Price Discovery 1
Market Equilibrium
Case Tutorial
Introduction
This case is designed to teach students about one of the most important functions of financial
markets; price discovery. The concept of price discovery is that while many people have different
opinions on the value of a particularly security, aggregating their opinions by allowing for them to trade
on an open market will effectively aggregate the knowledge that they hold and the resulting price is the
true value of the security.
When you observe that a stock is currently trading at a price on the stock market, you can accept that
everybody sees that price and has an opportunity to act accordingly. If a stock is say, $35.00, it is at
that price because nobody is willing to buy it for more than $35.00. Likewise, nobody is willing to sell it
for a price less than $35.00. Thus, an equilibrium price of $35 is formed and we say that that reflects
the value of security. Students will have a chance to trade with each other and form similar price
discoveries.
Trading, Information, and Strategy
The simplest analysis and trading strategy that students can follow is to trade based on boundaries.
Initially, all traders know that the stock’s value falls within {$20, $22, $24, $26, $28}. Therefore, if you
were to buy the security for less than $20 or sell it for more than $28, you will be guaranteed to make
money.
During trading, you will receive information that will allow you to reduce the boundaries and change
your trading strategy accordingly. i.e., if you receive information that tells you that Analyst #5 is
incorrect and the final value cannot be $28, the boundaries are now $20-$26.
The second principle that you can employ is that of expected value. The expected value is the
probability-weighted value of a security. At the beginning, the expected value is (20% * $20) + (20% *
$22) + (20% * $24) + (20% * $26) + (20% * $28) = $24.00. Purely following expected value, you
should be purchasing the security for any value below $24 or selling for any value above $24. This
does not guarantee a profit, but if you were to do this over and over again, in the long run, your profits
would be larger than your losses.
Like in the boundary strategy, when you receive information, you can alter your trading strategy based
on a new expected value. Based on the same information received above, you can calculate your
new expected value to be (25% * $20) + (25% * $22) + (25% * $24) + (25% * $26) = $23. The
information that you just received caused your overall impression of the stock to be worth less. This is
consistent with both strategies; strategy one told you that you could safely sell the stock for any value
above $26 (instead of $28 before the information), and strategy two told you that the new expected
value of the stock is $23, $1 lower than the expected value prior to the news release. Some
information may allow you to change your boundaries, or your expected value, both, or neither.
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Price Discovery 1
Market Equilibrium
Case Tutorial
The last strategy ties the market place’s price discovery mechanism into your strategy. Once you
realize that each trader has different information, and each trader is trading based on their information,
you can begin to infer what information that trader may have based on what the current market price is
for the security. More importantly, you can infer what knowledge the market holds in aggregate,
based on the market price of the stock. You may have narrowed the possible outcomes down to {$24,
$26}, and the market may trading at $24.50 You can consider inferring that $24 is the actual answer,
and other traders hold different information and are selling the stock (keeping the price low) because
of that information. In this case, despite your expected value being $25, you should consider the $24
outcome being very possible; other traders probably have the information set {$20, $24} and are
selling it at any price above $24.00. Since you have {$24, $26} you can safely purchase the stock at
any price below $24.00. The resulting market price of the stock should stabilize at $24 as the market
has just discovered the actual value of the stock.
Close-out and Risk free rate
There is no risk free rate of interest, so you don’t have to discount the values of the security. Your
position in GTT stock will be closed out at the final actual value of the stock. So, if the final value is
$24, all of your stock will be sold at the end of the case for $24.00. Alternatively, if you are short, you
will be forced to buy back all of the shares that you are short for $24.00.
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