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. 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?
2. 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?

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.