V.10:3 (115-118): Modeling The Stock Market by Paul T. Holliday

Modeling The Stock Market by Paul T. Holliday

The price/earnings ratio works perfectly well— for stocks. But, Paul Holliday points out, it doesn't work for stock indices such as the DJIA or the Standard & Poor's 500, where the effective interest rate works much better. To prove it, he's come up with a market model based on the theory that price is in proportion to earnings divided by interest rate and proceeds to demonstrate its use.

The price/earnings ratio has been highly regarded as an indicator of whether the market is over- or underpriced. But closer analysis reveals that for stock indices, the price/earnings (P/E) ratio does not perform as advertised. Rather, the effective interest rate is the key to determining if the stock market is fairly priced.

To illustrate, I developed a model of the market based on the premise that price is proportional to earnings divided by interest rate. (See sidebar, "Math model formulas.") The Standard & Poor's Composite Index (S&P 500) is used because it is a broad representation of the market. The earnings in the model equation are the average of the yearly earnings a year ahead of the price. Figure 1 shows the S&P 500 earnings and the average represented by the straight line on the semi-log grid. The model gives a closer match to the actual price when average earnings are used in place of the actual earnings, indicating that the price of the index is not dependent on the quarter-to-quarter variation of earnings. The interest rate in the model combines short- and long-term rates plus the inflation rate and is referred to as the effective interest rate pertinent to the stock market. An additional correction factor, amounting to a few percent, is added to account for changes in dividend yield.

The comparison of the model with the S&P 500 index for the past 35 years is shown in Figure 2. The mean error is 0.01% and the variance is 10.6%.