Kent Osband explores both the philosophical underpinnings of financial risk management and its statistical rigor in Pandora's Risk: Uncertainty at the Core of Finance (Columbia Business School Publishing, 2011). To accommodate those who want to pursue ideas without constantly tripping over formulas, he has divided the book into two parts: The text proper and a 100-page, math-laden appendix. Naturally, I will focus on the first part of the book.
Osband, an economist by training who spent some time in academia and more in the financial world-- most recently at Fortress before striking out on his own, is a challenging thinker. And that by self-description. He expects his readers to reject some of his ideas because, as he readily admits, "Some of what I'm saying is surely wrong; I just don't know which some." (p. 6) Theories about uncertainty are sometimes uncertain themselves.
Although Osband writes at some length about such concepts as money, debt, credit ratings, and regulatory oversight, these sometimes provocative discussions are intended to illustrate and advance his central arguments about the nature of financial markets. First, finance is characterized by uncertainty: "Finance deals, in effect, with dice that are not fair, might get switched between rolls, and are subject to freak interference. The objectively measurable risk, if there is one, gets shrouded with subjective uncertainty." (p. 11) Second, "markets measure the beliefs about risk rather than risk itself. And risk changes often enough that beliefs rarely have time to converge on the truth." As Osband contends, "Twentieth-century finance theory focused too much on risk, too little on changes in risk, and hardly at all on beliefs about changing risk." (p. 90) Third, markets are learning machines.
Market risk can never be tamed.
Our predictors are bound to falter because of tiny doubts or errors that mount over time. … Just as the change in mean is proportional to the variance, and the change in variance is proportional to the skewness, so too the change in skewness is proportional to the kurtosis. All these measures are known as cumulants. In general, each cumulant changes proportionally to the cumulant of next higher order, which gets progressively harder to identify and control. (p. 88)
In physics, the cumulant hierarchy is essential to understanding turbulence. Osband claims to be the first to apply it to beliefs and dubs it Pandora's Equation.
VaR, we all know by now, is not the be-all and end-all of risk management tools. In fact, the author argues, "using standard VaR to tame financial risk is like using cigarette filters to tame cancer risk." (p. 119) Curiously, for someone who is so completely at home in the world of statistics, Osband reaches out to discretionary traders to find a better way of estimating risk.
The answer lies in trading channels and the adjusted trading range (the vertical distance between the two channel lines). In general, Osband shows, "range-based estimators of volatility are far more precise than ordinary standard deviation estimators." (p. 134) In particular, "the width of the current day's trading channel can, in principle, estimate volatility better than ten days of closing prices, even when the regime stays the same." (p. 136)
Osband asks a lot of his readers: they "ought to have a sound grounding in economic history, finance theory, and statistics. They should be interested in economic policy. They should enjoy mathematical modeling. They should love thinking outside the box." (p. 6) Even for me, who is deficient on almost all fronts except perhaps the last, Pandora's Risk was decidedly a worthwhile read. Just think how much better it would be for the qualified, or maybe I should say, "quant"-ified reader.