Portfolio Management interview preparation

Questions

100

Traced to a firm

40

Firms

24

Updated

September 2026

Asked at

All firmsBLBlackRock4Vanguard4WMWellington Management4Amundi3ACAQR Capital Management3Neuberger Berman3SCSchroders3Man Group2MSCI2Northern Trust2AllianceBernstein1Apollo Global Management1Blackstone1BMBNY Mellon1Carlyle Group1Fidelity Investments1Goldman Sachs1Invesco1Millennium Management1MSMorgan Stanley1NUNuveen1PIMCO1SSState Street1TPTPG1

Topic

All topicsPortfolio theory5Factor models8Asset allocation11Rebalancing3Portfolio construction7Benchmarks and tracking error5Performance measurement8Risk management6Fixed income and LDI5Currency and global3Implementation and costs5Active versus passive6India markets7Brainteasers5Career and fit16

Level

AnyCoreIntermediateHard

Type

AnyTechnicalCaseMarket viewFitBrainteaser

1. 080There are n cars on a circular track and between them just enough petrol to complete one lap. Show that one car can finish the lap by collecting petrol from the others.BrainteasersHardtechnicalMillennium ManagementInvestments · London · 2024

   Say this

   Yes, and there is always such a starting car. Track the running fuel balance around the loop from any start point, find the position where that balance is at its minimum, and the car immediately after that point can complete the lap.

   Then walk it

   1. Set it up: let each car i have fuel f sub i and let d sub i be the fuel needed to reach the next car. Total fuel equals total requirement, so the sum of f minus d over all cars is exactly zero.
   2. Pick any car and walk the circle, keeping a running total of f minus d. Because the total is zero, the walk returns to where it started, so the running total has a well-defined minimum at some position.
   3. Start at the car immediately after that minimum. From there, every partial sum is the original partial sum minus the minimum, which is non-negative by construction. So the tank never goes negative and the lap completes.
   4. The intuition is that the minimum point is the worst moment in the journey, so you arrange to arrive there last, with everything already collected, rather than hitting it while your tank is nearly empty.
   5. Sanity check with two cars: one has all the fuel for the lap, the other has none. Starting at the full one works, starting at the empty one fails immediately, and the argument picks the right one.
   6. The finance version of this argument is worth saying out loud, because it is why this gets asked in an investment interview: the feasibility of a cash flow plan depends on the minimum cumulative balance, not the total. A fund with enough total liquidity over a year can still fail in month three. That is the same theorem, and it is how you size a liquidity buffer or a collateral waterfall.

   Where candidates lose it

   Trying specific examples and asserting it works, or getting lost in the case analysis. The whole problem is one idea: the cumulative sum returns to zero, so start just after its minimum. State that in one sentence, then verify it, then connect it to cumulative cash flow, because the interviewer is testing whether you can reduce a problem to an invariant.

   Expect next

   • How would you find that starting car algorithmically?
   • What if total fuel exceeds what is needed?
   • Where does the same argument appear in liquidity management?

   Reported by candidates at Millennium Management (Investments, London, 2024). Source: Wall Street Oasis.

2. 081Two assets each have twenty percent volatility and a correlation of a half. What is the volatility of an equally weighted portfolio?BrainteasersCoretechnicalAsset managementRisk management

   Say this

   About 17.3 percent. Portfolio variance is 0.25 times 400 plus 0.25 times 400 plus 2 times 0.25 times 0.5 times 400, which is 100 plus 100 plus 100, so 300. The square root of 300 is about 17.3.

