The writers of the Renaissance used reason to set mankind "at the world's center." By the Enlightenment of the 18th century, Reason had become integral in a full-fledged program to achieve the value of Freedom. The assumption of rationality is integral to the liberal world order, and we would be surprised if it did not exist in the stock market.


Consider our market discussion to date. We have suggested that the leptokurtic statistical behavior of stock prices originates from non-equilibrium trading between value investors and momentum investors. It is by this means that the market moves to extremes; but this trading process results in only a very approximate sort of economic efficiency. What is the cause of the long-term rational equilibrium behavior that every economics textbook describes? Does it actually exist? What is its function?


Steven Johnson (2001) makes a very useful distinction between the behavior of complex systems, which generate only complex patterns, and the behavior of complex adaptive systems, which generate complex patterns and achieve goals. Thermostatically controlled heating systems are an example of the latter; they use negative feedback to achieve a goal, holding the temperature of the house constant even though the temperature outside varies. To expand this point, in economics, the negative feedback supplied by prices is used to achieve overall efficiency. If a commodity (say a stock) becomes mispriced, its expected return will differ from that of other stocks; and its price will adjust so (in theory) the expected return of all investments will be equal.


The idea of an equilibrium efficiency results in a model of the economy that produces a cornucopia of goods and services from the optimized inputs of land, labor, and capital. We now ask how in the real financial markets long-term equilibrium efficiency occurs. 


In The General Theory, Keynes (1935), wrote that at a static equilibrium the marginal returns of all investments will be equal, and equal to the current rate of interest. That is:



     E(r)  =  I1   =  I2   =   I3  =   I4     =  the  current rate of interest

                  P1      P2        P3      P4


                                                           =  the marginal efficiency of capital    



      where:     E(r) = The expected return of an investment.

                       I(n)  = The yearly profit of one more unit of that type of investment.

                      P(n)  = The price of the investment.



    If           I1   =  I2          then                 I2                                                                                                                                                                                                                                                                                                                                                                                                                         

                  P1      P2                                  P2                                                                

                                                                               equals one, or an empirical constant


The consequences of this equilibrium equation are as follows:



1.      The Fed can control the prices of all assets in the economy (eventually) by changing the current rate of interest.


2.      Investors will adjust the prices of all their assets against the current rate of interest so that the rates of return on their investments will be equal.


3.      The ratio between the yields of any two investments will be a constant.



Assume no change in Fed policy and no change in short-term interest rates. Increases in the prices of bonds will decrease their yields and cause investment portfolios to become excessively weighted in favor of bonds. Portfolio managers will then, in the portfolio adjustment process, take profits on their lower yielding bonds and buy more profitable stocks. In what amounts to actually sell bonds and to buy stocks? Our discussion now becomes less theoretical; there are different ways to adjust your portfolio asset allocations to increase your future returns.



A Gaussian Statistical Model of the Market



 If you believe that the stock market is Gaussian, Modern Portfolio Theory allows you to construct an optimal portfolio; that is a portfolio that maximizes return for a given level of risk. There are substantial problems when implementing this model which factors in risk, that is variance;  in addition to an equilibrium mean:



1.      To allocate funds between long-term bonds and stocks, you must estimate two rates of return, two variances, and one covariance; that is you must correctly estimate five economic variables.


2.      This model is sensitive to the slightest change in any of the above.


3.      Its been shown that stock market returns aren't Gaussian anyway, they're Paretian, having a more extreme leptokurtic distribution.




 A Cyclical Model of the Market



By studying the behavior of relative asset prices for the years (1968-1999), we've shown that U.S. stock market is cyclical:



         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.



The correlation of this cyclical equilibrium model with the data is .95. Portfolio managers adjusting among asset classes according to their expected returns cause inflows and outflows of funds from the stock market, a consequential process that results in this econometric equation. Your stock allocation should increase when you believe that real capacity utilization will increase, and when inflation is substantially controlled.


However, that horrific September 11 at the World Trade Center illustrates that there is uncertainty in the world; in addition to financial risk.



A Non Cyclical Model of the Market



Consider a non cyclical model of the stock market using the same data:


         Bond Yields(t)
         -----------               = 1.39 = a constant
         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.



The correlation of this model with data is .92, compare this with the above. This is not the best empirical model of the stock market, but it is in accordance (more or less) with the economics textbooks, requires no estimation, and has very useful asset allocation consequences. Consider the advantages of a model which assumes expected returns and therefore all prices remain at a static equilibrium. This means that:



                                   %  stocks in a portfolio = a constant



This simple portfolio model (if we can call it that) handles cyclicality, risk, and uncertainty because in not completely efficient financial markets, you'll do the right thing. You'll buy stocks when their prices decrease, and sell them when investors' expectations become excessive, thereby buying low and selling high. Over time, you will increase the original return of your portfolio.


This model also allows investors to structure their portfolios according to their risk tolerances and income requirements, with bonds of varying maturities.



Long-term economic equilibrium presupposes a stable political environment. In the 1930s, the lights were going out all over Europe. In that fearsome investment climate, Keynes (1933) wrote:


         "I feel that general disaster for a great country like United States is a

          far more unlikely event than disaster for particular firms or industries,

          and that nine times out of ten it is a safe bet that the extremes of

          misfortune will not occur."


His confidence was justified. The Constitutional Convention of 1787 had designed the government along Enlightenment principles to produce the reasoned decisions that would preserve the freedoms of the American people. In "The Federalist, mainly in nos. 49 and 51," James Madison described how this was to be accomplished.


Will liberal democracy survive the 21st century? There is every reason to expect that it shall. The historian Arthur M. Schlesinger, Jr., however, predicts the renewed growth of doctrinaire creeds if the liberal democracies fail to construct a humane, prosperous, and peaceful world.