…of course all models are wrong. The model that is not wrong is reality and reality, by definition, is not a model. But risk management models have during this crisis proved themselves wrong in a more fundamental sense. They failed Keynes’ test – that it is better to be approximately right than precisely wrong. With hindsight, these models were both very precise and very wrong. 


                            Andrew Haldane

                           Bank of England
















Different endeavors, as Aristotle wrote, require different degrees of precision. Finance is not one of the natural sciences…We do need models and mathematics – you cannot think about finance and economics without them – but one must never forget that models are not the world….The most important question about any financial model is…how useful it is despite its assumptions. You must start with models and then overlay them with common sense and experience.


                               Derman and Wilmott

















                                         How the U.S. Stock Market Works



The philosopher Isaiah Berlin argued against the Early Enlightenment assumption that everything is calculable – from the movement of the heavens to society. He stated the philosophical basis of the Late Enlightenment and modern attitude that the quest for knowledge is unending:


…because there is no single criterion of meaning and no single method or set of rules for testing it, it does not follow that there are in principle no criteria at all, no methods and no rules which may apply in differing types of context and situations. 1









So what are the stock market rules that may apply in different types of context and situations? The first quote describes the failure of scientific history, the attempt to apply a single formula of statistical risk management to the financial system. The third quote describes what, we think, is the true situation. Financial models are useful to abstract the essentials of various types of situations –recognizing that we are still generalizing to a lesser degree-, but their usefulness is ultimately conditional upon the judgment of specific circumstances. 2


In the first discussion, our thesis is very simple. Even during market crash and financial seizure, individuals invest their capital expecting a better future. Even that condition elicits consistent investor behavior, whether ultimately profitable or not. In the second, the imperfect equilibrium of error-correction applies to the U.S. stock market and economy under normal market conditions. An analysis of the latter requires Granger’s Nobel Prize logic. In both cases, we use a simple (MBA level) linear regression model to describe the state of affairs. When financial markets are re-established and the economy is again at a state of imperfect equilibrium, we can reverse the following order of presentation:



Behavior of the Stock Market under a Condition of Market Crash and Financial Seizure


Consider the Earnings Per Share and S&P data series that covers the crucial stock market period, 1929-1932 (the trough of the stock market).


Year-End    EPS      S&P Observed    Calculated Regression Residual


  1929         1.69            22.05                          21.83                   .22

  1930         1.01            15.31                          15.20                   .11

1931          .40              7.89                            9.23                -1.34

1932          .05              6.79                            5.79                 1.00











The data can be summarized by the regression:     S&P = 5.31 +9.79 (Earnings Per Share).

                                                                                   ρ2 = .98 out of 1


Have we discovered a new law of nature? Not quite. This analysis of only four data points has no statistical consequence. The high ρ2 simply means that the linear regression model fitted the data very well during the market decline of the 1930s. There is, however, a useful generalizations from this analysis. Assume the EPS = 1. Then this regression analysis usefully calculates the characteristic P/E during that time period that was a surprisingly high 15.1 .


What does that say about investor expectations during a very difficult period? People invest in the stocks, expecting a brighter future. The fact that the P/E remained that high meant that investors expected that bright future; even at the market trough in 1932, the sum of the constant (representing that future) and multiplied EPS (representing the present) remained significantly positive.3  Now divide that constant by the calculated P/E. To place the long-term, short-term controversy in a context; using data from the 1930s, we can say that the stock market was about one-third motivated by long-term considerations and about two-thirds motivated by short-term considerations. That sounds about right today.


What does that P/E from the 1930s have to do with 2009? Actually, quite a lot. If you use a version of the Graham central value formula for stocks, or to be more rigorous a discounted cash flow model, you will arrive at a like P/E if you assume a positive earnings growth of around 8%/year. During the 1930s, individual investors who bought stock assumed that the situation had stabilized in whatever year they chose, and then expected an improvement from that point. In the 3/3/09 WSJ, Dennis Berman writes, “Read through the accounts of the Great Depression and one is struck by how politicians, policy makers, and regular people were caught off guard by the severity of the events that would engulf them.” Historians did not announce the beginning of the Great Depression in 1929.


On 3/2009 has the financial system stabilized? With necessary government interventions, the economies of the U.S., the EU, and other countries are now very complex systems. Their responses to fiscal and monetary policies will be very complex. We think the history of this financial crisis remains quite to be written; that is a reason for investors to be very cautious.



Behavior of the Stock Market Under Normal Conditions

Many investors either try to predict the stock market or assume that it is totally random. The stock market, in fact, contains both systematic and random components. In the following, we show that the pattern of the U.S. stock market is cyclical because the economy is.

Most econometric studies have been able to explain only 45% of the variation in absolute stock returns, a level of explanation not useful for investment decision making. Econometrics, however, explains changes in the valuation ratio of bond prices relative to stock prices.

We have found that more than 95% of the variation in relative stock prices is explained by a model that states: future capacity utilization and inflation determine relative stock prices. This article explains how the Fed’s error correction, under ordinary circumstances, makes the Gaussian regression model appropriate in a non-Gaussian world. Note that we have assumed a zero intercept.

                Bond Yields(t)
          ___________________                          = .022 * cap util(t+1) - .079 * infl(t+1)
         Stock Earnings Yields(t)
               where:                       Bond Yields are the long term AA utility rate.
                                                 Stock Earnings Yields are trailing S&P 500 operating

                                                 earnings divided by the current level of the S&P 500.

                ρ2 = .95 out of 1






Utilizing thirty-two years of S&P 500 data for the years 1968-1999, we found that this model explains more than 95% of relative stock market variation. In the United States, the stock market double discounts expected inflation, first through long term bond yields and second through relative stock prices.

However, during the course of several business cycles, growth in the S&P 500's earnings will dominate the cyclical terms located on the right side of this model; hence the observation that stocks are a hedge against inflation. The crucial assumption in any financial discussion is the assumed time horizon of the investment.

Since expectations of cyclical economic changes determine changes in this valuation ratio, a useful short-term decision rule can be developed, within your asset allocation guidelines:

     1. Buy stocks when you expect inflation to remain low or to decrease.

     2. Sell stocks when you expect inflation to increase.



When arguing a case, it is usually better to acknowledge a significant exception to the general rule, rather than to ignore specific circumstances and then torturing the data until it confesses. In the very complex economic situation of 2009, precedent of any sort can only be a general guide. As has always been true, but especially at present, judgment is required. Probably the best investment policy now is acting when specific conditions occur. We would note specifically: the trend in housing prices, the trends in commercial and real estate bank credit, and the resumption of quarterly EPS growth. Fraught situations sometimes require adaptive thinking.