Interview Question: Make A Market on Anything

I don't understand interview questions about "making a market" when it isn't applied to financial assets. What does it mean if an interviewer asks you to make a market on the number of windows in this building?

I just had an interview and my resume mentioned I was a runner, so the interviewer asked me to make a market for the time it takes me to run 5k. All I knew was that my expected time was 16m30s, and that i had to make a spread on this time so I said 16m20s and 16m40s. But what does this mean? Who's buying? What does it mean bid at 16m20s and sell at 16m40s?

Furthermore, how are you supposed to answer these types of questions? How do I set the spread size? Should it always be symmetrical? Is the interviewer hitting my bids/asks?

How to Make a Market on an Item in an Interview

This response was originally posted by user @oneshine", a sales and trading analyst.

In practice, there are three main determinants of your market (bid-ask):

Theoretical Value
This is what you think it's worth. If it's a market on the outcome of a die roll then you can make a tighter market since it is a known quantity (3.5). If it is something obscure, like the number of ping pong balls that can fit in the Empire State Building you will need to make your market wider. The interviewer wants to see that you are adjusting your market for risk due to uncertainty.

Last Price Traded
This is the going market price. Sometimes the trading price deviates from your theoretical value. In this case the trader needs to balance his faith in the market with his faith in his models. Interviewers don't usually give you the last traded price so this will probably be irrelevant.

Current Position
This is your net long/short exposure. Ideally, market-makers like to be flat, meaning they have no exposure to movements in the asset price. If you have accumulated a serious position you would want to make your markets asymmetric to make either buying or selling more desirable. For example, say you are extremely long an asset that is worth $.50. A reasonable market may then be $.40 -- $.55. This means you are willing to sell for less theoretical profit than you are willing to buy. You are giving up some "edge" to reduce your exposure. Generally, if you are flat your market should be symmetric (i.e. bid/ask are equidistant from theoretical value).

Confidence Interval
A trader's market is a balance of these three things. It is not uncommon for interviewers to ask for your confidence interval. In this case just remember that a higher confidence interval translates to a wider market. Also, don't give answers like 0-$1billion. In the real world the highest bid and the lowest ask determine the market. The tightest and fastest markets get the trade and no one will deal with absurdly wide traders.

Market Making Interview Question Example

User @marcellus_wallace", a sales and trading analyst, shared an example of making a market:

marcellus_wallace - Sales and Trading Analyst:
Taking your example of 400 windows in the building.

339.95-400.05. If you make a super tight market, your margins are garbage and your basically telling your interviewer how many windows you think there is. A market maker has little value in such a situation, your basically doing what HFT firm does. If you do know the exact value in this case 400, as mentioned your best bet would be skew the market one way or another, to get parties to transact. I will wait you out in this case till you sell to me at 400, which you make 0 then.

320-420. Ok if you think there is 400 windows, and I come in and bid 370. What do you do in that situation then hold firm at 420? Come down to 410? etc...

Again it's more of an art than science but the question gets you thinking.

Check out a video about how to answer this kind of question below:

Read More About Market Making Strategies on WSO

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In regards to time to complete a race wouldn't you bid at 16m40s and sell at 16m20s since the lower time holds a higher value. Anyway, seems like a weird question probably just to see your creativity and how you would respond to the question. Probably not looking for any set answer, could be wrong though.

Rise early, work hard, strike oil.
 
ChEM3:
In regards to time to complete a race wouldn't you bid at 16m40s and sell at 16m20s since the lower time holds a higher value. Anyway, seems like a weird question probably just to see your creativity and how you would respond to the question. Probably not looking for any set answer, could be wrong though.

You are definitely right in you example of the lower time having more value, hence the offer should be less than the bid. It is a little stupid of an interviewer to ask this because in practive that is never the convention.

 

Susquehanna used to ask these questions. They'd frame it in terms of a confidence interval. I.e what's your 90% confidence interval on the number of windows in this room. The idea is that for things you're more confident in, you can make a tighter market, and for things you know nothing about, you need to be wide. It's an overconfidence test more than anything.

