The discussion on prediction markets in the chapter on the price system in Tyler Cowen and Alex Tabarrok's Modern Principles of Economics, Second Edition (pp. 123-124) contains the following paragraphs:

Members of HP’s sales team bought and sold shares that paidoff when sales fell within a certain range. A typical security would pay out $\\\$1$, if and only if future sales were, say, between $10,000$ and $15,000$ units. Another might pay off if sales were between $15,000$ and $20,000$ units. The market con- tained $10$ types of securities—a range broad enough to include all the relevant possible sales outcomes.
By examining the prices of all $10$ shares, HP could assign a probability to any combination of outcomes. For example, if the price of the $5,000–10,000$ unit sales security was $10$ cents and the price of the $10,000–15,000$ unit sales security was $20$ cents, this suggests that the probability of selling $5,000 –15,000$ units was $30\%$.

How did the authors arrive at this figure of $30\%$?

  • $\begingroup$ If people are willing to pay only 10 cents for a chance of getting a dollar, that means they think they're about 10% likely to get a dollar. $\endgroup$
    – user253751
    Apr 12, 2021 at 9:24

1 Answer 1


It is this probability that is consistent with shares trading for their expected value. The expected value is given by: $$E(S_1+S_2)=E(S_1)+E(S_2)=p_1 \times1+p_2 \times1=p_1+p_2$$

where $S_i$ is the payment of share $i$, $p_i$ is the probability of payment of share $i$ (due to the sales figure falling in some range). So if the expected value is to equal the price of the security, then:

$$E(S_1+S_2)=P_1+P_2 \Rightarrow p_1+p_2=P_1+P_2 $$

Where $P_i$ denotes the price of share $i$. So the probability of one of them paying off equals the sum of their prices (note that the events of share 1 and 2 paying off are mutually exclusive).

In your case



Of course these calculations totally disregard the many complications that go into asset pricing (like discounting cash flows, accounting for having to wait for payment), but I assume the authors want to keep it simple to prove a point. The bigger picture you should take away from this answer is that share prices can be interpreted as reflecting information about (what investors believe to be) probabilities of future events.


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