On Self-Fulfilling Prophecy

In their excellent “Forecasting Stock Returns” in the Handbook of Economic Forecasting, David Rapach and Guofu Zhou write,

While stock return forecasting is fascinating, it can also be frustrating. Stock returns inherently contain a sizable unpredictable component, so that the best forecasting models can explain only a relatively small part of stock returns. Furthermore, competition among traders implies that once successful forecasting models are discovered, they will be readily adopted by others; the widespread adoption of successful forecasting models can then cause stock prices to move in a manner that eliminates the models’ forecasting ability..

Almost an article of faith currently, this perspective seems to rule out other reactions to forecasts which have been important in economic affairs, namely the self-fulfilling prophecy.

Now as “self-fulfilling prophecy” entered the lexicon, it was a prediction which originally was in error, but it became true, because people believed it was true and acted upon it.

Bank runs are the classic example.

The late Robert Merton wrote of the Last National Bank in his classic Social Theory and Social Structure, but there is no need for recourse to apocryphal history. Gary Richardson of the Federal Reserve Bank of Richmond has a nice writeup – Banking Panics of 1930 and 1931

..Caldwell was a rapidly expanding conglomerate and the largest financial holding company in the South. It provided its clients with an array of services – banking, brokerage, insurance – through an expanding chain controlled by its parent corporation headquartered in Nashville, Tennessee. The parent got into trouble when its leaders invested too heavily in securities markets and lost substantial sums when stock prices declined. In order to cover their own losses, the leaders drained cash from the corporations that they controlled.

On November 7, one of Caldwell’s principal subsidiaries, the Bank of Tennessee (Nashville) closed its doors. On November 12 and 17, Caldwell affiliates in Knoxville, Tennessee, and Louisville, Kentucky, also failed. The failures of these institutions triggered a correspondent cascade that forced scores of commercial banks to suspend operations. In communities where these banks closed, depositors panicked and withdrew funds en masse from other banks. Panic spread from town to town. Within a few weeks, hundreds of banks suspended operations. About one-third of these organizations reopened within a few months, but the majority were liquidated (Richardson 2007).

Of course, most of us know but choose to forget these examples, for a variety of reasons – the creation of the Federal Deposit Insurance Corporation has removed most of the threat, that was a long time ago, and so forth.

So it was with interest that I discovered a recent paper of researchers at Cal Tech and UCLA’s Andersson Management School The Self Fulfilling Prophecy of Popular Asset Pricing Models. The authors explore the impact of delegating investment decisions to investment professionals who, by all evidence, apply discounted cash flow models that are disconnected from investor’s individual utility functions.

Despite its elegance, the consumption-based model has one glaring deficiency.

The standard model and its more conventional variants have failed miserably at explaining the cross-section of returns; even tortured versions of the standard model have struggled to match data.

The authors then propose a Gendanken experiment where discounted cash flow models are used by the professional money managers who are delegated to invest by individuals.

The upshot –

Our thought experiment has an intriguing and heretofore unappreciated implication— there is a feedback relation between asset pricing models and the cross-section of expected returns. Our analysis implies that the cross-section of expected returns is not only described by theories of asset pricing, it is also determined by them.

I think Cornell and Hsu are on to something here.

More specifically, I have been trying to understand how to model a trading situation in which predictions of stock high and low prices in a period are self-confirming or self-fulfilling.

Suppose my prediction is that the daily high of Dazzle will be above yesterday’s daily high, if the opening price is above yesterday’s opening price. Then, if this persuades you to buy shares of Dazzle, it would seem that you contribute to the tendency for the stock price to increase. Furthermore, I don’t tell you exactly when the daily high will be reached, so I sort of put you in play. The onus is on you to make the right moves. The forecast does not come under suspicion.

As something of a data scientist, I think I can report that models of stock market trading at the level of agents participating in the market are not a major preoccupation of market analysts or theorists. The starting point seems to be Walras and the problem is how to set the price adjustment mechanism, since the tatonnement is obviously unrealistic

That then brings us probably to experimental economics, which shares a lot of turf with what is called behavioral economics.

The other possibility is simply to observe stock market prices and show that, quite generally, this type of rule must be at play and, because it is not inherently given to be true, it furthermore must be creating the conditions of its own success, to an extent.