 
Letsgomets:
Susquehanna used to ask these questions. They'd frame it in terms of a confidence interval. I.e what's your 90% confidence interval on the number of windows in this room. The idea is that for things you're more confident in, you can make a tighter market, and for things you know nothing about, you need to be wide. It's an overconfidence test more than anything.

This is a great point. I think a common mistake one does in such questions is to give too tight a confidence interval for a random variable you have little information about. In an interview I did with SIG, the interviewer asked me to give a market for the population in Nigeria. My market was too tight and the answer way off. Her point was to pay attention to "second-hand information" (knowing what you don't know) so that you avoid being overconfident. In this example, she could have hailed from Nigeria, clearly having an information advantage. The best answer should have been something like 2-100mm (very wide, but contains the real number).

 

the above about lower time having more value just complicates things. When doing these things the standard is that you buy/sell the actual number.

I dont understand your confusion about whos buying. You make a market, your bid is the price at which you are willing to buy, and your offer the price at which you are selling. When it relates to non financial instruments its the same thing as financial instruments. Ie number of windows, there is a true value, that is equal to the number of windows on the building, payoffs are calculated with respect to that true value.

Lets say there are 400 windows in total, and you make a price of 350-370. Your interviewer (if he knows the actual number), will lift you at 370, and on that trade will make 400-370. If he sold at 350, you would make 50.

 
derivstrading:
the above about lower time having more value just complicates things. When doing these things the standard is that you buy/sell the actual number.

I dont understand your confusion about whos buying. You make a market, your bid is the price at which you are willing to buy, and your offer the price at which you are selling. When it relates to non financial instruments its the same thing as financial instruments. Ie number of windows, there is a true value, that is equal to the number of windows on the building, payoffs are calculated with respect to that true value.

Lets say there are 400 windows in total, and you make a price of 350-370. Your interviewer (if he knows the actual number), will lift you at 370, and on that trade will make 400-370. If he sold at 350, you would make 50.

Can you explain how you got the pnl when he lifted you at 370? Don't understand where the 400 and the 50 pnl at sale come from?

Also is there any good books on market making or learning some of the fundamentals of a market maker?

 
wpsboys:
Can you explain how you got the pnl when he lifted you at 370? Don't understand where the 400 and the 50 pnl at sale come from?

Also is there any good books on market making or learning some of the fundamentals of a market maker?

When he lifts you at 370, it means he bought the asset from you at 370. The asset in this case is the number of windows in a way. If he buys it at 370, but its actually 400, he makes 30. Similarly if he sells it at 350, which means you bought at 350, if its 400 you make 50.

For example if you make a market on where a stock is in a months time. If its 100 now, lets say you make a market of 110-120, if someone buys from you at 120 and it ends up 140, you lose 20. (Btw in this example there is a specific price you should but I will let you think about what it is, or more specifically what determines it).

There arent many resources for market making because its more an art than science. Market making is really about price/size/width and then managing a book of risk. Those arent things you can write a book about.

 
derivstrading:
the above about lower time having more value just complicates things. When doing these things the standard is that you buy/sell the actual number.

I dont understand your confusion about whos buying. You make a market, your bid is the price at which you are willing to buy, and your offer the price at which you are selling. When it relates to non financial instruments its the same thing as financial instruments. Ie number of windows, there is a true value, that is equal to the number of windows on the building, payoffs are calculated with respect to that true value.

Lets say there are 400 windows in total, and you make a price of 350-370. Your interviewer (if he knows the actual number), will lift you at 370, and on that trade will make 400-370. If he sold at 350, you would make 50.

This is closer to what I wanted to get at: It seems to me that a popular strategy to answer these questions is the one I used: find the expected value, and throw on some arbitrary spread around it. But how do you choose a "good" spread size - something that might have statistical or logical backing? Why would I not choose 320-420?

And sometimes you do know the expected value. If I knew there were 400 windows, how do I methodologically set a spread, rather than just setting some spread that sounds nice (e.g. 395-405). Why not 399.95 and 400.05? Why not 390 and 410? Why not an asymmetric spread? Should I perhaps assume some number for volatility first?

The confidence interval approach might also work, but that's a quite a number of calculations in your head...

 
swordfish712:

This is closer to what I wanted to get at: It seems to me that a popular strategy to answer these questions is the one I used: find the expected value, and throw on some arbitrary spread around it. But how do you choose a "good" spread size - something that might have statistical or logical backing? Why would I not choose 320-420?

