Two interview Questions
- If you could play a game just once with two choices: take $1 or have a 0.1 chance of getting $10, what would you choose? How about $1 vs 0.1 chance of $15? How about 10000 vs 0.1 chance of $100k?
There is only once chance to play this game. Does it mean that we cannot make decision based on the EV?
Another question is like this, the interviewer ask me how confidence I am on my answer to a previous question, I said 90%. Then he said, now I offer you a trade, if your answer is correct, then I gave you $10, otherwise, you gave me 90. Would you like to accept this trade? Why and why not? If not, how much I should gave you?
Is this the same as the "take $1 or have a 0.1 chance of getting $10, what would you choose?" question? Just calculating the EV? But I think the difference is I am the one who gave the confidence level, and it seems it is different from probability distribution. What is the purpose of this question?
- Make me a 2-point wide market on the number of rooms in XXX Building. Adjust the market.
What is the optimal strategy to adjust the market? Actually, I do not know how to adjust the market. Is it trying to find the fair value as soon as possible? or to minimize the loss?
The situation is that I do not know the fair value, but the interviewer does. It seems that the interviewer wants me to find the fair value by adjusting my market. For example, suppose the number of rooms is 300, but I do not know that, and I guess it is 500, so I said 450-550. Then the interviewer say he will sell at 450. Then I adjust my market to 400-450, the interviewer say he will still sell to me. Then I adjust my market to 300-350,..., and so on. Finally, the interviewer told me what the fair value is, and ask me to calculate how much I loss.
Thanks so much!
No, you still do EV. With the .1 example, while it does not matter which one you do from an expected value standpoint, you would take the $1 because it is instant profit. On the second example (.15) you would take the chance because your EV is higher.
Not sure what he means by adjust the market, but it could be something along the lines of change your bid-ask by two rooms at a time since they would have to be facing each other.
To Gekko21,
Thank you.
How about this case: have a 0.1 chancing of getting $9, and have a 0.9 chancing of losing $1. He ask me whether I would like to play this game, and why? I think from an EV standpoint, it does not matter whether I play or not, right?
About the second question, it is like this, when I make a 2 point market, say 200 to 300, then he say he would like to buy at 300, then he ask me whether I want to adjust my market, how and why? I think when he wants to buy at 300, it means that the number of rooms is more than 300, so I adjust my market to 300 to 400, but actually, I do not know how to choose the spread and how to determine the starting point. Because If each time I choose a big spread, it is more likely that I include the fair value, but nobody will trade with me and it takes a long time for me to find the fair value. If I choose a small spread, then I may not include the fair value which will make me lose money. I do not know whether this is the right way to think it.
Ok, I'm not sure about the market spread question, but here's how to think about the betting game questions.
If you could play a game just once with two choices: take $1 or have a 0.1 chance of getting $10, what would you choose?
Given no further information then obviously the first one because that's a guaranteed dollar, versus an expected value of a dollar (but also with a downside risk of 0). This is assuming that you are typically risk averse.
But let's turn this on it's head. Let's say that the price of a sandwich is two dollars or higher in the time period after the bet, and you have no further money. If you don't eat you starve to death. Then you want the ten dollar bet because otherwise you don't eat. In real life this becomes more and more true if we keep adding zeros onto the end of the bet. Let's say I would force you to live for a month on the proceeds of the bet, and we now make the bet $100 versus $10000. You know you can't live on $100 so you are forced into the bet.
Let's turn it on it's head again. After some point, as the value of the bet rises this becomes less and less true. If you were again going to have to live on the proceeds of the bet and it was 10,000 versus 1,000,000 you would definitely not bet.
I think the probability in these kinds of bets is a side issue compared to understanding inherently at what point you would make the wager.
the illustrious monkeysama
I see. I like your point!
Is there any one who is familiar with market making?
deleted.
fionehong
It doesn't really matter what FV of the market is. Think about a real life example, your models may be valuing something at 10, but if the market is 15/16, either your model is way wrong or the market is way wrong. Either way, if you're trying to make markets, you'd still make it close to what it's actually trading it so that you have a chance of actually getting trades without accumulating a huge directional position.
I'm not really sure what the interviewer was trying to do with that question though, the only thing I can think of would be to raise your bid/offer if he lifts your offer and vice versa.
For #2, it'll normally start with the interviewer checking your thought process as to how you arrive on the number of rooms. When you finally make a market, he may say Interviewer: Ok. I lift you. What's your new market? YOU - X/Y Interviewer: Ok I'll sell you two lots. What's your market now?
etc
Yes! The interview is like this! And after I adjust my market several times, the interviewer will tell me the fair value, and ask me to calculate the money I loss. So my question is how to choose the new market?
