Jane Street Teaser Q
Hey guys,
I heard Jane Street offered the following question during their interview for assistant traders;
"Make me a 2-point wide market on the chance that a randomly selected number between 1 and 100 does not contain a 7"
Anyone have rough idea to what they would be looking for?
[EDIT]
Since there are 19 numbers b/w 0 and 100 that contain the 7, there is an 81% chance you won't draw a number containing a 7. So if I was going to make a spread, would the spread be something like bid .80 and .82?
Aren't there just 19 numbers?
100% sure its 20. I think you forgot to double count the 77?
Why would you double count the 77?
Sorry my-bad, confused this q with another involving 7s lol. Yes tbcthk your right, should be 19 numbers. So in that case theres a 81% chance you wont draw a number containing a 7.
So I guess the spread could be 0.80 and 0.82?
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I think I don't understand the question. Why would it be between 0.80 and 0.82? What's the link between 81% chance of not drawing a number containing 7, and the 0.80-0.82 market?
^ Same question as paperlec
It would be nice if someone who knew what they were talking about could explain how to respond to these sorts of "make me a market on X" questions...
When you get asked a question to "make a market on X," you are essentially being asked to give a range of values within which you think the quantity X lies. For example, if you think X=0.81, then you can make a market 0.80-0.82. If you are unsure that the value you calculated is correct, then you can make a wider market 0.78-0.84. When asked to "make a market on X," you are essentially being asked to make a market on a contract whose theoretical value is X. The point of these "make a market" questions is to see how confident you are about your answers (the width of the market you make). Also, if you calculate the wrong answer, they will trade with you and you will have to adjust your market.
Something still bothers me about this. Let's suppose that making a market on X includes, as suggested, giving a range of values within which you think X lies, or more generally, let's say that it includes giving some probability distribution for the value of X.
Now, given a single draw of an integer from 1 to 100, the result either will or will not include a 7, so this is a binary outcome. Also, we know by a counting argument that the chance of not-having a 7 is 81/100, or 81%.
Notice that we know, for sure, that that probability is 0.81. There isn't much use in making a market on the probability, such as 0.78-0.84, or 0.80-0.82 -- what would this mean? "How much would I give in order to have the right to a payoff that is N dollars if the probability in question is between 0.80 and 0.82, and, say, zero dollars otherwise?" Well I guess I would pay any amount at any odds, since this would be free money.
I'm still processing the notion of the "make me a market" type questions, so I claim no authority, but it almost sounds like in this particular case, the question is a red herring. One possibility is that the question is intended to see if the answerer will point this out.
Other "make me a market" questions involving guessing weights, etc., do involve unknown quantities that may lay within a range you select, or might be described by a probability distribution you choose, so if making a market in those cases includes you giving a range or a distribution for the unknown, that makes sense.
But as for this question... I would pay 81 cents for the right to collect a dollar if the number drawn did not have a 7, at least, I believe this would be the risk-neutral fair value of the opportunity. But a 2-point wide market? I honestly still can't see where a spread can be sensibly introduced in this case.
the real deal: thanks for your clarification. I think I was initially confused about the statement and now it's resolved. Thanks!
Play some liar's poker to get good at it.
Take it further. Why not quote 80.999-81.001 ??
Oh, because 100% of securities are quoted as infinite zeros... oh wait!
Guys, they ask you to "make a market" because as a trader your job is to collect the spread. If you simply gave every client the "fair value" for a product. you would make no money.
In this case, if you had a futures contract, let's call it SRU (Seven's R'US) and at expiry a random number between 1 and 100 is chosen. If you bought this contract, and at expiry, the chosen number does NOT contain a seven, the payoff is $100. However if the number does contain a seven, the pay off is $0.
Your trading desk buys and sells these contracts all day long before expiry. We know fair value for the SRU contract is $81, but you are not going to sell it to ur clients who want to purchase it... at $81; you'll sell it at $82. Furthermore, if a client comes at you wanting to offload some SRU, you'll buy it back at $80. bid/ask=80.00/82.00.
Are we clear here?
As for how wide the spread should be, that's a matter of liquidity. If another market maker wants to undersell you and offer it at 81.5 and bid at 80.5, then that's what clients will take. But market makers will only go so low on their spread before it becomes impractical to provide liquidity in the contract at all.
If you are the only market maker in the game, you could open it up to 76/86... or as wide as you want until clients stop coming... that's why trading desks dislike competition, when you're the only bookie in town... life is good
Good, and thank you. So "make me a market" is simply a request to set a bid/ask spread around some reference price, such as perhaps the fair price. The original poster asked for a rough idea of what this meant in the first place, and I had started to wonder the same thing.
The closest previous explanation offered said "you are essentially being asked to give a range of values within which you think the quantity X lies. For example, if you think X=0.81, then you can make a market 0.80-0.82", where in this case X was putatively the probability of getting a non-7 result.
But note that even though the answer -- have a spread from 0.80 to 0.82 -- was correct, the reasoning was spurious. We're not making a market in some unknown "probability of getting a draw without a 7", because that quantity is known to all parties, and no one would be "unsure" if it's anything besides 81%.
So, one very-clear translation of the original question could be, "What is the probability of getting a draw without a 7. Now, add and subtract one percentage point to that, and tell me the result." Yes?
Previous explanations in this thread, prior to the one immediately above, seemed to be conflating "make a market" questions involving actual unknowns, like say W the weight of the ocean, with this question involving an absolutely known, X, the probability of a non-7 draw. Apparently this was strongly misdirecting from the whole point of the original question, which was crystallized in the post immediately above, but I was trying to make some sense of it.
In fact, all of that is orthogonal to the issue of market-making, which (to reiterate) is evidently nothing more than setting a spread around some reference price. To approach a question like this, keeping the issue of determining a reference price, and the issue of determining a spread, clearly separated, is key I think in any clear explanation.
Now if that seems remedial to some posters here, that's fine, but most of this thread went without that being clearly articulated, for the benefit of those who were wondering what to make of the original question in the first place.
You're the only one who was even slightly confused
Astounding. :) Actually, friend, you simply can not back up that assertion, and it's laughable to make it. Your contribution to this thread seems to have amounted to -- woo hoo! -- pointing out that you shouldn't double-count 77. Now that is remedial.
Please note that there was, by intention, nothing particularly antagonistic, and nothing in any way abusive, in my posts above, that is, prior to this antagonistic and abusive one, also by intention. And especially, nothing ad hominem. Odds are very good (not certain, but good) that I've been posting to newsgroups (dial-up bulletin boards, usenet, blogs and other web-based discussion groups) for longer than you have been alive. I'm not saying that this an accomplishment beyond mere aging, but I can say that one thing I've observed, and you might like to do the same, is that the first poster to devolve from addressing the actual subject matter to issuing ad hominem spews, rarely winds up looking particularly smart, as oh-so-clever as he imagines his quip to be. :)
But unless you are prepared to provide actual evidence that among the set of all readers of this thread, the set of readers that had difficulty making sense of some of the explanations provided, is a singleton set consisting of me, you are just blowing hot air out of your orifices, and it would probably be better off for you to simply STFU. :)
And I will not be reading any further posts to this thread, so have fun attempted to prove that you are not the logic-impaired boor that you have just advertised yourself to be.
Thanks at any rate to FXTrader, for his clear (if needlessly impatient) posting addressing the actual thread topic in an articulate fashion.
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