And sometimes you do know the expected value. If I knew there were 400 windows, how do I methodologically set a spread, rather than just setting some spread that sounds nice (e.g. 395-405). Why not 399.95 and 400.05? Why not 390 and 410? Why not an asymmetric spread? Should I perhaps assume some number for volatility first?

The confidence interval approach might also work, but that's a quite a number of calculations in your head...

You are thinking about it a bit too scientifically, whereas its a lot more about strategy. Taking the simple case of just you and the interviewer, even if you know with 100% certainty the number of windows, its in your interest to make the widest spread possible at which you think your counterparty will actually trade. The wider your spread, the less probable your counterparty will trade (even though you could argue you giving a wide spread signals uncertainty). Therefore if you think your counterparty has a very different view from you, you might give a wider spread, or skew the spread one way (if you think that hes estimating 600 windows, you might skew the spread upwards to maintain a tight spread but a high offer price).

In practice, with multiple market makers, the spread is a function of liquidity. In theory, the spread should compensate a market maker for the price risk that is involved with unwinding a position (in liquid products) or hedging costs (with less liquid products).

 

Taking your example of 400 windows in the building.

339.95-400.05. If you make a super tight market, your margins are shit and your basically telling your interviewer how many windows you think there is. A market maker has little value in such a situation, your basically doing what HFT firm does. If you do know the exact value in this case 400, as mentioned your best bet would be skew the market one way or another, to get parties to transact. I will wait you out in this case till you sell to me at 400, which you make 0 then.

320-420. Ok if you think there is 400 windows, and I come in and bid 370. What do you do in that situation then hold firm at 420? Come down to 410? etc...

Again it's more of an art than science but the question gets you thinking.

 

Glad to know they switched countries in the last five years. During my interview there, I was asked to make markets on; population of Ethiopia, speed of a golf ball the instant it comes off of Tiger Woods' driver, german DM/USD exchange rate at the height of Germany's hyperinflation, etc.

Also, for what it's worth, Nigeria's population is > 150mm, so the point is to be careful and be thoughtful about marking markets.

 

I'm curious about this topic too and am going to resurrect the thread.

For example, if someone asked me to make a market on whether or not it was going to rain tomorrow, how would I choose the specific bid/ask price?

 
mango001:
I'm curious about this topic too and am going to resurrect the thread.

For example, if someone asked me to make a market on whether or not it was going to rain tomorrow, how would I choose the specific bid/ask price?

does 1 mean it will rain? 0 mean it wont?

Because when you're in a room full of smart people, smart suddenly doesn't matter—interesting is what matters.
 
mango001:
I'm curious about this topic too and am going to resurrect the thread.

For example, if someone asked me to make a market on whether or not it was going to rain tomorrow, how would I choose the specific bid/ask price?

Binaries are made between 0 and 1. 1 is chosen as the payoff if something will happen. So you are pricing a contract that if it rains pays off 1 and if it doesnt rain it pays off nothing. So the value of the contract will be somewhere between 0 and 1, and the fair value is basically the probability of the event happening as:

EV = p(rain) * 1 + p(no rain)*0 = P(rain)

so lets say its 60%, the value is 0.6, so you need to make a spread around that, ie 0.5 - 0.7

 
derivstrading:
mango001:
I'm curious about this topic too and am going to resurrect the thread.

For example, if someone asked me to make a market on whether or not it was going to rain tomorrow, how would I choose the specific bid/ask price?

Binaries are made between 0 and 1. 1 is chosen as the payoff if something will happen. So you are pricing a contract that if it rains pays off 1 and if it doesnt rain it pays off nothing. So the value of the contract will be somewhere between 0 and 1, and the fair value is basically the probability of the event happening as:

EV = p(rain) * 1 + p(no rain)*0 = P(rain)

so lets say its 60%, the value is 0.6, so you need to make a spread around that, ie 0.5 - 0.7

Sorry, but how did you get .5-.7

Are you assuming there is a 60% chance of no rain?

Because when you're in a room full of smart people, smart suddenly doesn't matter—interesting is what matters.
 
