The interview questions of Jane Street, Jump and Citadel Securities

Want to be one of the Jane Street traders earning $1.4m per head (if not more), or one of the Citadel Securities employees on track to earn $2m each this year? It won't be easy, as these kinds of electronic trading firms have notoriously difficult interview processes.

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Getting a job at the likes of Jane Street, Citadel Securities or Jump Trading requires a high degree of knowledge of probability. The interview process can vary wildly depending on which firms you apply to, but most have been known to ask some curious and deliberately confusing question to assess your probability skills under pressure. We've looked at public submissions from various sites like Glassdoor and Wall Street Oasis to find the most unusual examples.

Jane Street Interview Questions

• You are given the opportunity to bid for a treasure chest, which you know with 100% confidence to be priced anywhere between $0-$1000. If you bid equal to or above the price, you win the treasure chest at the cost of your bid. If you bid below the price, you do not earn the chest. You also have a friend who is willing to buy the treasure chest from you for one and a half times its value if you can obtain it. What should your bid be?

• You are playing a game where you and another person roll a 100-sided die. Whoever rolls the highest number receives $1 from the house, not the opponent. If you tie, you each get nothing. You are given the option to double the number of your roll for $0.2. How often do you double your roll? (You can read my answer to this question on The Bubble, our new anonymous community of over 3,000 finance professionals)

• What is the expected number of times you must roll a 6 sided die to get each face at least once? What is the expected number of rolls to get each face at least twice?

• You're betting on a two horse race with a group of people. They irrationally bet on whichever horse has won the most races in the past. You can bet on either horse , but you do not know which horse everyone else is betting on. What would be your betting strategy?

Questions at Jane Street will often have multiple parts, and you'll be told whether you get the first part wrong. They're testing your response to receiving that information with the second question, to see if you can respond to adversity. An example of a multi-part question is: 

•  You have 20 cards. 1 is black, the rest are red. You keep drawing cards and get $1 for each red, but if you draw the black, the game ends and you get nothing. How do you play, and what’s the average payout? 

• Now drawing the black card makes your score go negative, but you can continue drawing cards. What’s the strategy and expected payout now?

Jane Street also provides a guide to probability with some interesting insights, particularly in regard to market making. One such question is:

• When you roll a six sided die, you receive $1 for every pip on the side rolled (i.e. rolling a two earns you $2, a three $3 and so on). Assuming you must pay an agreed amount each time the dice is rolled, how would you make that market?

This is an interesting perspective, as you must also consider that the opposite party must agree to the conditions and have something to gain (good luck convincing them to sell a roll for $1). Jane Street says it would make the market "3 at 4, 10 up."

Citadel Securities Interview Questionss

• There are 100 prisoners and a room with a lightbulb. Prisoners are called in at random to turn the bulb on or off. Upon exiting, the room, they must guess whether they are the last of the 100 to enter the room. If they are correct, they go free, if not, everyone fails. Prisoners may communicate beforehand, but once the game begins, they are separated and have no idea who has or hasn't entered the room yet. What strategy would ensure the prisoners would be successfully released?
• How would I calculate the revenue of a company called Peloton without any source of data?
• How many basketballs can you fit on a school bus?

Citadel Securities might also ask interviewees to make markets on a given topic. Interviewees have said they were asked to make a market on the number of games played in the longest ever tennis match, and the combined goal difference of all English Premier League football champions.

Jump Trading Interview Questions

Jump Trading isn't thought to be as obsessed with brainteasers as Jane Street, but you'll still need to brush up on your probability fundamentals. Some of the quirkiest questions include:

• A bee starts at a hive. It has a 20% chance to move forward, a 50% chance to stay still, and a 30% to move backward. What percentage of the time does it spend in the hive?
• I'm dealing a deck of cards. You can stop it at any time and if the next card is red, you win. What is the optimal strategy for winning? (They seem to really like this one)
• There are four balls, two black and two white. You pick two and random and flip their color from one to the other and repeat. How many times would you do this to ensure all four balls are the same color?
• What is the probability that two people in a room full of 15 share the same birthday?

How do you answer probability questions in a quant interview?

Many of the questions above may have a 'right' answer, but getting there isn't the be-all and end-all. Method matters most.

For example, Jane Street alum Sam Bankman-Fried was once asked what the odds are that their interviewer was related to a professional baseball player. While there is obviously merit in estimating the number of pro baseball players in the US, and extrapolating that into a guess, SBF noted that the question was specific enough that there was a significant possibility that the interviewer only asked the question because they were related to one.

The questions aren't just about probability, but how you look for otherwise unseen angles in a piece of data. 

Brainteasers are only one part of the puzzle, of course. Firms will often ask behavioural questions or give you coding tasks based on your role. You can see examples of those kinds of questions here. 

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