The Money Formula: Dodgy Finance, Pseudo Science, and How Mathematicians Took Over the Markets

Written by quants who are appropriately cynical about their whole profession, this is an excellent book (for readers familiar with basic mathematical probability and willing to think as they read) on quantitative finance in general, the circumstances surrounding the global financial crisis of 2007–2008 in particular, and with concrete suggestions for improving the profession's responsibility. The first half (Chapters 1-5) provides an engaging albeit somewhat standard background and history: the random walk/Brownian motion model, the efficient market hypothesis (EMH) and the observation that stock prices changes are more variable than the former predicts; fundamental analysis and technical analysis; "modern portfolio theory", the idea there is an optimal portfolio, based on assumptions for numerical values of future mean growth and correlations, and noting that future correlations are hard to predict; "value at risk" and the difficulty in assessing extreme events. They give a good explanation of the background and meaning of the Black-Scholes pricing model and basic "vanilla" options via dynamic hedging and mention more exotic options. They describe the explosive growth in CDOs and CFSs in the run-up to 2007-8. The second half can be summarized as miscellaneous commentary on what the quants have done: here are a few examples. There are intrinsic difficulties in applying analogs of Black-Scholes to options (such as interest rates or credit risk) that are not explicitly traded and therefore cannot be directly dynamically hedged. The copula method for guessing correlations is bizarrely arbitrary and unjustifiable. There are no plausible "standard toy models" for interest rates or volatility. They give an informative classification of quant jobs (junior quant; model validation; quant developer; risk management; research quant; front office; quant trader). The most distinctive features and their central critiques are in Chapters 9 and 10. They give cute and memorable examples of the many misaligned incentives within the industry, and discuss systemic risks exemplified by the financial crisis of 2007–2008. In an Epilogue they give detailed suggestions for making the profession more socially responsible (partly along the the "skin in the game" theme emphasized by Taleb). I won't try to summarize their analysis here, but it should all be required reading for anyone wishing to comment knowledgeably on the quant world. In terms of what it says, this book is excellent, so my minor criticisms concern what it doesn't say. Some comments as a professional mathematician: They do not distinguish clearly between the specific Brownian motion model and the general martingale model; the latter is what the EMH predicts. In chapter 7 it is observed that estimates of future volatility change weekly, but so they should: the issue in testing a model is whether they fluctuate more than a martingale should. Their rhetorical question "why do abstract fields such as measure theory have a stranglehold on [finance models]?" has a partial answer I give at the start of a graduate course. Measure theory is the operating system (OS) underlying probability theory. By analogy, you can learn to use your iPad or iPhone apps without knowing the device has an OS, but if you want to do novel developments then you need to have an interface with the OS. The presumption that Math Olympiad champions would do more socially beneficial work ("mathematician cures cancer!???") in other fields suggests the authors have never spent an hour in a roomful of such people. They make a big deal of attacking the EMH, pointing out correctly that many people have profited by finding and exploiting different small deviations from EMH predictions. But (in principle and surely also in practice) if these are indeed different deviations then their overall effect should be stabilizing. Their exposition tends to conflate this with the "herd behavior" of everyone ignoring a risk or planning to get out before the day of reckoning, the background to the 2007-8 crisis.

I think it should be taught in all schools

Paul Wilmott is a researcher and quantitative finance consultant who’s worked as a fund manager and academic while David Orrell is an applied mathematician and founder of a scientific consultancy. In this book, they look at the theories and formulae that underpin the quantitative finance models used by hedge funds and other financial institutions and explain why they’re so flawed in a challenging but interesting read told in a breezy style. There’s a lot of maths and statistics in the early chapters of the book, which anyone with a maths/economics/engineering/econometrics background will probably find quite basic but if – like me – you worked really hard for that GCSE grade C, it’s quite challenging to follow and I found myself having to go over the explanations several times in order to follow the basic precepts behind modelling and the history of quantitative finance and the development of financial derivatives. However, once I got it I was able to follow the main thrust of their arguments about fundamental mistakes in the assumptions underlying the area and how there’s effectively a mathematical sleight of hand and jiggery pokery to make it seem as though the models are effective. The latter chapters, which look at how financial modelling puts the financial markets at risk. The chapters on the financial crash are particularly interesting and as someone with a regulatory background, the refusal of regulatory authorities to get to grips with this (in particular the failure of a governmental panel that one of the authors was invited to participate in) is absolutely chilling and a portent of bad things to come. All in all, if you have any interest in finance then I think you should check out this book because it’s a great summary of the subject and the extensive bibliography gives you suggestions for further reading on the subject.

Having studied economics I slowly started understandingvthat most of the things studied in uni just dont work in teal life. An eye ooener of the real world of finance.

Great book. I have been involved in the business aspects of electronic trading and HFT for about 15 years, and prior to that a regulator for about 5. While there is not a lot that is new, it is presented in a way that just hits home, for me at least. The foundations of finance are presented essentially as science and the simplifying assumptions are glossed over. I think the best part of the book, and indeed one of its constant themes, is that the *regime* where the model is valid is everything, instead of the "footnote" that it is treated as. Having both an undergraduate and graduate degree in Finance from some recognized institutions, I can attest, at least when I went to school, that the regime of validity of financial models gets short shrift, and that is overstating the point. The issues around regulators and regulation are understated based upon my first hand experience. They are a substantial catalyst to the problems.