Portfolio Management puzzles, solved step by step

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

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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?
Show the worked solution
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?
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
Try it first
Say the DV01 before you work it through.
Show the worked solution
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
Try it first
How many years to reach eight times?
Show the worked solution
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
Try it first
Which numbers belong in the decision?
Show the worked solution
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
Try it first
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
Try it first
What is the annual trading drag?
Show the worked solution
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?
081On average, how many tosses of a fair coin does it take to see two heads in a row? And why is the answer for a head followed by a tail smaller?Probability and expected valueCoreQuantitative asset managementHedge funds
Try it first
Which pair of averages is right?
Show the worked solution
Two heads in a row takes 6 tosses on average; head then tail takes 4. Each pattern has a one-in-four chance at any pair of tosses, but after a head, a tail wrecks HH and sends you back to the start, while for HT an extra head keeps you exactly where you were. Losing progress on a miss is what costs HH the extra two tosses.
Why do two equally likely patterns take different times to appear?
Picture two ladders. On one, slipping off the second rung drops you to the ground; on the other, slipping leaves you on the second rung. Both ladders need the same two good steps, but you will climb the second one faster. For HH, a tail after a head wipes out your progress; for HT, a head after a head leaves your progress intact, so HT arrives sooner.
For HH, a tail from state H sends you back to Start, which makes the expected wait 6 tosses; for HT, a head from state H keeps you at H, so no progress is ever lost and the expected wait is only 4 tosses.
How do you solve it in the room?
Name the states, write one equation per state, solve. Let the expected tosses still needed be E0 from the start and E1 after a head. Every equation says: one toss, plus the expected wait from wherever that toss sends you. For HH, E1 = 1 + half of 0 + half of E0, and E0 = 1 + half of E1 + half of E0. Substituting gives E0 = 6 and E1 = 4.
The relationship
$E_0 = 1 + \tfrac12 E_1 + \tfrac12 E_0, \qquad E_1^{HH} = 1 + \tfrac12 E_0, \qquad E_1^{HT} = 1 + \tfrac12 E_1^{HT}$
E_0 expected tosses still needed from the start
E_1 expected tosses still needed after one head
What it says in wordsEach state's wait is one toss plus the average of the waits in the states it can lead to.
For HT the second equation changes: after a head, a tail finishes and a head leaves you in the same state, so E1 = 1 + half of E1, which is 2, and E0 is 4. The same state method handles any short pattern, which is the point an interviewer at a quantitative fund wants to hear.
Where candidates lose it
The fast wrong answer is 4 for both, from reasoning that each pattern has a one-in-four chance per pair of tosses. That treats tosses as separate non-overlapping pairs, which they are not.
The other loss is getting 6 by recalling it without the state equations. The follow-up is always a new pattern, so show the method, not the memory.
What the interviewer asks next
How many tosses on average to see three heads in a row?
In a race between HH and HT, which appears first more often?
Where does the idea of losing progress on a miss show up in trading or risk?
082Let X be the market's daily return, symmetric around zero, and let Y equal X squared, the shape of a long straddle's profit. What is the correlation between X and Y? Are they independent?Statistics and forecastingCoreQuantitative asset managementHedge funds
Try it first
What is the correlation?
Show the worked solution
The correlation is zero, but X and Y are completely dependent. Because X is symmetric, a 2% fall and a 2% rise both give Y of 4, so the up-slope and the down-slope cancel and the covariance is zero. Yet Y is fixed exactly by X. Zero correlation rules out a straight-line link only, not a link.
How can a perfect relationship show zero correlation?
An umbrella seller does well when it pours and an ice cream seller when it is scorching; a stall selling both does well on any extreme day and badly on mild ones. Its takings depend completely on the weather, but not in a straight line. Correlation asks only whether a straight line fits, so a U-shaped link, rising on both sides, averages out to zero.
Plotting Y equal to X squared for returns of minus 2% to plus 2% gives a U of 4, 1, 0, 1, 4, and the best-fit straight line through those points is flat at 2, so the correlation is zero although Y is fixed exactly by X.
What does the algebra say?
Covariance is the average of X times Y, less the product of the averages. With X symmetric around zero, the average of X is zero and the average of X cubed is zero, so the covariance, and with it the correlation, is exactly zero. Using five equally likely days of minus 2, minus 1, 0, 1 and 2 per cent gives the same answer by hand: the covariance works out to 0.
The relationship
$\text{Cov}(X, X^2) = E[X^3] - E[X]\,E[X^2] = 0 - 0 = 0$
E[X] the average return, zero by symmetry
E[X^3] the average cubed return, also zero by symmetry
What it says in wordsFor a symmetric variable, the covariance with its own square is zero.
Now the portfolio point. A long straddleBuying a call and a put at the same strike, so the position profits from a large move in either direction. profits roughly with the square of the move, so its returns can show near-zero correlation with the market while depending heavily on it. A risk model that reads zero correlation as no exposure will treat the straddle as a diversifier and miss that it is a pure bet on the size of market moves.
Where candidates lose it
The trap is equating zero correlation with independence. Independence implies zero correlation; the reverse fails, and this question is the standard counter-example.
The second trap is saying the correlation is high because Y is a function of X. Correlation measures a straight-line fit, and a symmetric U has no slope.
