2024 Citadel Quant Trading Interview with Analysis from Real Quants
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- เผยแพร่เมื่อ 6 เม.ย. 2024
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Breakdown of the interview:
0:00 You work at a shoe factory, and you’re working on creating boxes with pairs of shoes. Currently in front of you, imagine there are 3 pairs of shoes (for a total of 6 individual shoes) with the following sizes: 2 size 4s, 2 size 5s, 2 size 6s. The factory defines an “acceptable” pair as 2 shoes that differ in size by a maximum of 1 size - so a shoe with size 5 and a shoe with size 6 would count as an “acceptable” pair. If you close your eyes, and randomly pick 3 pairs of shoes, without replacement, what is the probability that you end up drawing 3 acceptable pairs?
0:43 The candidate asks clarifying questions
1:17 The candidate breaks down the question and starts brainstorming solutions
2:06 Our instructor analyzes the candidate's initial response to the question and points out what he did well
2:54 The candidate walks through the methodology for his solution, and solves the question correctly.
7:43 Our instructor explains the theory behind this question, and whiteboards a solution for this question. He also shows a snippet of the written detailed solution from the Quant Blueprint course, along with a Python code simulation which shows that the final answer approaches 1/3 with infinite trials. Here's a written solution from the course: drive.google.com/file/d/1uJNv13dbqd405ILpq9pAbdBkPGkyKRN8/view
10:10 The interviewer asks the second question. Say you're flipping a fair coin until you obtain the first H. If the first H occurs on the k'th flip, you're given k balls. We're going to randomly put these k balls into 3 bins, labeled 1 2 and 3. Find the probability that none of these 3 bins end up empty.
10:34 The candidate dissects the question and asks clarifying questions.
11:03 The candidate works through some examples and logically breaks the question down to answer the question effectively.
17:55 The candidate has answered the question correctly, and now summarizes his approach.
20:37 Our instructor breaks down the approach the candidate used and whiteboards the fundamental probability theory behind this question.
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I took y'alls program last year and landed a quant internship this summer at a tier 1. Def the best interview prep content out there.
Thanks for the kind note, and glad to hear it. Congrats!
- Alex, Quant Researcher
Hello, where can I find the Quant Program?
Thank you.
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"Look at him! That's my quant. My quantitative! My math specialist. Look at him. Do you notice anything different about him? Look at his face...look at his eyes! His name is Yang. He won a national math competition in CHINA and he doesn't even speak English! Yeah, I'm sure of the math..."
- Jared Vennett (the Big Short 2015)
😂 my thoughts exactly
Broooo😂😂😂😂😂😂😂😂
Ted Jiang : [to camera] Actually, my name's Jiang and I do speak English. Jared likes to say I don't because he thinks it makes me seem more authentic. And I got second in that national math competition.
😂😂😂
"thats pretty racist" - mark baum
yea ion think ima get the job
"Ion" and "ima" is pretty much a giveaway
@@ramsesp5009 yeah the comment was a joke, you can't be that stupid to not detect that
@@ramsesp5009 RACIST
@@ramsesp5009 wdym?
It helps to have such a messy white board in the background to give the illusion you use it a ton.
Jesus no wonder Ive lost all my money
lmaoooo
Lmao!!😂
Maam i just wanna work at McDonald's as part time
The first question is so weird considering shoes usually have a left and right and you totally ignore that in your question, answer & explanation. Assuming two lefts don't go together, the real answer is 1/5.
This
exactly
There are left and right shoes?
@@FahrvergnugenTaglich 🤣
No the question still explicitly states “pairs” so they have to go together.
Thanks for making this video! This is super helpful.
Glad it was helpful!
that's my quant
MY QUANTITATIVE
@@airheadmrng MY MATH SPECIALIST
LOOK AT HIS EYES 😂
YOU NOTICE ANYTHING DIFFERENT ABOUT HIM
I'll give you a hint, his name is Yang !
He was supposed to close his eyes and answer the probability!!
