# Ten people are bidding on a stock at 90, while 100 people are offering to sell it at 91. What price is the next trade?

Slate:

Interviewees often say that since there are more sellers than buyers, the sellers get to determine the price. That logic usually yields an answer between 90 and 91. That&#8217-s exactly wrong. &#8220-They&#8217-re not thinking about what&#8217-s going on in the real world,&#8221- says Rubczyk. In reality, when there are more sellers than buyers, the price falls. So the next sale would probably be in the mid- to low 80s.

&#8220-Some candidates would say you can&#8217-t answer that question, because there&#8217-s no formula,&#8221- says Rusczyk. &#8220-If that makes their heads explode, that&#8217-s a problem.&#8221-

What would our Jason Ruspini have answered to that quiz?

## 4 thoughts on “Ten people are bidding on a stock at 90, while 100 people are offering to sell it at 91. What price is the next trade?”

1. Michael Giberson said:

The next sale would be in the mid- to low 80s?

It seems likely that the next sale would be at 90, or between 90 and 91, but likely nearer to 90 than 91. You have 100 people willing to sell at 91, but only 10 willing to buy at 90. Assuming new information arrives randomly across the 110 people at the margin, it is more likely that a seller gets information that leads the seller to accept 90 than a buyer gets information leading the buyer to accept 91. (Similar logic implies it is more likely that a seller gets information leading it to offer a price between 90 and 91 than a buyer to bid between 90 and 91.)

But mid- to low 80s?

Sure, there is no deterministic answer, no computable formula, but that doesn’t mean any answer is good. In any case, I don’t see how you could get an answer in the mid-80s in a situation in which bidders are standing ready to pay 90.

I guess I’m not smart enough to work for D.E. Shaw.

(And I wouldn’t offer to pay infinity for the St. Petersburg paradox gamble, either. While the theoretical value of the game is infinite, the payoff only approaches the ‘limit’ after an infinite number of coin flips. However, my lifespan is limited, and my patience is more so. Also, I doubt my offer to pay an infinite amount would survive review by the credit committee.)

2. Chris F. Masse said:

I highlighted this quiz because it sounded more complex than described in the article.

Thanks.

3. Michael Giberson said:

The next sale would be in the mid- to low 80s?

It seems likely that the next sale would be at 90, or between 90 and 91, but likely nearer to 90 than 91. You have 100 people willing to sell at 91, but only 10 willing to buy at 90. Assuming new information arrives randomly across the 110 people at the margin, it is more likely that a seller gets information that leads the seller to accept 90 than a buyer gets information leading the buyer to accept 91. (Similar logic implies it is more likely that a seller gets information leading it to offer a price between 90 and 91 than a buyer to bid between 90 and 91.)

But mid- to low 80s?

Sure, there is no deterministic answer, no computable formula, but that doesn’t mean any answer is good. In any case, I don’t see how you could get an answer in the mid-80s in a situation in which bidders are standing ready to pay 90.

I guess I’m not smart enough to work for D.E. Shaw.

(And I wouldn’t offer to pay infinity for the St. Petersburg paradox gamble, either. While the theoretical value of the game is infinite, the payoff only approaches the ‘limit’ after an infinite number of coin flips. However, my lifespan is limited, and my patience is more so. Also, I doubt my offer to pay an infinite amount would survive review by the credit committee.)

4. Chris F. Masse said:

I highlighted this quiz because it sounded more complex than described in the article.

Thanks.