Best Response

In practice, there are three main determinants of your market (bid-ask):

  1. Theoretical Value - This is what you think it's worth. If it's a market on the outcome of a die roll then you can make a tighter market since it is a known quantity (3.5). If it is something obscure, like the number of ping pong balls that can fit in the Empire State Building you will need to make your market wider. The interviewer wants to see that you are adjusting your market for risk due to uncertainty.

  2. Last Price Traded - This is the going market price. Sometimes the trading price deviates from your theoretical value. In this case the trader needs to balance his faith in the market with his faith in his models. Interviewers don't usually give you the last traded price so this will probably be irrelevant.

  3. Current Position - This is your net long/short exposure. Ideally, market-makers like to be flat, meaning they have no exposure to movements in the asset price. If you have accumulated a serious position you would want to make your markets asymmetric to make either buying or selling more desirable. For example, say you are extremely long an asset that is worth $.50. A reasonable market may then be $.40 -- $.55. This means you are willing to sell for less theoretical profit than you are willing to buy. You are giving up some "edge" to reduce your exposure. Generally, if you are flat your market should be symmetric (i.e. bid/ask are equidistant from theoretical value).

A trader's market is a balance of these three things. It is not uncommon for interviewers to ask for your confidence interval. In this case just remember that a higher confidence interval translates to a wider market. Also, don't give answers like 0-$1billion. In the real world the highest bid and the lowest ask determine the market. The tightest and fastest markets get the trade and no one will deal with absurdly wide traders.

 

I've been asked this before, and from what I have heard from other friends in the field, it is one of the most common questions in trading interviews. Ricky is right in that one should set a tighter spread if they have a higher confidence in their answer. It also tests your knowledge of asymmetrical information, so keep that in mind during the interview process.

 

the surer you are of answer the tighter you can be, the less sure you have to be WIDE. If, for example they ask you the population of Chicago, and you have no idea say, 1 million AT 10 million. Meaning you will buy 1 million people(you think it is higher than that) and you will sell 25 million(you think it is lower than that). If you are fairly certain it is 2 million people, you can make it 1.5/2.5 and trade with the guy all day.

 

majority of final round at JSC is like this. the traders will take you up on your markets and you will win/lose after the event is resolved. sometimes they will guarantee that they will trade if you make an n-wide market, so if you can get the true EV right you have a good shot at profit.

 

only if you are neutral, if you have a signifcant postion in either direction you may want to give up some theoretical profit in a certain direction in exchange for getting closer to having a neutral position as then you are affected less by market moves in an unfavourable direction.

 

You would be short 30 units, so don't screw that up haha.

Jack: They’re all former investment bankers who were laid off from that economic crisis that Nancy Pelosi caused. They have zero real world skills, but God they work hard. -30 Rock
 

First thing I'd be wondering is why did you gave me such a tight bid/offer... I mean you know next to nothing about where the true value is yet you've homed right in on a 1 window b/o. Why?

 

Yes, I'd be concerned about the width also, thats an extremely tight market, I'd suggest being wider.

Jack: They’re all former investment bankers who were laid off from that economic crisis that Nancy Pelosi caused. They have zero real world skills, but God they work hard. -30 Rock
 

you dont want to move your mkt to 1001/1002 after he lifts you you want to make ur bid in between ur first 2 prices say 1000.5/1001.5

at 1001 u become short---so u want to be able to buy back from him at less than that price

now obviously if he lifts u a 2nd time, then ur price is probably pretty off

IVY for Life
 

Curious, who are you interviewing for?

Also, I guess same question as you - What's the point in the question? Is he testing to see if I pick the right spread? Or is he seeing if I can do quick math? Or is he testing my logic/game theory?

What would be the perfect answer?

What if I say 100 bid 105 ask? Would that be wrong?

 

I LOVE this question because it has so much depth to it.

They are testing so many different abilities...

1) The big guestimate (you need to think logically to figure out how many windows are in the building)

2) Your ability to make a market.... too wide and no one deals with you... too tight and they hit/lift you and then they arb out their position with another player.

3) Your ability to assess your overall risk... example... building is roughly 50 stories tall... each floor is 100x100 and windows surround the building... each window is 10x10...