What the interviewer asks next
What if X is skewed, with bigger falls than rises? Is the correlation still zero?
Name a measure that would detect this dependence.
Why can hedge fund returns look uncorrelated with equities and still lose money in a crash?
084A bank earns a 16% return on equity, grows at 8% a year and has a 13% cost of equity. What price to book is justified? What happens if its return on equity falls to 13%?Valuation riddlesCoreFundamental asset managementIndian equity research
Try it first
At a 13% return on equity, what is the justified price to book?
Show the worked solution
1.6 times book at a 16% return on equity, falling to 1.0 times at 13%. The justified multiple is the return on equity less growth, over the cost of equity less growth: 8 over 5 at 16%, and 5 over 5 at 13%. When a bank earns exactly its cost of equity, a rupee of book is worth a rupee, and growth adds nothing.
Why does a bank earning its cost of equity trade at book?
Suppose a friend offers to take Rs 1 lakh and pay you exactly the return you could get anywhere else with the same risk. The deal is worth Rs 1 lakh; no more, however large your friend makes it. A bank reinvesting at a return equal to its cost of equity creates no value on the money it keeps, so its book is worth exactly book. Only the spread between the two rates earns a premium.
With growth at 8% and a 13% cost of equity, the justified price to book is 1.0 times where return on equity equals 13% and rises to 1.6 times at 16%; below 13% the line falls under book, because growth then destroys value.
Where does the formula come from?
Start from the dividend discount model. Next year's dividend is book times return on equity times the share paid out. To grow at 8% with a 16% return, the bank must retain half its earnings, since growth is return on equity times retention; that leaves a payout of 1 minus g over ROE. Substituting gives price over book equal to (ROE minus g) over (r minus g). At 16%, retention is 50%, payout 50%, and the multiple 1.6 times.
The relationship
$\frac{P}{B} = \frac{ROE - g}{r - g} = \frac{0.16 - 0.08}{0.13 - 0.08} = 1.6$
ROE return on equity, 16%
g long-run growth, 8%
r cost of equity, 13%
What it says in wordsThe premium to book is the return spread over the cost spread, both measured from the growth rate.
The limit is that every input is a long-run steady state. A bank with a cyclical credit cost earns 20% in good years and 8% in bad ones, and the formula wants the through-cycle figure. Say so, then say which input you would argue about first.
Where candidates lose it
The common slip is scaling: 13 is less than 16, so the multiple falls in proportion to about 1.3 times. The relationship is not proportional; it is anchored at 1.0 times where the two rates meet.
The deeper miss is not seeing that growth is only good when return on equity beats the cost of equity. Below 13%, faster growth lowers the multiple, and saying that out loud is what the question is testing.
What the interviewer asks next
The bank earns 11% on equity. What happens to the multiple if growth rises from 8% to 10%?
What return on equity does a price to book of 2.0 times imply at the same growth and cost of equity?
Why do lenders with similar returns on equity trade at very different multiples?
085An investor puts Rs 10 lakh into a fund that gains 20% in year one. Just before year two, the investor adds Rs 40 lakh, and the fund then falls 10%. What is the fund's time-weighted return, and how did the investor actually do?Performance measurementCorePerformance analysisWealth management
Try it first
Over the two years, how did the investor do in rupees?
Show the worked solution
The fund's time-weighted return is plus 8% over two years, but the investor lost Rs 3.2 lakh. Time-weighted return chains the yearly returns, 1.20 x 0.90, and ignores cash flows. The investor had Rs 10 lakh in for the gain and Rs 52 lakh in for the fall, so Rs 50 lakh became Rs 46.8 lakh, a money-weighted return of about minus 5.4% a year.
How can both numbers be right?
A cricket team's run rate says how well it batted; a spectator who arrived only for the collapse saw a bad match. Both are true. Time-weighted return measures what the fund did with each rupee over each period, so it judges the manager; money-weighted return weights each period by how much money was in, so it judges the investor's own timing. Here the timing was poor: most of the money arrived just before the fall.
Rs 10 lakh grew to Rs 12 lakh, the investor added Rs 40 lakh, and the Rs 52 lakh then fell 10% to Rs 46.8 lakh, so the fund shows plus 8% time-weighted while the investor lost Rs 3.2 lakh, about minus 5.4% a year money-weighted.
How do you get the money-weighted return?
It is the internal rate of return on the investor's own cash flows. Find the single yearly rate at which Rs 10 lakh put in two years ago and Rs 40 lakh put in one year ago grow to exactly Rs 46.8 lakh today. That is a quadratic, and its root is a growth factor of about 0.9462, or minus 5.4% a year.
The relationship
$10(1+m)^2 + 40(1+m) = 46.8 \;\Rightarrow\; m \approx -5.4\%$
m the money-weighted return, a yearly rate
10, 40 the investor's contributions, Rs lakh, two years and one year before the end
46.8 the ending value, Rs lakh
What it says in wordsThe money-weighted return is the one rate that grows the investor's contributions into the ending value.
This is why fund factsheets quote time-weighted returns: the manager does not control when investors add money. It is also why many investors earn less than the funds they own, because inflows tend to follow good years. Annualised, the fund's figure is 3.9% a year against the investor's minus 5.4%.
Where candidates lose it
The trap is reporting plus 8% as the investor's experience. The interviewer wants to hear that the fund's return and the investor's return are different quantities, and why.
The second slip is computing the investor's figure as a simple return on the total, Rs 3.2 lakh over Rs 50 lakh. That ignores that Rs 10 lakh was invested for two years and Rs 40 lakh for one. Name the internal rate of return as the correct tool.
What the interviewer asks next
Reverse it: the investor adds Rs 40 lakh after the fall instead. What changes?
Which return should appear on a fund factsheet, and which on a client statement?
Why do investors in aggregate often earn less than the funds they hold?

