Market Making Interview Game
Have recently done an interview at a top tier how should one approach this giving what has being said
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don't do 25, 24,23.... its faster to discover the fair price if you set your new b/a around 15 and use it to narrow it down
Thanks for the response.But if i sell at 25, change the spread to 14-16 and he then sells at 16delete i'm missing?
First of all, if you made the market 14 at 16, he would be buying 16 and you'd be selling. Second of all you have to balance a few things, one being your confidence in your guess and another in whether or not your interviewer is playing optimally. If you're confident then you can move less, and not cross own markets. If you're not confident, you don't want to anchor to a bad guess. To exhibit what I'm saying let's give an example of that same game. For the sake of this example I'm gonna tweak one or two things then what you did, but let's leave the actual fair value at 22 and pretend you know nothing. Let's also assume your interviewer is going to act optimally- I think normally they will. You make your first market 28 at 30 and he sells 28, you buy. Now, let's say you make your next market 24 at 26. This is where him playing optimally comes in- since he is going to play optimally and he knows its 22, he going to sell 24. He could make a risk free profit and buy 26 and lock in a $, but he would actually be leaving $ on the table. Now you know its below 24. Maybe you make your next market 19-21. He buys 21 and now you know its between 21-24. Yeah you've essentially "hacked" and locked in a loss on those trades, but you've now gained info that allows you to make a better market and thats especially important when your interviewer knows the answer and is acting optimally. Hope that helps, feel free to ask any follow-up questions.
Thanks for your thorough explanation (and agree on the correction). If you may, there are some questions that i have from the above.1) I'to recover once you know the othe, right?
1) I agree that they have to be acting optimally- if they weren't and/or you knew that they did not know the correct answer, then yes it could be disadvantageous to offer scalps like that. I disagree with 2nd part though. Yes you benefit more if you make more trades and now have a better idea of the correct value, but I also think that being responsive to what the market is telling you is important too. From your original play, you sold all the way down. You have not gained any info on a lower bound. Maybe you disagree with this and had a stronger prior on the length, but I have no idea how long the Great Wall is and wouldn't have been shocked if it were 7k km. In your game, thats a long way to come down when you're wrong. Every trade you made was a loser. I'd rather be a loser on both sides and know the correct value (or at least have some sort of range). You were a loser and didn't have a range on the fair value until he told you. Sure it's better when more trades are coming, but especially when you don't know when trading is gonna stop, I'd focus on price discovery and being responsive.
2) Not sure I totally understand what you're asking. I agree there's more value to knowing the answer when you can trade around it. However, I think everything you should do especially when you know nothing, should be in an effort to gain information. But yeah once you hit that other bound you can move somewhere in between the most recent guesses. To pickup my previous example above where we now know its between 21-24, and you seem to lean like its higher, I'd make the next market 22-24. Now your responses can be tighter. If he buys 24, then you know its 24 bc he's both bought and sold it. If he sells 22, then you can be 21-23 bc he bought 21s and sold 22 so its gotta be one of those. Idk if that answers what you were asking but hopefully you follow.
3) Sure its probably negative at first. Good luck coming up with a positive EV strategy on the first few trades when your counter-party knows the exact value and you know nothing. This game is about being responsive and finding that 2-way where you can get action on both sides around the correct theo (or close to it). It's balancing your own confidence with what the market is telling you, and I'm always gonna put more value on the latter.
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