields takes Rs 1.25 crore off the portfolio, one Rs 5 lakh notch at a time.
The relationship
$\text{DV01} = V \times D_{mod} \times 0.0001 = 100 \times 5 \times 0.0001 = 0.05 \text{ crore}$
V portfolio value, Rs 100 crore
D_mod modified duration, 5
0.0001 one basis point written as a decimal
What it says in wordsThe rupee move for one basis point is the value times the duration times one hundredth of one per cent.
Where does the straight-line answer stop being right?
The modified durationThe percentage change in a bond price for a one percentage point change in its yield, taken at the current yield. estimate is a tangent: it treats the price and yield relationship as a straight line. For 25 basis points the straight line is close enough, but for a 200 basis point shock the curve bends away from it and the true loss is smaller than DV01 times 200. That bend is convexity. Mention it in one sentence; the interviewer will often ask for it next.
Say also that DV01 assumes every yield in the portfolio moves by the same amount. If short rates rise and long rates stay still, a single DV01 number misses it, which is why desks also keep DV01 by maturity bucket.
Where candidates lose it
The common slip is out by a factor of 100: treating duration 5 as 5% per basis point and saying Rs 5 crore. The interviewer hears that you have not held a real rate position, where the size of one basis point is the first thing you learn.
The second loss is stopping at the number. Say that DV01 is linear, so it overstates the loss for large rises, and that it assumes a parallel move.
What the interviewer asks next
The portfolio doubles in size and duration falls to 2.5. What is DV01 now?
How would you cut DV01 by half without selling any bonds?
Why might a desk set a limit in DV01 rather than in duration?
077Money doubles every six years. How long does it take to grow to eight times, and roughly what annual return does that imply?Compounding and fee dragWarm upWealth managementAsset management
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How many years to reach eight times?
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Eighteen years, at about 12.2% a year. Eight is two times two times two, so reaching eight times takes three doubling periods of six years each. The return that doubles money in six years is 2 to the power one sixth, less one, which is 12.2%; the rule of 72 gives 12% as a quick check.
Why count doublings instead of dividing?
A rumour passed on by each listener to two new people reaches 2, then 4, then 8. Nobody counts that as adding 2 each round; it doubles each round. A compounding balance works the same way, so any multiple that is a power of two is just a count of doubling periods. Eight is two cubed: three doublings, eighteen years. Sixteen times would be four doublings, twenty four years.
Money that doubles every six years is worth 2 times at year 6, 4 times at year 12 and 8 times at year 18, and the smooth path between those points is a steady 12.2% compounded each year.
How do you get the annual return without a calculator?
Use the rule of 72: the doubling time multiplied by the rate is roughly 72, so 72 divided by 6 is 12%. The exact figure is 12.25%, and the rule of 72 is within a quarter point anywhere from about 6% to 12%. Give 12% first, then say it is a shade over, which shows you know the rule is an approximation.
The relationship
$(1+r)^6 = 2 \;\Rightarrow\; r = 2^{1/6} - 1 \approx 12.2\%$
r the annual return
6 years to double
What it says in wordsThe annual return is the sixth root of two, less one.
Portfolio managers ask this because clients think in multiples and managers think in annual rates. Being able to move between the two in your head is the whole skill.
Where candidates lose it
The fast wrong answer is 48 years, eight times six, which treats the multiple as a count of periods. It is the same straight-line habit that makes people underestimate what compounding does over a career.
The quieter loss is saying 12% and stopping. Give 12% from the rule of 72, then correct it to about 12.2%, so the interviewer sees you know where the shortcut comes from.
What the interviewer asks next
How long to reach 10 times at the same rate?
If fees take 1.5% a year off that return, how long does one doubling take?
Why does the rule of 72 get worse at very high rates?
078You bought a stock at Rs 800. It now trades at Rs 500, and your updated estimate of fair value is Rs 450. Do you hold it until it gets back to Rs 800?Behavioural and decision trapsWarm upAsset managementWealth management
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Which numbers belong in the decision?
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No. The Rs 800 you paid does not enter the decision; on your own numbers the stock is worth less than it trades for. Getting back to Rs 800 needs a 60% rise. Your own value of Rs 450 sits 10% below the Rs 500 price. Holding it is a fresh decision to own an overpriced stock.
Why does the purchase price feel like it matters?
Someone who paid Rs 2,000 for a concert ticket will go out in a storm with a fever rather than waste it, although the money is gone either way. The only question left is whether the evening is worth it now. Money already spent is sunk: it is the same whatever you do next, so it cannot help choose what to do next. The purchase price of a stock is exactly that kind of number.
The Rs 800 purchase price sits outside the decision, and the 60% rise needed to reach it is irrelevant; the live comparison is today's price of Rs 500 against your updated value of Rs 450, which says the stock is overpriced.
How do you say it so it sounds like judgement rather than a slogan?
Turn the question round. If you had Rs 500 in cash today and no history with this stock, would you buy it at a price above your own value? If the answer is no, holding it is the same bet in disguise. The anchoringLeaning on a reference number, here the purchase price, when judging something that does not depend on it. pull comes from the Rs 800, and the disposition effect, holding losers to avoid booking the loss, is a well documented habit among professional managers as well as individuals.
Then give the honest limits. Your Rs 450 is an estimate, so ask how confident you are and whether anything has changed that the price already reflects. A booked loss can also offset gains for tax, which is a reason to act, not to wait. Replacement matters too: the money should go to whatever has the best expected return per unit of risk, which may or may not be this stock.
