### Book Review: Puzzles of Finance

**Puzzles of Finance: Six Practical Problems and Their Remarkable Solutions**

by Mark P. Kritzman

I've decided to occasionally post reviews of books that might be interesting to the readers of this blog. Some of these books will have been recently published while other books reviewed here will have been around for a while. Mark Kritzman's fascinating book will be the first book review in what I hope will be a regular feature of this blog.

The title of this book accurately summarizes the contents of the book (which doesn't always happen). Mark Kritzman, a respected investment professional, researcher, and intellectual, wrote this book with a rather original and ingenious purpose: Writing a mathematical / logic puzzle book (a la Martin Gardner or Dennis Shasha) but using six thematic problems from finance. The six 'puzzles' considered are:

(1) 'Siegel's Paradox' (having to do with an anomaly in exchange rate calculations)

(2) likelihood of loss (it turns out that you can obtain a bewilderingly wide range of answers depending on how one approaches the problem)

(3) time diversification

(4) "why the expected return is not to be expected"

(5) Fischer Black's question "all stocks half the time or half stocks all the time?"

(6) irrelevance of expected return to option valuation (basically going through the derivation of the Black-Scholes & Merton's option pricing model)

It's worth noting that the book doesn't attempt to address so-called puzzles like the equity risk premium puzzle. The reason for this is consistent with the author's intention to write a book that focuses mainly on purely mathematical and logical puzzles in finance rather than more psychological or philosophical problems from finance.

The best features of this book -- a 'bonus' that is worth the price of the entire book itself -- is the last chapter which goes through the basics of quantitative finance in an succinct but accessible way, and the glossary which does a great job of defining some rather sophisticated terms from finance (in fact, the glossary is a lot better than a lot of finance & investing dictionaries I've seen). The last chapter and the glossary makes this book both accessible to a wide audience and useful even to people-in-the-know.

The relatively minor drawback of this book is that -- while the intention to write a Martin Gardner-esque book is a noble one -- the reader should not wind up being convinced that most problems in finance are purely mechanically mathematical or formally logical in nature. The biggest problems in finance usually come from philosophical and psychological issues -- e.g., overly rigid assumptions about human rationality -- that are buried underneath the math. In fact, focusing on the 'math' -- especially if 'math' is incorrectly thought of as just a bunch of equations and numbers instead of what it really is, a logical way of thinking -- may distract us from more puzzling puzzles of finance.

A more serious drawback, in my opinion, is that the book uses a purely efficient markets / lognormal approach to finance. I, and others, are increasingly disillusioned by this type of approach. In fairness to the book and the author, this book gets a lot of mileage -- especially in the likelihood of loss puzzle chapter -- out of the traditional approach and the author can't be faulted for writing an accessible book for a wide audience using textbook finance rather than concepts that even the experienced trip over.

I only found one typo in this book (which is an impresively low number of errata for a techincal book). On page 119 (of the hardback edition), in chapter 6, where it says "4,050 estimates of correlation" is incorrect. Doing a very simple pairwise combination calculation the answer I came up with is 4,950. When you add my figure to the "100 estimates of volatitilty" one gets the "5,050 risk estimates" for the portfolio selection problem discussed in the book.

Overall, this is a great book that both novices and experts can get interesting knowledge out of. It's worth buying the book just for the last chapter, the introductory overview of finance, and the thoughtful glossary of quantitative finance terms. Although I doubt that the solutions the book offers for the six puzzles of finance will be entirely satisfactory, I enthusiastically endorse Mark Krtizman's goal of getting his readers to approach problems in finance and economics using the type of logical problem solving mindset that Martin Garnder has advocated in his writings.