# Charles Davì

## The Not So Efficient Market (Theorem) Hypothesis

In Not So Efficient Market Hypothesis on October 10, 2008 at 12:26 am

#### Are Capital Markets Efficient?

Let’s examine the question using elementary game theory. That is, let’s assume that given any decision, each capital market participant acts in a way that maximizes his expected utility.

#### But How Would We Do That?

First we explore one example of incentive structures which leads to a sell off. Then we consider how the Efficient Market Hypothesis fits into the framework of economic knowledge and the notion of economic efficiency. Finally, we conclude that even if a capital market incorporates all available price-information, it is possible that the outcome is not an efficient allocation of capital.

#### The Sound And The Fury

Assume that Apocalypse Ann (A) and Tag Along Teds (T1, T2, …, Tn) are all traders that hold large positions in ABC stock. Assume that A is convinced that ABC is doomed because of recent conditions in the credit markets. She may or may not be correct in her prediction, but assume she honestly believes that ABC will be placed into receivership and liquidated, with little to no money left for equity holders.  Further, assume that each of T1, T2, …, Tn is aware of A’s belief. Personally, each thinks that A is out of her mind, that ABC is well positioned to ride the current credit crisis and that current equity valuations of ABC are rational. However, they know that given A’s belief, she will certainly liquidate her position.

Assume that each of T1, T2, …, Tn is a trader for a fund that has some rather jittery investors who are awaiting quarterly results and approaching a point in their investments where they have the right to withdraw their investment.  Assume that L is the maximum decrease in total value of any ABC position that any investor in any of the funds will accept for the quarter without withdrawing their investment; and assume that no trader wants its investors to withdraw.

Assume that based on historical data and current trading volumes, if the current price of ABC stock is P1, then the price after A liquidates a 100 share lot is expected to be P2 = Δ × P1, for some  0 < Δ ≤ 1. Let the number of shares held by A be k × 100; let S be the smallest number of ABC shares held by any one of  T1, T2, …, Tn; and let P be the current price of ABC’s stock.  For any Δ < 1, we can choose k such that $L < S \times P \times (1 - \Delta ^{k} )$. That is, the expected decrease in the smallest position of ABC’s stock held by any of T1, T2, …, Tn as a result of A liquidating her position is greater than the maximum decrease in total value that any investor will accept without withdrawing their investment. Therefore, each of T1, T2, …, Tn will try to sell their positions before A does so, further deteriorating the price of ABC stock. Moreover, each has an incentive to be the first to sell.

#### Interesting, But That Looks Like A Very Specific Scenario

While catered to fit our current economic context, the root of the problem comes from the interactions between two sets of facts: the group of investors (the Teds) with a contingent investment horizon that could shorten dramatically upon the occurrence of a particular event (if the price of ABC tanks, the Teds’ investment horizons collapse to the present because the investors will want their money back); and the fact that the occurrence of that event is in the control of another party that benefits (or at least believes they will benefit) from its occurrence.

In the example, Ann acts as an individual. In theory and reality, Ann could be an individual or a group of individuals. Ann could be a group of short sellers. Ann could be a large bank that was forced to liquidate its assets. It doesn’t matter. So long as Ann will certainly liquidate a sufficiently large enough position, the Teds will as well.

#### But Doesn’t The EMH Imply That ABC’s Price Would Go Back Up?

EMH proponents would argue that in the case of such a mass liquidation, white knights will run in and bid the price up again if the underlying equity were truly “worth it.” This must be true on some level, since the number of sales must always equal the number of purchases. However, prices move. And “sell offs” cause prices to fall. This fact cuts to the nature of prices and is beyond the scope of this essay. We simply note that the fire sale dynamic creates its own little race to the bottom: each Ted has an incentive to lower their asking prices given the possibility that another Ted will go even lower.  Thus, the Teds are playing a game where expected utility decreases the longer it takes for them to close a sale. This entire fiasco is a result of the incorporation of relevant price information. That is, the fact that Ann will liquidate is relevant price information, and is therefore incorporated into the Teds’ decision to liquidate.

#### Straighten Out Your Mind’s Eye

We need to get our epistemology straight before we examine the consequences of what I’ve just outlined. First, the Efficient Market Hypothesis (EMH) is just that, a hypothesis. While there are 3 different flavors, the general idea is that all available information is quickly incorporated into the price of a stock in the world’s most developed stock markets. This hypothesis was then tested with empirical research. Whatever your opinion on how well the research actually tested that hypothesis, just assume for our purposes that the research conducted to date did test the hypothesis, and failed to prove it false.

