5 ms·

What interview questions did D. E. Shaw ask Larry Summers?

24 points by gabrielroth 18y ago

tokenadult 18y ago
Cool. A press interview with Richard Rusczyk about his work before he founded the Art of Problem Solving website. http://www.artofproblemsolving.com/Forum/index.php http://www.artofproblemsolving.com/Forum/index.php Rusczyk always has something interesting to say.
- chris11 18y ago
  Yeah, I found the site when I was looking for material to study for the Putnam. It is a great site for learning about advanced math topics and even finding more challenging pre-college math material, by the way. I got the impression that he was really brilliant. Here's his blog:http://www.artofproblemsolving.com/Forum/weblog.php?w=1 http://www.artofproblemsolving.com/Forum/weblog.php?w=1
aswanson 18y ago
I've never done a trade in my life and it took all of about 12 seconds to get the right answers on the first two. They didn't list the third. Seriously, 5.4 MM for that?...http://www.bloomberg.com/apps/news?pid=20601087&sid=a4iGjejJVRko&refer=home http://www.bloomberg.com/apps/news?pid=20601087&sid=a4iG...
- slpsys 18y ago
  it's also a Slate article vs. HN. i'd expect them to post questions that dazzle the least common denominator, while still allowing them to understand what's going on after a brief explanation. i'd be worried if HN _couldn't_ solve problems understandable by Slate's target audience.
  - jibiki 18y ago
    Um, can someone explain the answer to the first question? Why wouldn't it go lower than the low eighties? Or higher, for that matter? How would the price change if there were 1000 sellers?
    - chris11 18y ago
      Basically the sellers end up bidding for the opportunity to sell. So basically some sellers won't be willing to sell below 89, more won't be willing to sell below 88, and even more won't be willing to sell be 87. And it works the other way too, so the lower the price gets, the more people are willing to buy. So theoretically, when the number of buyers equals the number of sellers, transactions end up occurring. This is assuming that the market is efficient, which isn't always the case. If there were 1000 sellers, the price would drop even lower, because there is more competition among the sellers.
      - jibiki 18y ago
        By this reasoning, equally valid answers would be $0.01 and $90.99.
        trjordan 18y ago
        The point of the question is that there is no mathematically "right" answer. The interviewer knows the answer from experience, and (s)he's testing two things: whether the interviewee's intuition on the market is right, and, if not, how well the interviewee takes to being corrected. Your answers are "right", in that they are possible, but they are not the numbers the interview wants to hear.
        jibiki 18y ago
        That makes more sense. I thought there was some obvious game theory principle I was missing, since somebody commented that they could answer the question without knowing anything about trading.
- chris11 18y ago
