Blog - Investing Notes

February 9, 2006 – Out-of-Sample Test for a Stock Market Model

In reviewing recent postings in the General Financial Markets category of the Social Science Research Network (SSRN), we found the April 2002 paper entitled "Solving the Price-Earnings Puzzle" by Carl Chiarella and Shenhuai Gao. In this paper, the authors investigate the interrelationships of stock prices (the S&P 500 index), earnings and interest rates (the Federal Funds Rate) during January 1979 to August 2001. They conclude that the stock index is proportional to aggregate earnings and inversely proportional to the interest rate. Their approach to modeling the S&P 500 index has some similarities to our Real Earnings Yield (REY) Model, but also some differences. In this entry we perform an out-of-sample test of their findings and compare the results to those of our REY Model, finding that:

The following chart shows:

(1) Log ( S&P 500 index ), the log of the actual S&P 500 index.

(2) Log ( E / FFR ), the log of aggregate S&P 500 earnings (E) divided by the Federal Funds Rate (FFR). This plot is the model proposed in the above-referenced paper.

(3) Log ( E / ( I + C ) ), the log of aggregate S&P 500 earnings (E) divided by the sum of the inflation rate (I) and a constant (C), where C is the average difference between the S&P 500 index earnings yield and the inflation rate over the entire period. C represents the real return investors require from earnings. This plot is our REY Model.

The sources and methods for constructing aggregate S&P 500 earnings and the inflation rate are as described in our REY Model section. Note that C is constant only for a given time period (in this case, the test interval). The model proposed in the paper (the red line) blows up in the early 2000s as the Federal Reserve implemented an extremely stimulative interest rate policy to combat recession (as also happened in 1992-1994). The plot for this model suggests that the stimulation is nearly removed at this point. In contrast, our REY Model (the blue line) stays well in touch with reality regardless of Federal Reserve policy. These results confirm our opinion that investors/traders act more on the direct threat of inflation to the real value of earnings than on any indirect threats from interest rates.

In summary, investors/traders pivot on earnings, but react to the inflation rate rather than interest rates.

Fore related research, see:

Blog Synthesis: Gunning for the Fed Model?; and,

Our blog entry of 9/21/05, finding that FFR changes are of little or no use in forecasting the behavior of the overall stock market.