In Mathematics and Statistics for Financial Risk Management ("MSFRM") Michael Miller has produced a very interesting effort that enjoys a unique position amongst the choices we have these days in risk management and the mathematics of risk management books. First, what this book is not: a foundational treatise brimming with abstraction and generalities. Proposition. Theorem. Lemma. Let there be a risky asset V such that... Let the price of the underlying asset follow the following process... &c. This book doesn't have the breadth of a bottom up treatment, with the exception of some appendix material and a couple of necessary diversions; rather, it assumes a certain level of sophistication from the reader, no more, and opts for practicality and depth. And this is a good thing! There are more than enough highly general treatments already in existence to choose from. Readers or autodidacts with a more mathematical or independent tilt can perhaps begin from a more general place, although the problems presented in MSFRM make the book potentially valuable to anyone. What level is assumed in MSFRM? Basic probability, calculus, and matrix algebra (although the former and latter is treated in chapters 3 and 6, respectively), perhaps consistent with an analyst or associate dealing with practical challenges. This book is not for a quant. What this book is: the stylized approach is top down instead of bottom up, obviating the need for excessive mathematical generalities, the very generalities that often leave an important readership frustrated, alienated, and confused about how to get from point A to point B. The author, on the back jacket, indicates he has "worked in risk management for more than ten years,..."; clearly, over this time, he's observed certain problems cropping up again and again, so much so that he decided to write a book on how to operate the tools to handle these problems. This is my inference since many of the ideas, problems, and tools discussed in the book have been a constant part of my professional life for over a decade. While impossible to be exhaustive, the material that made the cut is certainly well-informed and relevant, as Miller allocates some of the intellectual capital he has developed over the years and provides concrete problems that are interesting and unique. Subjects that I felt were presented well and supplemented with interesting problems for people to think about:
- Chapter 3 Basic Statistics: application to portfolio variance and hedging
- Chapter 5 Hypothesis Testing & Confidence Intervals: initially you expect a stock's vol to be 45%, but you have a estimated a different vol ex post from empirical data. Is this difference meaningful at a certain confidence level? How is VaR and Expected Shortfall related?
- Chapter 7 Vector Spaces: This chapter is interesting as it spends a bit of time on PCA and applications to yield curve decomposition and even cites current recent research in systemic risk measurement
- Chapter 9 Time Series Models: Spurious correlation, AR() processes and applications to rate models.
Stylistically I would classify MSFRM as a mixture of Carol Alexander's Quant Methods in Finance (cf chapters 6 or 9) and Euan Sinclair's Vol Trading (a book stemming from Sinclair's experience as an options' trader and hedger). It is very easy to comment on things that I would have liked to have seen more of or that I deem relevant. For example: applications of the materials covered to option markets or other asset classes in addition to stocks and bonds; the Cholesky decomposition, ubiquitous in our work, is introduced in chapter 6 but not really extended to, say, a multi-asset simulation or pricing and greek calculation (although I get the impression the author tried to stay away from potential coding problems). That being said, editing what stays and what goes is a thorny problem that can easily become impossible and for which there is no right answer and depends on one's perspective and experience. Judging MSFRM on its own merits I give it a solid 4 stars with the caveat that there is a select demographic out there that will find the book to be 5 stars. The people that will find this book the most useful will be able to immediately implement most of the material presented in a practical manner (note that I didn't download the excel examples provided by the publisher, but they are available). As someone that manages hedging and risk management teams myself, this is certainly a book that I would recommend to practitioners. Finally, it is clear that the author and the people he thanked in the acknowledgments spent quite a bit of time proofreading the final copy. The writing is clear, well-articulated, and thoughtful.