The Mathematics of Financial Modelingand Investment Management

12-FinEcon-Model Sel Page 343 Wednesday, February 4, 2004 12:59 PM

Financial Econometrics: Model Selection, Estimation, and Testing 343

Empirical Evidence of Cointegration in Equity Prices

It is now time to discuss the empirical evidence that support various

types of models. The usual tests do not reject the random walk hypothe-

sis for more than 90% of stocks investigated. The average correlation of

the S&P 500 computed in the 2001–2003 period is roughly 17% as

shown in Exhibit 12.1. The distribution of the eigenvalues of the correla-

tion matrix has the distribution shown in Exhibit 12.4. The distribution

of the eigenvalues is quite close to the theoretical shape for large portfo-

lios of a random matrix with the exception of a number of eigenvalues.

Cointegration is more difficult to ascertain. A number of academic

studies have found contradicting evidence about mean reversion around

exponential trends. Poterba and Summers^18 found positive evidence of

mean reversion of stock prices around exponential trends. This early

EXHIBIT 12.4 Distribution of the Eigenvalues of the S&P 500

(^18) J. Poterba and L. Summers, “Mean Reversion in Stock Prices: Evidence and Impli-
cations,” Journal of Financial Economics 79 (1988), pp. 22–25.