Even if we assume that the EMH is supported by empirical evidence, its name is still a misnomer. While it does assume that information is observed and then quickly incorporated into the price of a stock, that process does not fit nicely into any well accepted notion of efficiency. For the EMH does not treat information as a good to be efficiently allocated. It boldly assumes that information is automatically available and incorporated to the maximum extent: to the point where no one could create an opportunity for arbitrage through the use of any information. This assumption is in and of itself puzzling and undermines the notion that information has value, which it clearly does. So, I prefer to think of pricing, which includes the incorporation of available price-information, as anterior to efficiency. That is, if assets are accurately priced, then resources will be allocated efficiently among those assets. This allows us to separate the EMH itself (the informational aspect) from its implications (efficiency). So, the EMH implies that the equity prices of companies trading in the most advanced capital markets will accurately reflect all available information, and that therefore capital will be distributed efficiently within those markets.

#### So How Is That Inefficient?

Good Question. As discussed earlier, the main purpose of assuming the EMH is true is to convince us that the markets distribute capital efficiently. (The observation and incorporation of information is itself interesting and important, but the goal is to allocate goods based on that information). While there are competing definitions of efficiency, the general gist is that a market is said to distribute capital efficiently if there’s no better way to distribute capital than the distribution created by the market: there might be other distributions that are just as good, but no distribution is better. “Good” and “better” are clearly imprecise terms, and we should have some definition of utility that we seek to maximize in the capital markets. However, the outcome of the Ann and Ted scenario is sub optimal under any reasonable definition of utility.

The purpose of the capital markets is to distribute capital to companies. The EMH takes as one of its corollaries that this distribution is efficient. However, as demonstrated above, the separation of control over an event and contingent investment horizons keyed to that event can lead to changes in equity prices that have nothing to do with the financial health of the underlying company. The result is that a company that becomes subject to such a situation will have a higher of cost raising capital through equity.

#### Q.E.D.

Assume that the state of affairs before the ABC sell off was efficient. We assume that when all other variables are fixed, there is only one efficient cost of equity capital for any company. Therefore, all variables other than the sell off being fixed, because ABC’s cost of equity capital has deviated from an efficient level, the state of affairs after the sell off must be inefficient.  So, something else must have changed if the state of affairs after the sell off is to be efficient. In theory, this is entirely possible. In reality, however, given that panic sales usually go to cash or cash equivalents, it is not likely. Thus, theory agrees with common sense: even if the EMH is true, panic sales are still possible and lead to inefficeint results. That is, whether or not the timely observation and incorporation of relevant price-information is a necessary condition for efficient allocation of capital, it is not a sufficient condition.

1. Are cash and equivalents priced efficiently?

Is volatility priced efficiently?

Was the equity premium priced correctly?

Is debt efficiently priced?

Single firm, market, future firm.

Does the excercise seem as inefficient in the reverse case where equity is bid up?

2. To your first 4 points: I assume that the market was efficient in all respects before the sell off. This may or may not be true in reality. But it doesn’t matter. The point is, even assuming markets are efficient ex ante, liquidity problems can lead to inefficient results ex post.

3. To your last point: Yes, the reverse is also inefficient. It would push capital costs downward (and asset prices up) to an extent that exaggerates bona fide changes in economic conditions (e.g., the U.S. housing market).

4. I think your initial model is flawed you. You assume that each market participant is maximizing expected utility. However you then assume that A somehow signals to the T’s her intent to sell which is clearly not utility maximizing behavior. A would simply liquidate her position without notifying the others. I suppose your model would still work if the T’s rush to sell at the same time as A driving the price down. It does not seem plausible to me that A wants to sell but somehow the T’s can sell first.

5. Hi Matt,

I never state that A intentionally “signals” anything, I simply state that the T’s are aware of her intent. Imagine that A is a bank which has publicly disclosed large exposure to sub prime MBS. The T’s know that eventually A must draw on its other liquid assets (e.g., ABC Stock) to meet obligations. So, A doesn’t signal, but the T’s are aware. Therefore everyone is maximizing expected utility.

6. […] the correlation of default between certain investments, creating a short term shortage of cash, leading to massive and collective sell offs across asset classes. That should sound familiar. Such a scenario would arguably create […]

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