50 Stories X 10 windows per side X 4 sides = 2000 windows.... or 40 per floor....

Being off by a single floor throws you off by 40 units... these are all things you have to be able to determine into making your market

If you made a market that tight thats telling me 2 things... either you are a sucker that has no clue what they are doing making that as a market or that you know exactly how many windows are in the building and im the sucker....

If i asked you the question... then you are the sucker...

"Oh the ladies ever tell you that you look like a fucking optical illusion" - Frank Slaughtery 25th Hour.
 

[quote=trade4size If you made a market that tight thats telling me 2 things... either you are a sucker that has no clue what they are doing making that as a market or that you know exactly how many windows are in the building and im the sucker....

If i asked you the question... then you are the sucker...[/quote]

You don't mind elaborating do you? How does me making a tight market and knowing how many windows there are make you the sucker?

 

If you are making a tight market and know how many windows there are why would I trade with you. I am operating under the assumption this game settles against how many windows there actually are and that there are only 2 players.

Tighter markets usually means more transparency and a large number of players.

"Oh the ladies ever tell you that you look like a fucking optical illusion" - Frank Slaughtery 25th Hour.
 

The problem is that if you're far off in your initial estimate, you'll lose a lot of money before you get the correct value. If you had a wider spread to reflect your uncertainty, you wouldn't lose as much.

 

You cannot know PnL until you have information pertaining to time t+1; that is, if you trade at 9am, and say hypothetically that all quotes are stopped, you are in the dark.

Now, if after the initial trade you gain information regarding the most recent quote, then you can calculate PnL. For example, lets say that as a sell-side trader I bought an asset at 20 at 9am. At 9:01am, the market bid-ask is 21-23; I sell at the 'ask,' meaning that if a client comes to me wanting to buy, I can sell at 23; my current PnL is therefore $3. If I close out the position by selling, then I lock in the $3 profit. If there is no quote at 9:01am, I technically cannot calculate PnL (no quote is different than no change in quote; the latter implies no change in PnL).

Skewing the spread has to do with predicting what others in the market will do, not necessarily what you believe the 'true value' to be. For example, if I quote 20-22 as the market for the age of 1st year S&T analysts, and this keeps getting bid up until something like 28-30, a value I as a market maker certainly do not believe to be fair, I can adjust the 'bid' and/or 'ask' to influence the markets behavior. If I no longer want to sell, make the ask extremely high to disincentivize participants from coming to buy from me. If I want to no longer buy, in anticipation of the market for 1st year S&T analyst ages correction, make the bid extremely low to the point where less market participants will sell to me.

For the interview, if its making a market on something easy as above, say something like "Well this seems like a pretty intuitive market to make : quote(bid, ask)." If its something difficult, obviously take your time in coming up with a bid-ask. Explain the intuition behind the the values (what you expect the true value to be) and the spread (representing how certain you are). Giving ambiguous answers will piss off the interviewer.

 

[quote=ChapelThriller]>

For example, lets say that as a sell-side trader I bought an asset at 20 at 9am. At 9:01am, the market bid-ask is 21-23; I sell at the 'ask,' meaning that if a client comes to me wanting to buy, I can sell at 23; my current PnL is therefore $3. If I close out the position by selling, then I lock in the $3 profit. If there is no quote at 9:01am,

This is wrong. You sell at the 'bid'. The only way you can lock in your profits would be to hit the 21 bid. If you sold at 23 you are going to have to wait until the bid gets to 23, whether that be the whole market or just one person who has to purchase this.

In your example your guaranteed profit would be a dollar, not three.

"The way to make money is to buy when blood is running in the streets." -John D. Rockefeller
 

You can "mark-to-market" to get the PnL. For example:

Market is $20 at $21, and you're a market maker and you get filled on the offer (i.e. you sell for $21). Your PnL is now $0, because to exit the position, you would "take" the market (assuming it's still $20 at $21) and buy for $21 to close out.

In another scenario, suppose the market moves to $19 at $20 after you sell for $21. You can now buy it back for $20, so your marked to market PnL is +$1. The opposite applies if the market moves against you to $21 to $22.