Where candidates lose it
The trap is answering the question as asked, with a view on how long the stock might take to get back to Rs 800. That accepts the anchor, and the interviewer is testing whether you reject it.
The opposite slip is a flat sell with no reasoning. Say the sunk cost point, give the would-I-buy-it-today test, then note that your Rs 450 value is an estimate that deserves a second look.
What the interviewer asks next
Your value was Rs 900 instead of Rs 450. What changes?
Why do managers hold losers longer than winners, and how would you guard against it in your own process?
How would you explain this to a client who refuses to sell below cost?
079An Indian investor holds a US stock that rises 8% in dollars over a year, while the rupee weakens 5% against the dollar. What is the investor's return in rupees?Currency and global returnsWarm upGlobal investingIndian wealth management
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Pick the rupee return.
Show the worked solution
About 13.4% in rupees. The stock turns each dollar into 1.08 dollars, and each dollar now buys 5% more rupees, so each rupee invested becomes 1.08 x 1.05, or 1.134 rupees. The extra 0.4% over simple addition is the currency gain earned on the stock gain.
Does a weaker rupee help or hurt this investor?
A student in India whose parents send a fixed dollar allowance from abroad is better off when the rupee weakens: the same dollars convert into more rupees. An Indian investor holding dollar assets is in the student's position, so a weaker rupee adds to the return. Say the direction first, because half the candidates who get this wrong get the sign wrong, not the arithmetic.
The stock's 8% dollar gain and the rupee's 5% fall add to 13%, and the extra 0.4% comes from the currency gain applying to the grown dollar amount, taking the rupee return to 13.4%.
Where does the extra 0.4% come from?
Follow Rs 100. At the start it buys a dollar amount; a year later that amount has grown 8%. The 5% currency gain is earned on the grown amount, not the original one, so the currency also earns 5% on the 8% profit, which is 0.4%. For small moves the cross term hardly matters; for a 30% stock gain with a 10% currency move it is 3 points.
The relationship
$1 + r_{Rs} = (1 + r_{\$})(1 + r_{FX}) = 1.08 \times 1.05 = 1.134$
r_$ the stock's return in dollars, 8%
r_FX the change in rupees per dollar, 5%
r_Rs the return measured in rupees
What it says in wordsThe home currency return is the local return compounded with the currency return.
Run it the other way as a check. If the rupee had strengthened 5% instead, the return would be 1.08 x 0.95, less one, which is 2.6%: a good stock year mostly erased by currency. That is why global allocations report returns in both currencies.
Where candidates lose it
The costly slip is the sign: treating a weaker rupee as a loss and answering 3%. It shows the candidate is thinking about the rupee's health rather than about which currency the investor owns.
The smaller slip is 13% from simple addition. Say 13.4%, and name the cross term, so the interviewer hears that you know returns multiply.
What the interviewer asks next
What if the rupee strengthens 5% instead?
How would the investor hedge the currency, and what would that cost or earn?
Over ten years, why might currency matter more than the one-year cross term suggests?
080A fund turns over 120% of its portfolio a year, and each round trip, selling a holding and buying its replacement, costs 40 basis points. What is the annual drag on returns from trading?Funds, ETFs and implementationWarm upPortfolio implementationMutual funds
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What is the annual trading drag?
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About 0.48% a year. Turnover of 120% means the fund sells and replaces the equivalent of its whole portfolio 1.2 times a year. At 40 basis points per round trip, the drag is 1.2 x 40, or 48 basis points. On a Rs 1,000 crore fund that is Rs 4.8 crore a year, taken from returns rather than charged as a fee.
What exactly is a round trip, and why count it that way?
Trading in a car costs you twice: the dealer pays less than it is worth when you sell, and charges more than it is worth when you buy the next one. A fund switching one stock for another pays the same two-sided cost, so the natural unit is the round trip: one sale and one purchase together. Reported turnover is usually the lesser of purchases and sales over average assets, which counts each switch once, so 120% maps to 1.2 round trips.
Turnover of 120% is 1.2 round trips a year at 40 basis points each, a 48 basis point drag; beside an assumed 1.00% expense ratio, the investor's true cost is 148 basis points, and the trading part never appears on the factsheet.
The relationship
$\text{drag} = \text{turnover} \times \text{cost per round trip} = 1.2 \times 40 = 48 \text{ bp}$
turnover portfolio replaced per year, 120%
cost per round trip spread, market impact, brokerage and taxes on a sale and a purchase, 40 bp
What it says in wordsMultiply how many times the portfolio is replaced by what one replacement costs.
Why does this matter if the expense ratio looks fine?
The expense ratio covers the manager's fee and running costs. Trading costs are paid inside the portfolio, through worse prices and brokerage, so they reduce the return without ever appearing in the expense ratio. A fund with a modest fee and high turnover can cost more in total than a pricier fund that trades little. For a Rs 1,000 crore fund, 48 basis points is Rs 4.8 crore a year.
Say the limitation too. The 40 basis points is an average; impact rises with trade size, so a fund that grows while keeping the same turnover usually pays more per round trip, not less.
Where candidates lose it
The common slip is doubling the answer to 96 basis points on the grounds that turnover counts both the buy and the sell. The usual definition already counts each switch once, and the cost per round trip already includes both legs.
The second slip is saying the cost is already in the expense ratio. It is not, and the interviewer asks precisely to see if you know where trading costs hide.
What the interviewer asks next
The fund doubles in size and keeps the same turnover. What happens to cost per round trip?
How would you estimate a fund's trading costs from its published numbers?
Why do index funds usually have far lower turnover than active funds?