Another way to do the first problem: there are really only 15 unique ways of choosing pairs. Let's label the shoes 4a, 4b, 5a, 5b, 6a, 6b. First we choose the partner for 4a; there are 5 choices. Now there are 4 shoes left. Now take the first one of those and choose it's partner; there are 3 choices. Now there are 2 shoes left, so there are no more choices to make. 5*3=15. So there are few enough possibilities to just think through them all. If 4a is paired with 4b, we are guaranteed to succeed, so that is 3 ways to succeed, depending on how the other shoes are paired. If 4a is paired with 5a, then 4b must be paired with 5b. And if 4a is paired with 5b, then 4b must be paired with 5a. That is 2 more ways to succeed. If 4a is paired with 6a or 6b, we have already failed. So there are 5 ways to succeed out of 15, or a 1/3 chance.
I think that you missed the word "random" in the task definition. You can't "chose", you toss the cube
They didn’t miss anything. Their solution is the cleanest solution out of all the ones discussed here, including the one used by the person in the video
does the quant think shorting GME is the play?
"Question 1: You find yourself in a position where you need to short $GME due to market demand from peasant retail investors, and there are no shares available in the market to open short positions on legally to offset this buy pressure, but this must be done otherwise our entire business model will be liquidated. Do you know how to hit 'F3' on a keyboard?"
GME doesn’t trade based off fundamentals. That is a stupid question.
@@kurtisbobke9000 tick tock
This seemed like a really weird way to say how many invalid sets can be made and whats the probability randomly selecting a valid set from all possible sets. The selection bit trips people up a lot. It doesnt matter because everything gets paired. Its really just asking of all possible sets of {445566}, imagine all the valid {(45),(54),66)} and invalid sets {(64),(64),(55)} (*2 ways this could happen*) - were written on a scraps of paper and thrown in a bag, whats the chance of picking out a scrap that had a valid set, or what is the probability of not picking a scrap that has (46) or (64) in any of the 3 pairings. If the bag had every variation of A1A2.. how many scraps would have AC pairings in any of the 3 pairs (A1C1, A1C2, A2C1, A2C2).
Yeah really can't stand people in the industry they're over paid & can't stand people not in the industry cause they have no desire to learn the basic arithmetic that would allow them to escape their indefinite indentured servitude.
@@bobthebuilder9416 can you elaborate please?
I got to admit, I'm confused on the last question with flipping a coin and bins being empty.
First question: 1/5 * 2/3 + 1/5 * 1/3 = 1/5 (left and right shoes).
3 pairs of 6 shoes, no replacement. Fix the first shoe, you have 5 options left. Only 2 of those make a valid pair, and once chosen fist valid pair, remaining has 2/3 and 1/3 prob for each choice
More elegant way to do the last question is to view each toss as going to bin A, B, C or ending the game with probss 1/6,1/6,1/6,3/6. wlog A gets the first ball. P(B empty) = P(fill B before ending) = 3/4. P(B, C both empty) = 3/5. Inclusion-exclusion -> P(B or C empty) = 2*3/4 - 3/5 = 9/10.
I dont doubt your logic, but how do you arrive at the 3/4 and 3/5 probs?
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Closed my eyes and came up with 1/3 as the answer to the first question. When he started talking, I thought to myself wow I’m way off I didn’t do any of that. Then he finalized the answer at 1/3. Either he over complicated it, or I got lucky.
Idk man all i know is that i can spam the F5 button the fastest 😂
qtπ, what's your name?
For the first one,
Why couldn’t it have been as simple as taking the average of the equally likely 2 conditions?
2/6 of picking a size 5. That goes with any of the remaining 4/4 shoes so 2/6 x 4/4 = 1/3
We don’t even need to compute after this. Since we know the situations are equally likely and we want an average, the probability of one valid scenario is the probability of all (both) valid scenarios
For the sake of completion:
4/6 of picking a size 4 or 6. Either size can only go with 2/4 of the remaining shoes. So 4/6 x 2/4 = 1/3
(1/3+1/3)
/2
= 1/3
Would it hurt me to use this simpler method in an interview!?
Wrong
I think they missed a pair of two lefts (or two rights) as invalid.