 

thanks for your response peyo! So suppose we went through several changes in the spread, now I am long 20, then we should use the final ask to calculate the pnl right? Another question is that how fast should we respond in an interview? I am used to record the transactions when doing this, is it allowed? Also I read the posts in another discussion but don't understand when to lift the bid over the average sell(which is admitting that I was wrong in the previous spread). Thanks again.

 

So once I get lifted, keep track of my avg buy/sell & factor that into my new bid/offer. So my new bid shouldn't be the same as the price I got lifted. He also mentioned a kid he interviewed with:

"One kid actually had an interesteing strategy that i interviewed. Forgot what we were doing or the numbers involved, I asked him to make me a market on X in size he was comfortable with, he made 490-500 with 0.01 gbp per pt (the true number was like 550). I lifted him at 500 and then the next market he made was like 590-600 at 0.01 gbp per point. I sold it and then he made like 540-550 in 10 gbp per pt. I asked him what the strategy was. And he explained that he figured as ive prepared my questions and have been doing interviews i probably know the true answer, so he made his first makret at his estimate at a very small size, then when i lifted he made a market way higher again in very small size. He explained that the if I bought again then it was the right thing to do to move it that much higher, if i sold, he would book a cost of 0.9 gbp, but that would be a cost to finding out that the level was in a 100 wide range, where he was then comfortable showing a makret 10 wide in larger size. So his strategy if i bought at 600 was to then show 590-600 in 0,01 gbp again until he found the 100 wide range where he could make a larger market where his spread of 10 would be 10% of the range of values, whereas before it could have been 1%.

Now the downside to this strategy is if the true value is like 1000, and he makes 490-500 in 0.01, so i buy at 500, then buy at 600 I might sell at 695 at 0.01, then have him make a market of 640-650 in larger size and lift that, so id take a tiny hit to make him believe that the true value was lower.

But I really liked how he approached it. The kid grasped the fact that you wont make money in this exercise, I probably know the true answer, so the game is to minimize the loss in a way."

So now I wondering should I should go with the strategy of keeping my new bid under what I got lifted at or should I go with the strategy above which goes against dervistrading philosophy to keep my bid below the avg sell price.

 

Depends, as with most things in life there is no hard and fast rule.

If you arent confident in pinpointing a range that is narrow enough then the strategy above is probably a good start. Note that the word narrow is defined by the range of values it can be normalized by how wide you have to make the spread. Lets say its the numbers of windows on a building, you have to make it 10 wide, and you can estimate with 99%+ confidence that its within a range 100 wide. So lets call 50 each side of your mid point average a 3 Sigma move. So lets say 17 is a 1 sigma move. So your spread is 10, so you make 5 from your fair value mid on each trade, so your sharpe ratio is approx 0.3. I would say you would probably want this closer to 1. So therefore if your 1 sigma is 17, you would want to make a market that is closer to 35 wide.

However, you still need to make a market that is 10 wide, so you can vary your sizing at this point. Lets say your range is 400-500 and so you make 445-455. You get lifted at 455. Now you know the answer is above 455, but lets say you still are confident in your 500 upper limit. Now your range is 45 wide. So your 1 sigma is now 7.5, so to get a 1 sharpe your market can be 15 wide. Still not there, but if you do these initial quotes for small size, and then get slowly bigger as you narrow down the possible range, you can get your average sharpe to a place you originally wanted even though you have had to make markets tighter than you would have liked.

In short, theres a lot of different ways to go about it, so you have to think on your feet how to best approach it. In the end ,you want to make sure every decision you made is defendable post fact, so think before every decision, why exactly are you doing this and does it make sense?

 

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Namaste. D.O.U.G.

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  • Director/MD (5) $648
  • Vice President (19) $385
  • Associates (86) $261
  • 3rd+ Year Analyst (13) $181
  • Intern/Summer Associate (33) $170
  • 2nd Year Analyst (66) $168
  • 1st Year Analyst (202) $159
  • Intern/Summer Analyst (144) $101
notes
16 IB Interviews Notes

“... there’s no excuse to not take advantage of the resources out there available to you. Best value for your $ are the...”

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success
From 10 rejections to 1 dream investment banking internship

“... I believe it was the single biggest reason why I ended up with an offer...”