But Iceberg Risk is more than a novel; indeed, it is really two books in one: each chapter covers the intuition of its subtopic first, through the clever device of Devlin and Conway's saga within Megabucks Investment Bank; and then delves more directly into the mathematics. Of the math, the reader is encouraged to explore "about as much or as little as you want", a feature I especially appreciated given my low-calorie mathematical diet. And, just as the novel part is an entertaining read, the quantitative part is a useful summary of the mechanics of portfolio management theory.
Part I of Iceberg Risk covers the statistics of probability, covariance and correlation, Pascal's triangles and Bernoulli variables, IID versus non-IID estimates of tail risk, Tchebyshev's inequality, the Kuhn-Tucker conditions for the solution to a Lagrangean optimization, mixtures of discrete and continuous probability measures, De Finetti's theorem, the problems with VaR and the ubiquitous (in finance) normality assumption, and even computer sex (read the book!). Osband gives us a quick introduction to matrix math (though it is even more sparse than the helpful section in Markowitz' 1959 book) before concluding the first half of the book with conditional multivariate normality.
Part II of Iceberg Risk offers a unique and thoughtful approach to overcoming the deficiencies of standard risk assumptions for portfolio management. In this part of the book Osband covers convex and nonconvex utility, regret aversion, choice theory, the appraisal ratio of Treynor-Black and even delves into the Bayesian approach to statistics. Partition functions are introduced as a method of combining conditional return distributions with multi-regime risk aversion. Without resorting to Monte Carlo simulation techniques, Osband proposes a numerical approach to generating risk estimates, since there is no closed-form equation available to solve the issue. He even shows how to account for options and other nonlinear payoff assets.
Osband's approach to risk management is fresh and appealing. It would be worthwhile reading for risk managers and portfolio managers. One aspect I liked very much about his writing style is that the characters represent very distinct human traits, much like those of another of my favorite authors, Ayn Rand. For example, we are introduced to the concept of regret aversion when Conway meets Regretta:
"He spun around to see a raven-haired woman dressed in black. She was beautiful, but with the saddest eyes Conway had ever seen. 'Pardon me for eavesdropping,' she said, 'But if Dr. Know-nothing can't help you, maybe I can.' 'Go away, Misery Girl,' snapped Devlin. 'We don't need you.' 'Oh, I think you do,' she said... 'Now here's what I think you need to do. First measure every outcome in terms of its gross percentage return... Second, square that return and take the negative inverse. Third, form the probability-weighted average of the various negative inverses. Fourth, pick the portfolio that generates the highest probability-weighted average. Am I being clear?' Devlin and Conway were blown away. 'She does math,' mumbled Devlin to himself."
Osband makes the observation that "The mainstream seems less interested in managing risk than the appearance of risk." Readers of Osband's Iceberg Risk might just become a bit less mainstream for the reading.
If we use the model for a normal distribution, a five-standard deviation credit loss event should only happen once in every 7,000 years, but in the market place, we see this happen once or twice in a decade. A book that talks about hidden risk and the deficienies of VAR in capturing credit risk is another very entertaining read by Tavakoli called "Credit Derivatives" (Second Edition).