So, if the number of permutations of 6 shoes taking 2 at a time are 15:
Pick 1. "L4" "L4" "L4" "L4" "L4" "R4" "R4" "R4" "R4" "L5" "L5" "L5" "R5" "R5" "L6"
Pick 2. "R4" "L5" "R5" "L6" "R6" "L5" "R5" "L6" "R6" "R5" "L6" "R6" "L6" "R6" "R6"
The valid ones are those who meet the minimum size difference, but also are from a different foot. There are 7 possibilities:
Pick 1. "L4" "L4" "R4" "L5" "L5" "R5" "L6"
Pick 2. "R4" "R5" "L5" "R5" "R6" "L6" "R6"
Which makes the probability of getting a valid pair to 46%
I believe you must also have the context onto consideration.
lol That's what I thought too. When he said factorial I was like...this guy is an idiot.
Exactly, that's what I was thinking. They should've used something other than shoes if they intended the question to be answered this way.
two out of three duhh!
Citadel will hire him and make him naked short GameStop Stock
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Wow. I'm a bit perplexed seeing her been mentioned here also Didn’t know she has been good to so many people too this is wonderful, I'm in my fifth trade with her and it has been super.
She is my family's personal Broker and also a personal Broker to many families in the United states, she is a licensed broker and a FINRA AGENT in the United States.
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I'm new at this, please how can I reach her?
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There is always a HARD code test. Where is the HARD code test?
Here the shoes are not explicitly mentioned to be distinct ( 2 size 6 are assumed to be different, which I don't think is mentioned or clarified ) but while solving he is just assuming that to be the case. Let me know if I am thinking it wrong or missed a part where its clarified. Also the pairs are ordered too which is again not clarified. I think the answer will change if we say that 2 size 6 are identical and the pairs are not ordered.
It will not
They're supposed to be different. They're left and right shoes.
For the first question, I don't think there's a need to subtract the "double counting" part. 3*8*4! = 576 is the number of ways AT LEAST 1 pair consists of a 4 and a 6. That's already the complement of what we want. By subtracting the number of ways you can have 2 pairs of a 4 and a 6, you end up with the number of ways EXACTLY 1 pair consists of a 4 and a 6. You end up getting that 1 pair of a 4 and a 6 is not legal but 2 pairs of them are legal....
And HFT is only as good as their being fast/first. There's zero sum and then there's quants.
Doesnt treating this problem as a permutations of a string type problem only works if we are choosing one shoe at a time?
If we choose two shoes at a time, wouldnt this change the answer?
How can you choose 2 shoes at a time in a different way than choosing 2 separately? Either way there is no replacement and you end up with a pair.
Asian vs Asian
Can somebody who has gone through the interviews comment on if they are really this easy?
I did Jump Trading internship interview and the questiona where this kind of difficult
@@oscarromero9702 these are easy
I got 66
The only word I understood was probabilities, am I quant now hahahaha
What’s the point of all this when you all just gonna front run with your algos and trade routing 😂
truth spoken 😁
Algos need math and to figure out math you need to be a problem solver and have critical thinking skills.
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Did he count 6 quickly! or did he just know? or is the interview rehearsed?
Most people working with higher orders of mathematics know factorials up to 10 at the very least, as they pop up considerably in probability. Personally, my high school math teacher didn't let any of us leave class until we knew our "factorial tables" till 10 as well!
It's similar to how most people know the multiplications tables or squared values up to a certain number, just a little less intuitive.
@@tejaskala516 Cool!! Thanks for the explanation!
I must be really stupid because after she said the question I answered 32% with is 1/3 so I guess my math in my head is much better than this….why make thing complicated
yeah wtf
Can someone help me with the second probability question? the video is a little convoluted and I can't follow it.