  Here's a forum with the type of questions that more likely to be asked. These questions are more difficult. http://www.wilmott.com/categories.cfm?catid=26 http://www.wilmott.com/categories.cfm?catid=26: Example brainteaser: "Last night I sat behind two wizards on a bus, and overheard the following: A: I have a positive integral number of children, whose ages are positive integers, the sum of which is the number of this bus, while the product is my own age. B: How interesting! Perhaps if you told me your age and the number of your children, I could work out their individual ages? A: No. B: Aha! AT LAST I know how old you are! Now what was the number of the bus?" Discussion: http://www.wilmott.com/messageview.cfm?catid=26&threadid=68570 http://www.wilmott.com/messageview.cfm?catid=26&threadid...
  - deleted 18y ago
    [deleted]
  - jibiki 18y ago
    Wow, I read through the discussion. No way in hell anyone would be able to answer that in an interview, unless they'd seen it before.
    - shrughes 18y ago
      It's definitely answerable in an interview situation. Some people should be able to answer it, no problemo, in a minute or two.
      - jibiki 18y ago
        I don't think you understand the problem. Even if you manage to find 4, 4, 3, 1 and 6, 2, 2, 2, you still have to verify that if the sum is 12, then there is only 1 possible product. You'll note that nobody in the linked thread succeeds at this (one guy proves that 12 works by exhaustive search, not really a possibility in an interview...)
        shrughes 18y ago
        Well, I saw it before, and it took a several minutes then, maybe 5 or 15, I don't really remember. Then you have to consider that companies like D.E. Shaw end up hiring people who would end up giggling at how long somebody slow like me would take to solve the problem.
deleted 18y ago
[deleted]
tomsaffell 18y ago
[Warning: Spoiler] > Of course, you can't offer the guy infinity dollars. So the interviewee is forced to either settle on a real world number—as much as the player can afford—or delve into marginal utility theory I don't think that as much as the player can afford is a real world answer, unless it means as much as the player can afford to lose. There is a 50% chance he'll walk away with $1. As Wall Street have proven, it's not about maximizing expected returns, it's about optimizing returns within bounds of acceptable risk.
- ardit33 18y ago
  I agree with you. Unless I misunderstood the question; the theoretical "right" answer is just wrong. Let's make it more practical. There is 100k in the table. A guy tells you, head you double the money, tail, you stop, and get what is there, but you have to pay a fee. Obviously, up to 100k for the fee, it is no brainer, head you end up with at least 200k, tail, you go home with 100k, same as the fee you paid. BUT: are you willing to pay 120k? 150k? Mathematically, you should, as the probablity of winning is a lot larger, but realistically you have 50% chance that you might loose 50k right away. Assuming that all your savings are 100k, would you have the stomach to a accept this risk? Most normal people, probably not. But according to this lawfirm, you should. Maybe this thinking got us in trouble in the first place.
  - tokenadult 18y ago
    according to this lawfirm hedge fund
- aristus 18y ago
  It bugged me too, but hey, that's journalism. My gut said 3 bucks. That's about as much as I would want to lose on a Martingale bet.
  - trjordan 18y ago
    But you're playing the house to his Martingale bet, right? If the game was repeated, you should be willing to bet all your money on it, since the odds are in your favor. I think the question checks your ability to understand the mathematical potential payoff, but also to weigh that against the real-world consideration of risk.