L_(i)	the i-th worst daily loss, Rs crore
5	the number of days in the worst 5% of a 100-day sample

D/P	the dividend yield, the payout ratio times earnings over price
g	long-run growth in earnings and dividends, 10%

18	demat accounts, crore, a round assumption
1.5	accounts per individual
0.40	share holding a meaningful portfolio
0.01	share of those above Rs 50 lakh

VIF	variance inflation from the overlap
(12-k)/12	the correlation of two windows k months apart
t*	the corrected t-statistic

Try it first

What does value at risk leave out?

Why do risk managers prefer expected shortfall?

Where candidates lose it

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Why is 4.5% against 7% the wrong comparison?

How do you put them on the same footing?

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Why is the headline account count a trap?

How do you defend the 1 in 100?

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Which OLS assumption breaks?

How do you get to about 1?

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Why effective duration rather than the usual formula?

What does negative convexity cost the holder?

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Why turn duration into rupees at all?

Where does the straight-line answer stop being right?

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Why count doublings instead of dividing?

How do you get the annual return without a calculator?

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Why does the purchase price feel like it matters?

How do you say it so it sounds like judgement rather than a slogan?

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Does a weaker rupee help or hurt this investor?

Where does the extra 0.4% come from?

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What exactly is a round trip, and why count it that way?

Why does this matter if the expense ratio looks fine?

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