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Some Notes on Financial Econometrics

| | Posted in: Big Ideas

Financial econometrics gives empirical life (and death) to financial market models. Where has this rapidly growing branch of economics been, where is it now and where is it going? In the October 2006 revision of his article entitled “Financial Econometrics”, Andrew Lo provides an introduction to four decades of the field’s most influential academic papers. Some of his key points are:

On center stage:

“…randomness is central to both finance and econometrics. Unlike other fields of economics, finance is intellectually vapid in the absence of uncertainty; the net-present value rule and interest-rate compounding formulas are the only major ideas of non-stochastic finance. It is only when return is accompanied by risk that financial analysis becomes interesting, and the same can be said for econometrics. In contrast to many econometric applications where a particular theory is empirically tested by linearizing one of its key equations and then slapping on an error term as an afterthought, the sources and nature of uncertainty are at the core of every financial application. In fact, the error term in financial econometrics is the main attraction…”

On statistics:

“The uniqueness of financial econometrics lies in the wonderful interplay between financial models and statistical inference, where neither one dominates the other. …the economic justification for randomness in financial asset prices is active information-gathering on the part of all market participants. It is only through the concerted efforts of many investors attempting to forecast asset returns that asset returns become unforecastable.”

A metaphor for an important limitation of empirical analysis:

“Perhaps the most basic challenge to empirical work in finance is the wealth of data available to financial econometrics, and the many false positives that can result from repeated analysis of such data. It is no exaggeration that if one tortures a dataset long enough, it will confess to anything!”

A few questions with neither answers nor clear ways to determine answers:

“How do we conduct proper statistical inference for financial time series, which are usually non-stationary, non-Gaussian, skewed, leptokurtic, and neither independently nor identically distributed?”

“How do we decide which portfolio managers have skill when the standard errors of the usual performance statistics are so large that over 500 years of monthly returns are required to yield any kind of statistical significance?”

“Is there a way to adjust simulated portfolio returns to account for backtest bias?”

“What is the best way to measure the likelihood of rare events and manage such risks if, by definition, there are so few events in the historical record?”

“How should we construct optimal portfolios of securities if estimated means and covariance matrices are subject to so much estimation error?”

“How can we estimate the risk preferences of an individual or institutional investor, and are these preferences stable over time and individuals?”

“Is the extraordinary investment performance of certain portfolio managers due to their extraordinary risk exposures, or does genuine alpha exist in the investment management business?”

In summary, financial econometrics does not yet have its Hari Seldon.

The article lists the seminal papers of financial econometrics.

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