Quant Finance
19 financial mathematics questions of the kind asked in quant finance interviews. Each carries a model answer, the concepts a complete response must hit, and graded feedback on your own attempt.
A quick model-review test for a leveraged-finance analyst.
A borrower generates $90m EBITDA, pays $24m of cash interest, $18m of cash taxes, and $20m of maintenance capex. It has a 50% excess-cash-flow sweep and begins with $10m excess cash after working capital. How much term…
Mental math screen. Expect several of these in rapid succession, no calculator.
An investment compounds at 9% annually. (a) Roughly how long to double? (b) What is it worth after 24 years, as a multiple? (c) A fund returns 2.5x over 6 years. What is the approximate annualised return?
A quick sizing exercise for leveraged finance screens.
A company has $80m of EBITDA. The market can support 4.0x secured debt and 5.5x total debt. How much secured and unsecured debt can it raise?
Risk analysts are routinely asked to translate a rate sensitivity into an approximate P&L.
A bond portfolio has a DV01 of $85,000. What does that mean, and what is the approximate P&L if yields rise by 12 basis points? What would you check before relying on the answer?
A desk analyst must estimate risk quickly before reaching for a pricing system.
You are long $10 million face value of a corporate bond priced at par with spread duration of 4.5. Its credit spread tightens by 20bp, while Treasury rates are unchanged. Estimate the price and dollar P&L impact.
A basic arithmetic screen on an FX or macro desk where a wrong quote convention can reverse the trade conclusion.
EUR/USD rises from 1.0800 to 1.1016. What happened to the euro and the US dollar? If you were long EUR/USD with $10m of dollar notional at entry, approximately how much would the position gain before financing and…
A first-round check that a research candidate can separate a strategy outcome from the market outcome it rode along with.
A paper portfolio returns 8% in a month while its benchmark returns 5%. What is the portfolio's active return? Is that enough to call the signal good?
Mezzanine teams use this arithmetic to check whether reported leverage captures debt that is compounding rather than being paid in cash.
A borrower has $180m of first-lien debt and a $60m mezzanine note with a 10% annual PIK coupon. EBITDA is $40m and does not change. What are total debt and total leverage after one year, assuming no repayments or other…
An execution-trading interview checks that a candidate can reconcile fills before offering an opinion on execution quality.
You buy 1,000 shares in three fills: 200 at $24.90, 500 at $25.00 and 300 at $25.10. What is your VWAP? If the arrival mid-price was $24.95, what was your implementation shortfall in dollars before commissions?
A junior case-study check on whether an analyst separates cash paid at closing from future funding.
You buy an LP interest with reported NAV of $120m at 75% of NAV. The interest has $35m of unfunded commitments, expected to be drawn evenly over the next two years. What cash is paid at closing, what is the simple total…
Researchers are expected to explain a simple factor test before writing a complex model around it.
You believe companies with the strongest earnings revisions will outperform. Explain how you would test that idea using decile portfolios. What result would make you interested, and what result would make you sceptical?
A common follow-up that tests whether you can translate a merger spread into market-implied odds.
A target trades at $45. A cash bid offers $50, and you estimate a $35 break price. Ignoring time value, what completion probability is implied by the market price?
A simple math question to test whether candidates can separate cash yield, PIK and exit value.
A $100m mezzanine note pays 8% cash and 4% PIK for five years, with no warrants. Roughly what is the total value received at exit before fees?
A common secondaries case-study modelling prompt.
What are the key inputs in a cash-flow model for an LP secondary purchase?
A numerical treasury follow-up that tests whether a candidate hedges the economic net exposure rather than gross invoices.
A US parent expects to collect €12m from customers and pay €9m to suppliers in 90 days. The EUR/USD forward rate is 1.1000 dollars per euro. What is the net exposure, what forward should it enter, and what dollar amount…
Foundational maths underpinning every valuation method.
Derive the formula for a growing perpetuity. Then value: (a) $100/year forever at a 10% discount rate, (b) the same cash flow growing at 3%, and (c) $100/year for 10 years at 10%.
A sizing follow-up tests whether you distinguish an estimated edge from a known probability.
A trade wins 55% of the time and loses 45% of the time. It makes or loses 1% of the capital allocated. What is full Kelly sizing, and why might a trading desk use less?
A standard numerical follow-up after discussing transaction exposure.
A US company must pay €10m in three months. The three-month EUR/USD forward rate is 1.0800 dollars per euro. How would you hedge it, what dollar cost do you lock, and what happens if spot settles at 1.1300?
A market-risk interview for a portfolio whose normal-day VaR understates gap and volatility risk.
A portfolio is short index puts and long a smaller number of single-stock puts. Its one-day VaR is stable, but the risk manager is worried about a sharp equity sell-off. What would you test beyond VaR, and why?
Write your answer, get it graded on technical accuracy, completeness and communication, and see exactly which mechanic you missed.
Firm names indicate where a question type is commonly reported in interviews. They are not sourced from, endorsed by, or affiliated with the firms named.