24 points by gabrielroth 18y ago

Cool. A press interview with Richard Rusczyk about his work before he founded the Art of Problem Solving website. http://www.artofproblemsolving.com/Forum/index.php http://www.artofproblemsolving.com/Forum/index.php Rusczyk always has something interesting to say.

chris11 18y ago
Yeah, I found the site when I was looking for material to study for the Putnam. It is a great site for learning about advanced math topics and even finding more challenging pre-college math material, by the way. I got the impression that he was really brilliant. Here's his blog:http://www.artofproblemsolving.com/Forum/weblog.php?w=1 http://www.artofproblemsolving.com/Forum/weblog.php?w=1

aswanson 18y ago

I've never done a trade in my life and it took all of about 12 seconds to get the right answers on the first two. They didn't list the third. Seriously, 5.4 MM for that?...http://www.bloomberg.com/apps/news?pid=20601087&sid=a4iGjejJVRko&refer=home http://www.bloomberg.com/apps/news?pid=20601087&sid=a4iG...

slpsys 18y ago
it's also a Slate article vs. HN. i'd expect them to post questions that dazzle the least common denominator, while still allowing them to understand what's going on after a brief explanation. i'd be worried if HN _couldn't_ solve problems understandable by Slate's target audience.
- jibiki 18y ago
  Um, can someone explain the answer to the first question? Why wouldn't it go lower than the low eighties? Or higher, for that matter? How would the price change if there were 1000 sellers?
  - chris11 18y ago
    Basically the sellers end up bidding for the opportunity to sell. So basically some sellers won't be willing to sell below 89, more won't be willing to sell below 88, and even more won't be willing to sell be 87. And it works the other way too, so the lower the price gets, the more people are willing to buy. So theoretically, when the number of buyers equals the number of sellers, transactions end up occurring. This is assuming that the market is efficient, which isn't always the case. If there were 1000 sellers, the price would drop even lower, because there is more competition among the sellers.
    - jibiki 18y ago
      By this reasoning, equally valid answers would be $0.01 and $90.99.
      - trjordan 18y ago
        The point of the question is that there is no mathematically "right" answer. The interviewer knows the answer from experience, and (s)he's testing two things: whether the interviewee's intuition on the market is right, and, if not, how well the interviewee takes to being corrected. Your answers are "right", in that they are possible, but they are not the numbers the interview wants to hear.
        jibiki 18y ago
        That makes more sense. I thought there was some obvious game theory principle I was missing, since somebody commented that they could answer the question without knowing anything about trading.
chris11 18y ago
Here's a forum with the type of questions that more likely to be asked. These questions are more difficult. http://www.wilmott.com/categories.cfm?catid=26 http://www.wilmott.com/categories.cfm?catid=26: Example brainteaser: "Last night I sat behind two wizards on a bus, and overheard the following: A: I have a positive integral number of children, whose ages are positive integers, the sum of which is the number of this bus, while the product is my own age. B: How interesting! Perhaps if you told me your age and the number of your children, I could work out their individual ages? A: No. B: Aha! AT LAST I know how old you are! Now what was the number of the bus?" Discussion: http://www.wilmott.com/messageview.cfm?catid=26&threadid=68570 http://www.wilmott.com/messageview.cfm?catid=26&threadid...
- deleted 18y ago
  [deleted]
- jibiki 18y ago
  Wow, I read through the discussion. No way in hell anyone would be able to answer that in an interview, unless they'd seen it before.
  - shrughes 18y ago
    It's definitely answerable in an interview situation. Some people should be able to answer it, no problemo, in a minute or two.
    - jibiki 18y ago
      I don't think you understand the problem. Even if you manage to find 4, 4, 3, 1 and 6, 2, 2, 2, you still have to verify that if the sum is 12, then there is only 1 possible product. You'll note that nobody in the linked thread succeeds at this (one guy proves that 12 works by exhaustive search, not really a possibility in an interview...)
      - shrughes 18y ago
        Well, I saw it before, and it took a several minutes then, maybe 5 or 15, I don't really remember. Then you have to consider that companies like D.E. Shaw end up hiring people who would end up giggling at how long somebody slow like me would take to solve the problem.

deleted 18y ago

[deleted]

tomsaffell 18y ago

[Warning: Spoiler] > Of course, you can't offer the guy infinity dollars. So the interviewee is forced to either settle on a real world number—as much as the player can afford—or delve into marginal utility theory I don't think that as much as the player can afford is a real world answer, unless it means as much as the player can afford to lose. There is a 50% chance he'll walk away with $1. As Wall Street have proven, it's not about maximizing expected returns, it's about optimizing returns within bounds of acceptable risk.

ardit33 18y ago
I agree with you. Unless I misunderstood the question; the theoretical "right" answer is just wrong. Let's make it more practical. There is 100k in the table. A guy tells you, head you double the money, tail, you stop, and get what is there, but you have to pay a fee. Obviously, up to 100k for the fee, it is no brainer, head you end up with at least 200k, tail, you go home with 100k, same as the fee you paid. BUT: are you willing to pay 120k? 150k? Mathematically, you should, as the probablity of winning is a lot larger, but realistically you have 50% chance that you might loose 50k right away. Assuming that all your savings are 100k, would you have the stomach to a accept this risk? Most normal people, probably not. But according to this lawfirm, you should. Maybe this thinking got us in trouble in the first place.
- tokenadult 18y ago
  according to this lawfirm hedge fund
aristus 18y ago
It bugged me too, but hey, that's journalism. My gut said 3 bucks. That's about as much as I would want to lose on a Martingale bet.
- trjordan 18y ago
  But you're playing the house to his Martingale bet, right? If the game was repeated, you should be willing to bet all your money on it, since the odds are in your favor. I think the question checks your ability to understand the mathematical potential payoff, but also to weigh that against the real-world consideration of risk.