Quant Trader: Making a market
Make a market
About 15 minutes, start to finish.
Open withLet me work out a fair value out loud first, then I'll give you a price to buy and a price to sell.
The clock
Stage by stage
Close each stage out loud, so they always know where you are.
- 1Fair value out loud3 min
That's my fair value and how I got it. Here's my market.
- 2A width that pays for what you don't know2 min
That's my width and why. Here's how much I'll trade.
- 3Size2 min
That's my size on each side. Go ahead and trade.
- 4Update after a trade or a reveal5 min
That's my new fair value after what just happened. Here's my new market.
- 5Your position3 min
That's my position and what it's worth now, so I'm leaning my prices.
How people lose this round
My market is 7 at 7.
No gap means no expected profit and all of the risk. The spread is what pays you to stand there.1 at 12, to be safe.
Nobody would ever trade on that. They want a market you'd really trade, with your reasons.They bought, so it must be worth more. I'll raise my fair value.
A trade is news only if the other side could know something you don't. Ask, then decide.I'm short 10, so I'll lower my prices.
Lower prices make people buy more from you, so you get shorter. Lean up to buy back, and keep fair value where it is.Same width as before the reveal.
You know more now, so less can happen. Narrow the market to match.
A worked answer
The notes in the margin mark where the candidate asked, put a number on it, took a hint or caught a slip.
- Interviewer
I'll roll two dice. Make me a market on the higher of the two. It pays that number in dollars.
- You
Before I quote: have you seen the dice, or do we both know nothing?
Asks whether the other side knows more. - Interviewer
Nobody has seen them.
- You
Then fair value first. The higher die is at most k when both dice are, which has chance (k/6)². So the chance it's exactly k is (2k − 1)/36: 1, 3, 5, 7, 9 and 11 out of 36, for 1 up to 6. The average is 161 over 36, about 4.47.
Works the fair value out loud. - Interviewer
Your market?
- You
4 at 5. The outcome swings about 1.4 either way, but neither of us knows more, so I only charge for holding the risk. A one-dollar width earns me about 50 cents a trade on average. I'll trade up to 10 on each side.
Width and size, each with a reason. - Interviewer
I buy 10 at 5.
- You
So I'm short 10 at 5. Same market, 4 at 5, since you know nothing I don't.
- Interviewer
Now I roll one die and show it: a 3.
- You
The hidden die averages 3.5, so the higher one is about... no, that's mixing averages. Let me count it. The hidden die makes the higher one 3, 3, 3, 4, 5 or 6. That's 24 over 6, exactly 4.
Drops a shortcut and counts instead. - Interviewer
Where are you?
- You
Short 10 at 5 with fair value at 4, so up 10 dollars on paper.
Marks the position at the new fair value. - Interviewer
New market?
- You
Only one die is unknown now, so less can happen. I'll narrow to 3.5 at 4.5.
- Interviewer
You're short 10. Anything you'd change?
- You
Yes. I'd lean up, so I'm more likely to buy back: 3.75 at 4.75. Fair value stays at 4. The lean just makes a seller more likely to hit my bid.
Takes the hint, leans, keeps fair value. - Interviewer
I sell you 10 at 3.75.
- You
Now I'm flat. I sold 10 at 5 and bought 10 at 3.75, so I've locked in 12.50 whatever the other die shows.
- Interviewer
You were up 10 on paper. Where did the other 2.50 come from?
- You
I bought back at 3.75, a quarter under fair value, on 10 lots. That's the extra 2.50.
- Interviewer
I show the other die: a 6. What's your profit now?
- You
Still 12.50, because I'm flat and the 6 doesn't touch me. Had I stayed short 10 at 5, a final value of 6 would have cost me 10.
Shows what getting flat was worth. - Interviewer
What if I'd seen the dice before you quoted?
- You
Then your buy would be news. You'd only buy at 5 if the higher die were a 6. I'd quote wider, trade fewer lots, and move my prices up after a buy before trading again.