No Such Thing as a Random Walk

Investors defy risk models.

December 21, 2010

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17292_footprintsDespite the appearance of a “Great Moderation” something went terribly wrong in the late 2000s. It wasn’t quite that too many people in too many countries were buying homes they really couldn’t afford. It wasn’t that too many people were packaging too many obscure securities for too many people chasing too little yield. It wasn’t that too many people in financial services were too little scrutinized by too few regulators with too few laws to ensure fair and transparent markets.

Sure, those were background factors. But what happened to the risk management systems? What happened to the random errors that, according to the financial models, cancel each other out? How come the improbable moved from the remote to the commonplace?

Some researchers at the World Bank have an answer. It ain’t pretty. “A Flaw in the Model…That Defines How the World Works,” is the title of a paper by Volker Bieta, Hellmuth Milde and Nadine Weber. In their argument, the flaw is relying on models developed in the natural sciences where arbitrary and willful human influence has been carefully screened out.

“The old view regards financial assets as claims on cash flows whose magnitude and variability are exogenously given. The prices of these assets are based on current information about future cash flows. A market is called ‘informationally efficient’ if all information available at a given point of time is indeed used by market participants. As a result, according to the efficiency model, all information available is reflected in existing market prices.

“However, this view is misleadingly simple and seriously incomplete.  For example, according to the old view, information is available at zero cost. This is of course nonsense because information is never a free good. As a consequence, we observe information insiders and information outsiders in the world around us. Informational asymmetry is an empirical fact. In addition, the old view ignores the existence of conflicts of interest, incentive schemes, and agency problems.”

This is, of course, not the first swipe at the efficient market hypothesis. What gives it richness is its pointed language.

“Consider a banker who climbs a tree and starts sawing the branch on which he is sitting. Wouldn’t you think that this banker is bird-brained? Be assured he is not as in his fantasy the branch does not break and he does not fall down. The banker’s fantasy is based on the assumption of irrelevance—the backbone of modern financial theory: Actions of market participants are irrelevant for the state of the market. This means in our analogy that the banker’s action of sawing does not change the state of the branch.

“However, there is more to this story.  Bankers do not only dream that the branch, which symbolizes the price of a financial asset, does not crash; they also observe that it sways somewhat. To explain this movement, which is not at all related to the sawing, bankers invented a coin tossing force majeure to decide whether the branch moves to the right or to the left depending on the random outcome of the tossed coin. The assumption of a random walk is explained by the efficient market hypothesis and the model of perfect competition that create a situation in which all parties are price takers and only decide about quantities. Yet in such a situation, someone has to decide about the price; this is where the force majeure—also called the auctioneer—enters the picture, setting the price based on presumably randomly incoming supply and demand quotes.”

Against this, they remind fans of stochastic approaches to price movements that informational assymmetry counts, and creates rather different scenarios than a purely random walk would. (And even the pioneer of random financial walking, Burton Malkiel, admitted as much recently.) For, event uncertainty may follow a random path (the swaying of the tree branch) but human intervention (sawing the branch off) creates behavioural uncertainty. Thus:

“As soon as two active players are involved, we can no longer ignore behavioral uncertainty.  Examples include poker and chess. There is no room for an exogenous density function since the player who is able to checkmate the other will not toss a coin to determine her move. Players will take the move leading to the highest payoff, which is decided by a set of rules that determine each player’s compensation under different actions. These rules create incentives for players to act in certain ways dependent on the opposite player’s actions, which are generally unknown. Hence, with multiple active players, we face information asymmetry; we are no longer situated in perfect markets and are confronted with the principal-agent-model, where the principal is the information outsider and the agent is the information insider. The insider (agent) can and should use her advantage. Every decision taken by the insider (agent) has consequences for both players.”

No point mentioning three-dimensional chess; the one – or rather two – dimensional game makes the point: the action of one player is contingent on the action of the other, according to the rules of the game.

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