# Powerful: Carlson

Very loosely speaking, and in line with some of the analogies to physics given in this book, structured finance could be viewed as the “quantization of corporate finance”. The authors succingtly give a hint to this viewpoint when they write in chapter 2 that structured finance is an “ensemble of micro-processes” that allow one to describe a corporation as a “sum of discrete packets of quantifiable value”. The latter can then be “bundled” and then sold, and the proceeds used to purchase “new discrete packets of quantifiable value.” In this context the authors drive home the point that this is dynamic process, far removed from conventional accounting and mere ink blots on a balance sheet. Bringing about these processes takes creative work and ingenuity, coupled with an understanding of legal reasoning and regulation, and requiring in-depth practical understanding on the part of analysts charged with placing value on the resulting deals.

A great deal of space in the book in fact is devoted to just what constitutes “value”, and some fairly esoteric mathematics and philosophical musings are utilized to assist in the characterization of value. Readers without the background in these areas may find the book rough going at times, and may find it difficult to appreciate the ramifications of what the authors are doing. With such a background though readers will find many interesting (and sometimes amusing) discussions in this lengthy book. All this being said, readers should not expect though that the entire book is devoted to mathematical techniques and philosophical dialog. This is readily apparent in chapter five, where “subjective” considerations such as “credit intuition” and the ability to identify what is “just enough” collateral backing for adequate return are emphasized.

The authors’ emphasis on the analytics behind structured finance includes some highly interesting discussions on various mathematical techniques and concepts. Some of these include:

1. Darboux integration. The authors should probably say that the empty set should have a measure of zero, rather than the empty set, since the measures they consider are real-valued, and not set-valued (although measures can of course be set-valued in general). In addition, they should say that the measure of the ‘union’ of a countable number of elements is equal to the sum of the measures of each element when they state the requirement of countable additivity. Also, the authors need some kind of discussion as to why the weaker notion of countable ‘subadditivity’ will not suffice for insuring that the set of assets behind investments are measurable quantities. Lastly, why not use the ordinary Riemann integral instead of the Darboux integral in this context? Some explanation as to the choice of the latter would have been helpful, that adds to their comment that the Darboux sum is a “generalization and extension of the Riemann sum.” They are equivalent of course in terms of the calculated values obtained by each, but the Darboux integral is frequently advertised as being “easier to define” than the Riemann integral.

2. “Back of the envelope” calculations, which are usually viewed as kind of a “first crack” at problems, are given an organized treatment in this book, almost to the point of formality. They are to be distinguished from the corporate “indirect” measure of payment quality, which relies on proxy data, by utilizing data directly from the structure of the transaction. Most interesting in this discussion is the authors’ allusion (perhaps unknowingly) to ‘Bayesian belief networks’, when they write about belief systems able to correct themselves using feedback from data.

3. Cumulative loss curves. The reviewer can attest to their utility, at least in the context of mortgage analytics, and the difficulty in accounting for recoveries. The authors give useful hints on how to construct loss curves, and how to interpret their geometry (the inflection point etc). Along these lines the reviewer sees no a priori reason why growth curves such as the ‘double logistic curve’ could not be utilized here, even though no real example of growth behavior based on such a curve is available. Can the geometry of such growth curves as the double logistic curve be ruled out or are there examples of loss growth where the losses follow the “flat” part of such a curve? Such behavior in losses would fly against the S-shaped paradigm of “accelerate, reach a maximum, decelerate, taper off” expoused in this book and many others on credit analytics. The double logistic curve or more generally curves with multiple periods of degeneracy (“flat periods”), might find a better home in accounting for recoveries, although the reviewer knows no example where such has been done.

4. Not surprisingly, an entire chapter is devoted to Monte Carlo simulation. Monte Carlo simulation is the bread-and-butter of the entire world of modeling, not just financial, and every analyst is expected to be an expert in its use and the fundamentals behind it. In addition, modelers must be aware of the abuses of Monte Carlo simulation as well as its limitations. Some of these limitations are brought out by the authors, but they sell (rightfully) Monte Carlo simulation as being one of the “basic weapons” of financial modeling.

5. Prepayment modeling, also of great interest in mortgage modeling, is discussed by the authors predominantly for the case of automobile loans and home equity loans. The former are not “sensitive to interest rates” while the latter are, and this entails of course that the subject of prepayment modeling have an intersection with that of the (vast) field of interest rate modeling. The reviewer can attest to the non-trivial nature of modeling home-equity payment behavior and the risk analysis of home equity loans, due in part to the way in which such loans “sit behind” first liens in event of mortgage default. The most important part of the discussion on prepayment modeling though definitely has to do with the proper definition of ‘duration’. This term has probably caused more confusion to newcomers to financial modeling, due fully to its everyday use as a measure of time. Noticeably missing, but not at all fatal to their discussion, is any discussion on competing risks in prepayment modeling, and the use of copulas, the use of the latter of which has been blamed for the extreme financial events beginning in 2007. Copulas are discussed in the book in the context of general data analysis but not in-depth.

6. Dimension theory, in particular, that of spaces of non-integer dimension, finds its place in the book in a discussion of Hausdorff dimension. For the reviewer this part of the book was difficult to fathom, not because the notion of Hausdorff dimension is difficult to formulate mathematically but rather the manner in which it is motivated by the authors. This is not to say that their discussion is incorrect, but rather that it is hard to connect it with what is found in the standard literature on fractal geometry. In addition, anyone who has tried to apply fractal geometry to practical modeling knows how difficult it is to compute the Hausdorff dimension, due in part to the inability in a numerical computation to distinguish between open and closed sets. The discussion on the connection of Hausdorff dimension with correlation in revolving portfolios is fascinating however, and deserves scrutiny, particularly from a philosophical standpoint.

As alluded to above, the book is not just about mathematical techniques. In fact, discussions of a purely philosophical nature take place at various places, and some of these can be thought provoking at times, and somewhat strange at others. Some pages are devoted for example to the philosopher Martin Heidegger, which is quite surprising given the practical tone of the book and the fact that Heidegger’s philosophy is sometimes blamed as being a precursor to the deconstructionist school that has irritated many in the scientific profession and labeled in financial circles as “anti-capitalist”. By the same token, the ancient philosopher Aristotle is given top-billing also in the book. The discussion is fascinating and of extreme importance, touching as it does on how the Aristotelian notion of ‘phronesis’ gives a “grounding” for risk management and decision-making in general.

In general the combination of mathematical techniques, philosophical musings, historical anecdotes, and the practical emphasis makes this book very unusual and at the same time very powerful. For these reasons it might also make it somewhat inaccessible to typical analysts, who are usually under pressure to derive results, and may not have time to fully appreciate the meaning behind what they are doing. The book therefore could serve well those educators who are responsible for training future financial analysts, ensuring that they have a thorough grounding in the ethics, practice, and limitations of financial modeling.

Note: This book was read and studied between June 2011 and October 2011.

**Lee Carlson, Mathematician
**