Lesson 2 of 7
Why efficiency is hard to test
Every test of market efficiency is also a test of a pricing model, so a rejection never says which one failed. Fama named the problem himself.
By Javier Sanz
Founder of ValueScreener. Built Ninety Nine, a securities services provider, and sold it to a tier-one global bank; ran operations and internationalization at Alpaca, the brokerage API.
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In one minute
- Testing whether prices reflect information requires a model of what returns should be, so every test is a test of two things at once.
- When a test rejects, it cannot say whether the market was inefficient or the model of expected returns was wrong.
- That is why a measured anomaly never settles anything, and why both sides of the value premium argument survive the same evidence.
This is the most useful idea in the whole efficiency literature for a practical investor, and it is the one least often explained. It is also not an objection raised by critics: it is stated by Fama, in his own lecture, about his own field.
What a rejected test actually tells you
- 1Test finds excess returnsA rule earns more than the model predicts
- 2Two explanationsEither prices were wrong, or the model of expected returns was
- 3The data cannot separate themThe same numbers support both readings
Fama's own statement of it
He puts it in two sentences. We cannot test whether the market does what it is supposed to do unless we specify what it is supposed to do, which means we need an asset pricing model that says what rational expected returns look like in equilibrium. If the tests reject, we do not know whether the problem is an inefficient market or a bad model of market equilibrium.
He calls it the joint hypothesis problem and attributes the emphasis to his own 1970 review.
What it does to every anomaly
The same finding, read two ways
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A study finds that cheap companies earned more than the model said they should.
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Reading one: the market was wrong about those companies, and the excess return is the correction.
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Reading two: the model was wrong about what return those companies should earn, because they carry a risk the model does not measure.
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Nothing in the data chooses between the two, because the model is an input to the test rather than an output of it.
This is why the risk reading of the value premium cannot be refuted by more data, and why the mistake reading cannot be either. Both sides are arguing about the model, not about the returns.
The consequence for a reader
What survives the problem
Two things do, and they are what this academy is built on.
Statements about a specific company's filed figures are not joint hypotheses. That a company's operating cash flow has been below its reported profit for nine years is a fact about two published series, and no pricing model is involved in checking it.
And statements about what a price implies are not either. Saying that today's price requires residual income to grow at 5 percent a year forever is arithmetic on the price and the accounts. It contains no claim about whether the market is efficient, and it can be checked against the company's own history.
The joint hypothesis problem is fatal to sweeping claims about markets. It leaves the narrow, checkable work untouched, which is a good reason to spend your time there.
Check yourself
Why is a test of market efficiency always a test of two things?
- Because two data sets are always used
- Because judging whether returns are excessive requires a model of what returns should be
- Because both prices and volumes must be tested
Show the answer
Answer: B.
Without a model of expected returns there is no benchmark to call a return excessive, so the model is inside every test.A study finds cheap companies earned more than the model predicted. What does that establish?
- That the market is inefficient
- That the model is correct
- Either that prices were wrong or that the model was, with no way to tell which from the data
Show the answer
Answer: C.
This is the joint hypothesis problem exactly: the rejection is of the pair, not of either half.Which kind of statement escapes the problem?
- A claim that a factor earns alpha
- A claim about a company's filed figures, or about what its current price arithmetically implies
- A claim that markets overreact
Show the answer
Answer: B.
Facts about two published series, and arithmetic that solves a price for the assumptions inside it, involve no model of expected returns.Sources
- Fama, "Two Pillars of Asset Pricing", Prize Lecture, 8 December 2013, published 2014: the statement that market efficiency cannot be tested without specifying an asset pricing model, and that a rejection cannot distinguish an inefficient market from a bad model, which he names the joint hypothesis problem emphasised in his 1970 review.
What this leaves out
- The problem is about testing, not about whether markets are efficient. It says the question is hard to answer, not what the answer is.
- Alpha and excess return are used here as they are in the literature: relative to a stated model.
- Nothing here is advice about any security.