If the fixed value is less than the probability-induced alternative, take the latter.
Bear in mind the above two logics would hold from a statistical standpoint. The only caveat to such a question is (and this scenario is not covered in your question above) when the fixed value is astronomically large and the probability-induced alternative is better off (ie. choosing between 100k and 0.1 probability of landing 1.1MM). In such an instance, I'd explain statistically I would still pick the probability-induced alternative; however, from a risk-reward standpoint, I'd take the fixed value simply because I'd want to lock in the size of my profit.
Logically, if I interpret the question correctly, I would do it like this. Assume 300 is the fair value.
I may quote a 250-350 spread (where the fixed value is somewhere close to the midpoint such that liquidity is ensured while I have sufficient room to manoeuvre regardless the side he takes). If he offers to buy at 350, you could adjust your market to say 225-325 thereafter. If someone then offers to sell a room at 225, you make a $125 profit from the two transactions.
In short, you respond accordingly depending on whether you're oversubscribed on the bid or ask side to "lure" other market participants to take the other position to enable you to close out with a profit. The size of your spread (and deviation from the fair value) will obviously determine your liquidity and profits accordingly. In the above instance, having sold a room for 350, you could obviously set your spread in any way such that the bid amount is at least 250 (ie. X-250, where X
To edtkh,
Thank you!
In fact, I do not know what the fair value is. It seems that the interviewer wants me to find the fair value by adjusting my market. For example, suppose the number of rooms is 300, but I do not know that, and I guess it is 500, so I said 450-550. Then the interviewer say he will sell at 450. Then I adjust my market to 400-450, the interviewer say he will still sell to me. Then I adjust my market to 300-350,..., and so on. Finally, the interviewer told me what the fair value is, and ask me to calculate how much I loss.
Is it more clear?
[/quote] 1. In short, if the fixed value offered to you is equal to (or greater than) the probability-induced alternative, take the fixed value. Logic: A bird in hand beats two in the bushes.
If the fixed value is less than the probability-induced alternative, take the latter.
Bear in mind the above two logics would hold from a statistical standpoint. The only caveat to such a question is (and this scenario is not covered in your question above) when the fixed value is astronomically large and the probability-induced alternative is better off (ie. choosing between 100k and 0.1 probability of landing 1.1MM). In such an instance, I'd explain statistically I would still pick the probability-induced alternative; however, from a risk-reward standpoint, I'd take the fixed value simply because I'd want to lock in the size of my profit.
Logically, if I interpret the question correctly, I would do it like this. Assume 300 is the fair value.
I may quote a 250-350 spread (where the fixed value is somewhere close to the midpoint such that liquidity is ensured while I have sufficient room to manoeuvre regardless the side he takes). If he offers to buy at 350, you could adjust your market to say 225-325 thereafter. If someone then offers to sell a room at 225, you make a $125 profit from the two transactions.
In short, you respond accordingly depending on whether you're oversubscribed on the bid or ask side to "lure" other market participants to take the other position to enable you to close out with a profit. The size of your spread (and deviation from the fair value) will obviously determine your liquidity and profits accordingly. In the above instance, having sold a room for 350, you could obviously set your spread in any way such that the bid amount is at least 250 (ie. X-250, where X
This makes it even simpler. Let's denote the bid-ask spread with X-Y.
When you make a market quoting X-Y, the other party will hit the ask if Y is less than the fair value (ie. he buys below market price). Conversely, he will hit the bid if X is more than the fair value (he sells above market price). Obviously if he keeps hitting the ask, you know the room is more expensive than what you're currently offering him. There's really no way to gauge where the fair value is unless you keep shifting the X-Y spread until such a time where he switches from buying at Y to selling at X (or vice versa). However, since you mentioned in your caveat you would be told what the fair value is in the end, calculating your loss is easy.
Let's say the fair value is 300 (unknown to you until you're done with the third trade) and you do the following trades:
Trade 1: You quote 400-500. He sells at 400. Trade 2: You quote 100-200. He buys at 200. Trade 3: You quote 250-350. He buys at 350.
Clearly, your P&L from Trades 1, 2 and 3 are -100 (you buy at 100 above fair value), -100 (you sell at 100 below fair value) and +50 (it makes no difference whether he hits the ask at 350 or buys the 250 in this instance; it generates the same P&L for you here) respectively. You essentially make a net loss of -150.
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