The Present and Future of Empirical Finance

More and more data, greatly increased computing power, a rising number of research enthusiasts, an increased number of finance journals, and sophisticated techniques have been the characteristics of empirical finance in the past 30 years. Topics of current interest relate to conditional means, conditional variances, and conditional distributions. These topics will remain in the forefront for years to come and perhaps be joined by questions that will shake the foundations of finance theory. For example, will we find that market data are characterized by jump diffusions—that is, diffusions with breaks—rather than standard diffusions? In the third of a century since my first investigations into finance theory, empirical finance has changed dramatically—from only a few active workers to hundreds, maybe thousands, of researchers. The number of finance journals has grown from one to dozens, and the techniques have become considerably more advanced. The availability of much more data and greatly increased computer power have produced impressive research publications. Many of these publications have relatively little practical usefulness, however, and in fact, the purpose of much of the work is unclear.I avoid the most popular procedures that have developed (which are covered by several excellent textbooks on financial econometrics) and survey the work that is going on and the work that needs to be done with conditional means, conditional variances, and conditional distributions.For the future, I see, first, continued investigation of topics already under scrutiny. In particular, conditional distributions will continue to be a major subject as finance learns how to generate more of its fundamental theories in distributional forms: arbitrage and portfolio theory, efficient market theory and its consequences, the Black-Scholes formula, and so forth.Structural breaks are also likely, however, in the present framework. In particular, I foresee renewed study of the “facts” researchers found through using basically a linear foundation for studying prices, returns, and volatility. An example of these facts is the conclusion that returns are nearly white noise; that is, they have no serial or autocorrelation.I see problems in the new field of continuous-time finance theory. The mistake that I see is starting with the assumption that a price or a return can be written in terms of a standard diffusion, which is based on a Gaussian distribution. The approach served well in the early days of econometrics but only for mathematical convenience; it was not tested. The assumption in continuous-time theory is dangerous because we have no way to test it. We have no continuous-time data.Finally, I find interesting the recent results indicating that our market data behave in a way that is more consistent with jump diffusions—that is, diffusions with breaks—than with standard diffusions. If this finding holds, the majority of current financial theory will probably have to be rewritten with “jump diffusion” replacing “diffusion” and with some consequent changes in theorems and results. As with all radical new ideas, this change will certainly be opposed by some.