Interview
A Jane Street Trading Mock Interview with Graham and Andrea
- Interview Simulation Context: Graham (trader with ~2 years tenure) and Andrea (new full-time hire) simulate a quantitative trading interview using a problem Jane Street historically used but is not currently administering.
- Game Variant 1 (Static Die): The player has 100 rounds; in each round, they may roll a 20-sided die (replacing the current face) or accept the current face value in dollars without ending the game.
- Andrea initially hypothesizes a "roll until 20" strategy, estimating ~$1,800 total earnings.
- Through iterative calculation, Andrea evaluates thresholds for stopping rolls:
- Accepting 19–20 yields ~$1,750.
- Accepting 18–20 yields ~$1,767, identified as the local maximum before diminishing returns set in.
- Accepting 17–20 yields a lower expected value (~$1,757), confirming the optimal threshold is accepting 18 or higher.
- Game Variant 2 (Consumable Die): Rules change such that accepting money removes the die, forcing a mandatory roll before money can be taken again.
- Andrea initially estimates a "top 50%" (11–20) strategy yields
$511, which is inferior to a baseline "take every roll" strategy ($525). - Andrea derives a mathematical function to maximize earnings: $E = \frac{1000x(2-x)}{1+x}$, where $x$ is the fraction of acceptable outcomes.
- The calculated optimal strategy is accepting any roll of 6 or higher.
- An alternative "intuition check" confirms that since the average gain per turn is ~$5, accepting a 6 (above average) is mathematically sound given the cost of a lost turn.
- Andrea initially estimates a "top 50%" (11–20) strategy yields
- Game Variant 3 (Adversarial Casino): Returning to Variant 1 rules, but the casino now chooses to re-roll the die immediately after the player takes money, with the goal of minimizing player earnings.
- Andrea identifies the scenario as a game theory equilibrium where both parties set thresholds to deter the other.
- Initial guess: An equilibrium threshold around 10 or 11.
- Iterative adjustment: Andrea tests a 11+ threshold, calculating an expected return of ~$775; she then adjusts the threshold lower to 8–20.
- Recalculated expectation for 8+ threshold yields ~$910.
- Final conclusion notes the true equilibrium likely lies between the tested thresholds of 8 and 11.
- Interview Evaluation Criteria:
- Clarification: Andrea is commended for spending 1–2 minutes clarifying rules to ensure alignment with the interviewer's intent.
- Communication: The interviewer values "thinking out loud" as a primary assessment tool, noting that verbalizing the process aids in calibration and reveals the candidate's reasoning structure.
- Problem Solving: Success is measured by the ability to break complex problems into solvable sub-parts and iterate on strategies based on feedback or intermediate results.
- Collaboration: The format is designed to replicate the interactive nature of a trading desk conversation rather than a rote test of knowledge.
- Forward-Looking Context: Jane Street emphasizes that interviews are intended to feel like "exciting discussions" rather than adversarial tests, aiming to reduce candidate anxiety through supportive interviewer behavior.