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Set out the theory of efficient markets and show the ways in which markets can fail to be efficient.

FRM® Part II · Risk Management and Investment Management · Factor Theory · FRM2.IM.1.f

The idea

An efficient market is one in which prices fully reflect available information, so no strategy earns abnormal returns after adjusting for risk and costs. The weak form covers past prices and volumes, making technical analysis useless. The semi-strong form covers all public information, so fundamental analysis cannot win. The strong form covers private information too, so even insiders cannot profit. Each form includes the one before it. Markets can fail through behavioral biases and noise traders. They can also fail through limits to arbitrage, such as short-sale constraints, financing limits and the risk that mispricing widens. A third source is information costs. Grossman and Stiglitz argued prices cannot be perfectly efficient, or nobody would pay to gather information. Tests are joint tests of efficiency and an asset pricing model, so apparent alpha may only reflect a faulty model.

Formulas

Abnormal return in an event study with the market model

AR = R − β × Rm

R
the stock's return on the day
β
the stock's market-model beta
Rm
the market's return on the same day

Assumes a zero intercept, as in the bank's questions; with an intercept, subtract it too. Sum the daily abnormal returns for the cumulative abnormal return, keeping the sign of a negative market day.

A practice question

From the question bank, with the reason each wrong option is wrong.

Evidence that corporate insiders consistently earn abnormal profits by trading on undisclosed information would most directly contradict:

  1. the weak form of market efficiencyWhy not: The weak form concerns information in past prices and volumes, not private information.
  2. the strong form of market efficiency - correct
  3. the semi-strong form of market efficiencyWhy not: The semi-strong form concerns public information; insider profits come from non-public information.
  4. allocational efficiency of capital marketsWhy not: Allocational efficiency is a different concept, about capital reaching productive uses, not about information in prices.

The strong form says prices reflect all information, public and private. Persistent insider profits are the standard evidence against it.

A harder one

A strategy has earned a CAPM alpha of 3% a year for 30 years. A colleague concludes that markets are inefficient. The best response is that:

  1. the conclusion is valid, because any positive alpha proves mispricingWhy not: Alpha measured against a model may merely reflect omitted risk factors.
  2. the conclusion is valid only if the alpha is at least 3% every yearWhy not: A consistent alpha size is not the issue; the model is.
  3. efficiency requires every alpha to be exactly zero in any sample, so the strategy must be a statistical error rather than a real patternWhy not: Efficiency concerns expected abnormal returns; sample alphas can differ from zero and the problem here is model specification.
  4. tests of efficiency are joint tests with a pricing model, so the alpha may reflect omitted risk factors - correct

This is the joint hypothesis problem: a significant alpha means either mispricing or a deficient pricing model.

The hardest tier

In an event study the market model is: expected daily return = beta x market return, with beta of 1.2 and a zero intercept. Over three days the stock returns 2.0%, 0.5% and -0.3%, while the market returns 1.0%, -0.5% and 0.2%. The cumulative abnormal return is closest to:

  1. 1.50%Why not: Uses market-adjusted returns with beta = 1 instead of 1.2.
  2. 2.20%Why not: Sums the raw stock returns without removing the expected return.
  3. 1.36% - correct
  4. 3.04%Why not: Adds beta times market return instead of subtracting it from each day's return.

Abnormal returns: 2.0 - 1.2 = 0.80; 0.5 + 0.6 = 1.10; -0.3 - 0.24 = -0.54. Sum = 1.36%.

In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.

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