My solution is summing from k=3 to infinity : 1/2^k * (1-3k/(k+2 choose 2)) where 1/2^k is the probability that k happens and 3k is the number of ways for at least one bin to be empty and k+2 choose 2 is the number of ways to organize k balls into 3 bins. According to chat gpt it converges to 1/10, but I don't know how to evaluate it for myself
The answer to your problem is: 2
The way he sets it up is 1-∑((1/2^k)*(3*2^k-3)/(3^k)). 3*2^k-3 is the number of ways where at least one bin is empty, where 3 is choosing which bin should be empty, and 2^k is arranging the balls in the remaining bins, and -3 is compensating for the fact that we double counted the cases where all balls are in one bin (e.g. we counted the case where all balls are in bin A both by choosing bin B to be empty and then putting all balls in bin A, and also by choosing bin C to be empty and then putting all balls in bin A). 3^k is the number of ways to put balls in 3 bins. The sum is simplified by first distributing the fraction to get ∑(3/3^k-3/6^k), then splitting the sum to get ∑(3/3^k)-∑(3/6^k), then applying the rule for the sum of a geometric series to both sums to get 3/2-3/5, which is 9/10, and 1-that is 1/10
‘qualifications’ doesn’t buy genius
He definitely won that math olympiad in china
Students in elementary school in asia can answer this question in 3 seconds..
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this is great! think your advisor would get on the phone with an unknown? i'm in dire need of proper portfolio allocation
Finding financial advisors like Monica Lisa Payne who can assist you shape your portfolio would be a very creative option. There will be difficult times ahead, and prudent personal money management will be essential to navigating them.
Thanks for this. could easily spot her website just after inputting her full name on my browser. she replied my inquiry and we scheduled a consulting session sometime tomorrow.
If you have 6 shoes, and you pick 3 pairs, you have all the shoes, Duh! Common sense is more important than education.
You lost me after 17 seconds 😂
Why do they have to explain their reasoning throughout working on their answer. So many uhms and aahs. Cant they speak after finalizing the answer?
This guy spent way too much time on the first question. lol
I love "quant math" (probability and complexity theory for eg) and quant programming but GME ma nibba
So many “um” and “uh”
Seems like math nerd genius. Math and engineering top degree. I graduated 2.6 GPA from none target in history and communications. Possible get in?
not at all
@@liminfer8380 bro how you know? You have to be a genius math grad nerd?
bruv this paragraph is wild
@@tgp120 bro gotta be some spots for frat party dudes and not just 4.0 math and finance nerds from Ivy league. I need get in
@@davidc4408 dawg sue your midwife i think they tapped your head a bit too hard
Wendy’s. The answer is Wendy’s.
is that a wig?
Interviewer: are you willing to steal from retail investors?
Quant: yes
Interviewer: you're hired
smart money does care about retail, retail makes up a tiny portion of the total trading volume
Edwin lin son?
ChatGPT could have answered all the questions in less than 10 seconds without as many “uh, ums”.
0
I am 34 years old living in pakistan. I have retail branch banking experience of 9 years and two years experience working for a UK based asset management company that have a back office in pakistan as operations analyst overseeing the bank reconciliation and reporting area. I have a dream of working for a wall street firm. Could someone guide me to reach there?
No ..they only hire from Ive leagues not from some shitty third world country.
@@aliasone9827 why?
@@aliasone9827Are you trolling my troll?
@@aliasone9827lolllllllll
The big banks have global operations. I'd suggest getting a job at one of them. Dont shoot for the moon. You wont join them in a front office role, but maybe an operations role like you do now if your CV is strong. If you are extraordinarily talented at programming with top tier math skills then apply to quant roles, if a big bank doesnt take you, a smaller firm might. Again you dont need to target WS firms directly. Dont listen to the person saying they dont hire non-Ivy/dont hire from Pakistan, that's not remotely true.
Really? What the heck does this have anything to do with the market? Lol.
Wow this is boring
Does your mom still swallow?
How the fuck does this even matter in trading
There is a much easier way to explain this lol
So quants are just thr next level of math olympiads...
Not really these are basic probability concepts
Is everyone usually like this when in interviews? He seems to be thinking a lot and still repeat phrases which doesn't make any sense. The question is simple yet he took a lot of time to solve it. Also completely ignoring the fact that shoes meant for left and right are different?
It's just weird.
Saying he works at a shoe factory… are they playing jokes or is that a hint on the racy(ist) side…. Really?….