   Then walk it

   1. Set it up in variance terms, always. Each asset's variance is 400 in percent-squared units, and the covariance is the correlation times the two volatilities, so 0.5 times 20 times 20, which is 200.
   2. Portfolio variance equals w1 squared times var1 plus w2 squared times var2 plus 2 w1 w2 times covariance. That is 0.25 times 400 twice, plus 2 times 0.5 times 0.5 times 200, giving 100 plus 100 plus 100 equals 300.
   3. Square root: 17.3 percent. So combining two identical-risk assets at 0.5 correlation cut risk by about 13 percent of its original level, which is the whole diversification benefit in one number.
   4. Know the boundary cases cold, because they are the follow-up. Correlation 1 gives 20 percent, no benefit at all. Correlation 0 gives 20 over root 2, about 14.1 percent. Correlation minus 1 gives zero, a perfect hedge.
   5. The general result worth having memorised: for n equally weighted assets with equal volatility sigma and common correlation rho, portfolio variance is sigma squared times rho plus 1 minus rho over n. As n goes to infinity, volatility tends to sigma times the square root of rho.
   6. That limit is the useful part. With 20 percent volatility assets at 0.3 average correlation, no amount of diversification gets you below about 11 percent. That is the systematic floor, and it is why diversification stops helping.

   Where candidates lose it

   Averaging the volatilities, or adding them and forgetting the covariance term is multiplied by two. Work in variance, then take the square root at the end. And have the asymptotic result ready, sigma times root rho, because the follow-up is almost always 'and with a hundred assets?'

   Expect next

   • What if correlation were zero, or minus one?
   • What is the limit with a hundred such assets?
   • How does that connect to the diversification floor?
3. 082A fund is up fifty percent one year and down fifty percent the next. What is its average annual return, and what did the investor actually get?BrainteasersCorephone / first roundAsset managementPerformance analysis

   Say this

   The arithmetic average is zero, but the investor is down 25 percent. A hundred goes to 150 then to 75. The gap is volatility drag, and it is the reason geometric return is the only one that describes what an investor experienced.

   Then walk it

   1. Compute it: 1.5 times 0.5 equals 0.75, so terminal wealth is 75 percent of the start. The geometric return is the square root of 0.75 minus one, which is about minus 13.4 percent a year.
   2. The general relationship: geometric return is approximately arithmetic return minus half the variance. Here volatility is enormous, so the drag is enormous, and the approximation is only rough at this size of move.
   3. Practical consequence one: a fund can advertise a positive average annual return while every investor lost money. That is why performance reporting standards require compounded, annualised figures.
   4. Practical consequence two, and this is the portfolio management point: reducing volatility raises compounded return even if you do not change the average. That is the whole mathematical case for risk control, rebalancing and diversification, rather than just a comfort argument.
   5. Put a realistic number on it so it does not sound like a trick. A portfolio with a 7 percent arithmetic return and 20 percent volatility compounds at roughly 5 percent. Cut volatility to 12 percent and it compounds at about 6.3 percent. Same expected return, 130 basis points more wealth every year.
   6. And the asymmetry to name: recovering from a 50 percent loss needs a 100 percent gain. Losses and gains are not symmetric in wealth terms, which is why drawdown control matters more than chasing the last few percent of upside.

   Where candidates lose it

   Saying the average is zero and stopping, or getting the recovery arithmetic backwards. The interviewer is testing whether you instinctively think in compounded terms. Tie it to the portfolio conclusion, that lowering volatility raises compounded wealth for the same average return, or you have answered a maths question rather than an investment one.

   Expect next

   • What return do you need to recover from a 50 percent loss?
   • So how much is volatility worth in compounded terms?
   • Which return would you show a client?
4. 083How large is the Indian mutual fund industry? Work it out from scratch.BrainteasersIntermediatetechnicalIndian asset managementMutual funds

   Say this

   Build it from flows and market value. Monthly SIP flows of roughly 25,000 crore rupees, plus lump sums, against an equity market capitalisation of around 400 lakh crore. Industry assets under management are of the order of 70 to 75 lakh crore rupees, so a bit under 900 billion dollars.

