Monday, April 12, 2010

Fabbozi et al., Quantitative Equity Investing

Quantitative Equity Investing: Techniques and Strategies (Wiley, 2010) by Frank J. Fabozzi, Sergio M. Focardi, and Petter N. Kolm is a dense book. More than 500 pages long and replete with mathematical formulas, it is intended for students, academics, and financial practitioners, especially those who have a working knowledge of linear algebra and probability theory. It may not be bedtime reading, but it thoroughly and clearly covers topics that other books only allude to. For anyone who wants to know how quantitative equity investing strategies are developed this is an ideal text.

The three major themes of the book are financial econometrics (linear regressions and time series), factor-based trading strategies, and portfolio optimization. The authors also look at some issues of trade execution, such as transaction costs and algorithmic trading.

It is impossible in this short space to do justice to even a single topic in the book. I have somewhat arbitrarily chosen to sample a tiny section, just over a page, with the subhead “Time Aggregation of Models and Pitfalls in the Selection of Data Frequency.” The authors invoke the familiar distinction between continuous- and discrete-time models. Continuous-time models resemble the differential equations found in physics; an example is the Black-Scholes option pricing model. Discrete-time models, by contrast, have definable time steps. For instance, if we are looking at the returns of a model we might specify a daily, weekly, or monthly time frame. The authors ask two companion questions. “Given a process that we believe is described by a given model, can we select the time step arbitrarily?” And “Can we improve the performance of our models considering shorter time steps?” (p. 174)

The authors write that “there is no general answer to these questions. Most models currently used are not invariant after time aggregation. [That is, we cannot successfully use the same model at different time steps.] Therefore, in the discrete world in general, we have to accept the fact that there are different models for different time steps and different horizons. We have to decide what type of dynamics we want to investigate and model. . . . Using shorter time steps . . . might result in a better understanding of short-term dynamics but might not be advantageous for making longer-term forecasts.” (p. 174) This might seem intuitively obvious, but we must remember that most chartists claim that patterns are time invariant. What works on a one-minute chart, they claim, works equally well on a daily chart.

This book does not take on the “softer side” of equity investing. It sticks to its quantitative knitting, combining theoretical analysis with practical recommendations. For example, suggestions for mitigating model risk, ways to perform portfolio sorts, and conditions under which VWAP is an ideal trading strategy (one condition is that the trader’s strategy has little or no alpha!). As such, it should be required reading for everyone who either builds quantitative models or aspires to do so.

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