Prices and Information
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The efficient markets hypothesis is often synonymous with the phrase, “prices reflect all available information.” This sounds really smart, right? And it is really easy to explain to people. “Ah, you see, if I have this information and you have this information, then everyone else must also have this information and therefore it is already reflected in the price of this asset.”
However, other times you will hear economists say that prices are substitutes for information. They invoke this in the context of discussing markets. They will say something like, “No one needs to know why the price of oranges has gone up. The fact that the price of oranges has gone up sends them a signal to buy fewer oranges.” Markets can work with minimal information.
But isn’t this a contradiction? How is it possible that prices reflect all available information, but somehow simultaneously act as a substitute for information?
To explain why this is not a contradiction, it might help to appeal to an analogy from cryptography.
A lot of people use online banking services. In order to do so, they have to connect to the internet and log in with a name and a password. This password is pretty important. Anyone who has your password can transfer your money and send payments. Choosing your password is important. You want a password that people would not guess so that no one can log in to your account. However, it is also important that your bank doesn’t just store that password somewhere. If they do, it doesn’t matter how good your password is, anyone who gains access to the database can log in to your account. But without storing this password, how can the bank know that it is you who is logging in?
One thing that the bank could do is to use your password as an input in a cryptographic hash function. Doing so produces an output called a hash value that is of fixed length. The output that is produced by this hash function is unique. It can only be generated by using your password as an input in the function. Any change to your password would change the output. But most importantly, while using your password as the input will always produce the same output, knowledge of the output cannot be used to recover your password.
Thus, what a bank could do is store a hash of your password. Anyone with access to the database will just see what looks like an incomprehensible string of letters and integers. There is no way for this person to reverse engineer your password from this information. Furthermore, entering this string of letters and integers as the password won’t help the person get into your account since that would require using the hash itself as an input in the hash function, producing a completely different hash. The only way for someone to log in would be to enter the correct password, which is then passed through the hash function and generates a hash that can be matched to what the bank has stored. If it is a match, you can get access to your account. If not, the person trying to login (including if it is actually you) will not be able to do so.
At this point you might be wondering what this has to do with prices and information. Recall the claim that prices both reflect information and act as a substitute for information. Now, think of the online banking example. Some valuable information (your password) was passed through a hash function to produce an output. This hash value reflects valuable information in the sense that it could only have been produced from your precise password. However, the hash value doesn’t reveal any of the underlying information that generated it. Anyone looking at the hash value would not be able to determine what generated that particular value. Yet, the hash value communicates something important to the bank since the bank can check this value against the stored valued to determine whether you should be granted access to its services.
Markets work in much the same way. There are people that populate markets who possess with their own unique knowledge, preferences, and constraints. When new information is revealed, this information is combined with the knowledge, preferences, and constraints of these people and that results in a change in their behavior. These behavioral changes manifest themselves in market interactions. The corresponding change in the price reflects the particular knowledge, preferences, constraints, and information of these actors. Nonetheless, one cannot use the price to recover the particular knowledge, preferences, constraints, and information simply from observing the price. And yet, the change in the price communicates a message even to those not privy to the new information that caused the price to adjust their own behavior such that the goods in the market are allocated to their most high-valued use.
When an economist says that prices reflect information, this is not meant to say that you can recover the information necessary to determine why a price is what it is or why a price changed (although it is sometimes possible!). What is meant is that we shouldn’t expect prices to change in response to information that is already widely known.
Markets are where information is turned into price changes, which in turn communicate incentives to get resources where they are valued most. It is precisely the fact that markets tend to coordinate the behavior of buyers and sellers in a market despite the fact that one cannot always reverse engineer changes in prices to obtain the information that precipitated the change that makes markets so remarkable and so worthy of study.
Prices as hash output - that's brilliant and makes perfect sense to me as one familiar with cryptography. I'll try it out on some others who are not so familiar with cryptography and see how it goes.