   Then walk it

   1. Route one, top down from the market. Indian listed market capitalisation is roughly 400 to 450 lakh crore rupees. Domestic mutual funds own something like 9 to 10 percent of it, which gives 35 to 45 lakh crore of equity assets, and equity is a bit over half of total industry assets.
   2. Route two, bottom up from flows. SIPs run at about 25,000 crore a month, so 3 lakh crore a year, and SIPs are maybe a third to a half of gross equity inflows. Accumulate a decade of that plus market appreciation and you land in the same place.
   3. Route three, sanity check per capita. There are roughly 4 to 5 crore unique mutual fund investors in a country of 140 crore people, so penetration is still under 5 percent of the population. That is the number that makes the growth case, and it is the number an interviewer is really fishing for.
   4. Compare to the benchmark: Indian mutual fund assets are around 16 to 18 percent of GDP, against 120 percent plus in the United States. That gap is the industry's entire growth thesis.
   5. State the composition too, because it changes the answer's meaning: roughly half equity, a large chunk in debt and liquid funds dominated by corporate treasuries, and a fast-growing passive segment driven by EPFO and by large cap index funds.
   6. Then say what you would check: the AMFI monthly data release gives assets, flows, folio counts and the SIP book. Naming the actual source and admitting your estimate has a 20 percent error band is better than pretending to precision.

   Where candidates lose it

   Guessing a number with no route to it. This is an estimation question, so the structure is the answer: build it two ways, cross-check, and give a range. Also get the units right; confusing crore and lakh crore is an instant credibility loss in an Indian interview, and quoting US-scale numbers for India is the other common tell.

   Expect next

   • What share of Indian household savings is that?
   • How fast is the passive share growing?
   • What would take penetration from 5 to 15 percent?
5. 084A fund charges one percent a year and the market returns eight percent. How much of the investor's terminal wealth does the fee take over thirty years?BrainteasersIntermediatetechnicalAsset managementWealth management

   Say this

   About a quarter. At 8 percent, one rupee becomes 10.06 over thirty years. At 7 percent it becomes 7.61. So the fee takes roughly 24 percent of the terminal wealth, even though it was only 1 percent a year.

   Then walk it

   1. The arithmetic: 1.08 to the thirtieth is about 10.06, and 1.07 to the thirtieth is about 7.61. The ratio is 0.757, so 24 percent of the wealth is gone.
   2. The reason the effect is so much bigger than it sounds: the fee is charged on the whole balance every year, so you lose the compounding on every rupee of fee as well as the fee itself. The loss grows with the horizon.
   3. A quick approximation worth knowing for the interview: the fraction of terminal wealth lost is roughly the fee times the number of years, so 1 percent over 30 years is about 30 percent, slightly overstated because of compounding effects. It gets you to the right order instantly.
   4. Now scale it to a real decision. An Indian equity fund with a 1.8 percent regular plan expense ratio against an index fund at 0.2 percent is a 1.6 point gap. Over 30 years that is roughly 35 to 40 percent of terminal wealth. That is the entire active-passive debate expressed as a number.
   5. And the asymmetry that makes it decisive: the fee is certain and the alpha is not. To justify the 1.6 percent the manager needs to beat the index by 1.6 percent consistently, and SPIVA-style data says most do not over that horizon.
   6. The caveat, so it does not sound dogmatic: fee is only one term. A cheap fund tracking a badly constructed index, or a cheap fund the investor panics out of, can do worse than an expensive fund they hold through a drawdown. Cost is the most reliable predictor of relative performance, not the only one.

   Where candidates lose it

   Answering '30 percent, it is just one percent times thirty years' without doing the compounding, or the reverse, getting lost in the arithmetic and never producing a number. Do the estimate fast, then convert it into the real decision, regular plan versus index fund, because that is what makes the answer land in an asset management interview.

   Expect next

   • Now do it for a 1.8 percent Indian regular plan against a 0.2 percent index fund.
   • What outperformance would the manager need to justify the fee?
   • Is cost the best predictor of fund performance?

Firm tags come from public, anonymous candidate reports on Wall Street Oasis: strong signal, not sworn testimony. Firms are named as the places a question was reported, not as partners of Fin Maverick. Answers are written for this page to show how to think out loud; they are not scripts to recite.