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

V	portfolio value, Rs 100 crore
D_mod	modified duration, 5
0.0001	one basis point written as a decimal

r	the annual return
6	years to double

r_$	the stock's return in dollars, 8%
r_FX	the change in rupees per dollar, 5%
r_Rs	the return measured in rupees

Try it first

Why is the headline account count a trap?

How do you defend the 1 in 100?

Where candidates lose it

What the interviewer asks next

Try it first

Why turn duration into rupees at all?

Where does the straight-line answer stop being right?

Where candidates lose it

What the interviewer asks next

Try it first

Why count doublings instead of dividing?

How do you get the annual return without a calculator?

Where candidates lose it

What the interviewer asks next

Try it first

Why does the purchase price feel like it matters?

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

Where candidates lose it

What the interviewer asks next

Try it first

Does a weaker rupee help or hurt this investor?

Where does the extra 0.4% come from?

Where candidates lose it

What the interviewer asks next

Try it first

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

Why does this matter if the expense ratio looks fine?

Where candidates lose it

What the interviewer asks next

Try it first

Why do two equally likely patterns take different times to appear?

How do you solve it in the room?

Where candidates lose it

What the interviewer asks next

Try it first

How can a perfect relationship show zero correlation?

What does the algebra say?

Where candidates lose it

What the interviewer asks next

Try it first

Why does a bank earning its cost of equity trade at book?

Where does the formula come from?

Where candidates lose it

What the interviewer asks next

Try it first

How can both numbers be right?

How do you get the money-weighted return?

Where candidates lose it

What the interviewer asks next