This excellent book is focused on the demise of Long-Term Capital Management (LTCM) - a hedge fund which imploded in 1998. I must confess a certain nostalgia for the pre-2008 financial world in which a "crisis" could be fairly readily resolved. The LTCM mess appears quaintly insignificant in light of what we have lived through since but it has important lessons for us even now. This is a book which every investor should take the time to read. It is a wonderful antidote to the arrogance which can be engendered through a few successful trades.

Dunbar takes us through the application of mathematics to trading and options valuation resulting in the Nobel Prize winning Black-Scholes-Merton formula for calculating option values. One criticism is that he may spend a bit too much time on the personal backgrounds of the actors and not quite enough on the mathematics but this is a quibble. I cannot go into detail in an article of this length but it is important to note that any data dependent model or formula is just that - dependent on data. And, unfortunately, all of the data we have is about the past while the thing we really care about is the future. What models do - in very simplistic terms - is to analyze past data concerning the amount of daily fluctuation in prices to calculate the probability of future fluctuations. Well established statistical tools such as standard deviations and normal distributions are used to map out what the past data tells us about the likelihood of future price movements of various sizes. As a result, models based upon past data are, in a real sense, merely a manifestation of the oldest argument that fathers and sons have had since the dawn of time - will the future really be similar to the past?

It didn't take long for the invisible hand to lead math whizzes to apply their insights in an effort to "do well by doing good" - in this case, to make money by removing "inefficiencies" from the relative pricing of various securities and derivatives. Dunbar takes us through these efforts - culminating in LTCM and its thunderous demise. It is interesting that, over and over again, the mathematical models tended to produce nasty surprises for their users. The book provides a good explanation of these episodes - although, again, more detail would have been helpful.

**Strike One** - The initial effort to apply the formula went bad quickly. Scholes and Merton were employed by a brokerage house and, by applying the formula, discovered that National General new warrants were substantially underpriced. They loaded up and then, in Dunbar's words, "disaster struck." National General was acquired and the terms were bad for warrant holders. The warrants expired worthless and the mathematicians scratched their heads. It doesn't really take a rocket scientist to figure out that, when looking at options and warrants, the past is not always prologue to the future. There are many companies facing future events (takeovers, drug approvals, lawsuits, accounting scandals) that can have enormous impacts on valuation. Past data may not tell us about future volatility and may lead us to underestimate the potential for a large upside or a large downside.

**Strike Two -** On the other hand, if one looks at the market as a whole, it is possible that large movements in the price of a single stock will be swamped by action in other stocks so that - like a crowd of shoppers - the entire market may be subject to mathematical prediction and that past fluctuations in market prices may allow us to predict the probability of future volatility. At the outset, this appears to be a reasonable proposition. At the very time, that some companies experience bad news, others will experience good news. Equity mutual funds selling one stock will quickly have to buy another in order to stay fully invested. Market makers will jump in to create liquidity if the market falls and buy at bargain prices. The availability of Index Options set the stage for the phenomenon of "portfolio insurance" - a mechanism involving options and futures which protected investors from losses due to a decline in the Index. Sadly, this experiment blew up during the infamous 1987 Crash in which the market lost 20.5 per cent of its value in one day (in today's market this would be a 3000 plus decline in the Dow or a 350 point decline in the S&P 500). According to prevailing mathematical assumptions, an event of this kind would not be expected to happen even once in the 3 billion year plus life of the Universe. But it happened. Dunbar could go into a bit more detail about why it happened but two key insights emerge. The first is that stock market price changes may not be governed by normal distributions but, as some mathematicians were asserting by 1987, may be subject to "wild randomness" or even Chaos Theory and, therefore, more likely to experience extreme increases or decreases in price than would be suggested by conventional statistical analysis. The second is that the very emergence of mathematical analysis and portfolio insurance itself may have changed the markets and made past data irrelevant to predictions of future price action. LOR, the portfolio insurance company, had to immediately move aggressively into the futures and options markets and this may have set off a wave of selling that exacerbated the decline. The Brady Commission put part of the blame (but certainly not all of it) on this phenomenon. Perhaps, we have a kind of Heisenberg Uncertainty Principle at work here; once we measure something, analyze it, and use that analysis to trade, we have forever changed the very thing we purported to measure.

**Strike Three -** This brings us to LTCM, at its zenith an envied repository of wisdom, market savvy, mathematical wizardry, and enviable profitability - also, alas, more than a pinch of arrogance. In fact, in December 1997, LTCM forced investors to take back $2.7 billion of capital because LTCM concluded it was an unnecessary cushion and its return would enable LTCM to produce a higher return on the remaining, now smaller capital total. LTCM tended to make paired or hedged trades and used enormous amounts of leverage. The reasoning was that, if one trade went bad, the paired trade would automatically increase in value so that there really wasn't any risk. This set up self-sufficient "money machines" for which capital was not really necessary in order to limit risk because risk was limited by the mechanism of the machine itself.

In layman's terms, if Bookie A is favoring Dallas to beat the Giants by 14 points and Bookie B is favoring Dallas to beat the Giants by 7 points, I can bet $5000 on the Giants with Bookie A and $5000 on Dallas with Bookie B. If Dallas beats the Giants by more than 14 points, I win with Bookie B and lose with Bookie A. If Dallas loses or wins by less than 7 points, I win with Bookie A and lose with Bookie B. My worst case is a break even and I can win both bets if Dallas beats the Giants by more than 7 but less than 14 points. So there is no way I can lose. Or is there? There are, sadly, at least two risks I have ignored. One is **Counterparty Risk** - the risk that the bookie with whom I have a winning bet goes bankrupt and doesn't pay off, leaving me to pay off the other bookie with my own money. The other is **Collateral Risk** - I have placed these bets on credit. If both bookies detect that my finances are shaky, they may both demand collateral to support my position so that they can be sure they will be paid if I lose.

Dunbar's book does not provide the kind of detail I would like but it appears that LTCM made several bad bets that turned out not to be properly hedged. The most notable was a bet on Russian bonds. It was hedged with a complicated currency forward contract. Unfortunately, just as the bonds defaulted, the Russian government took action making the forward contract unenforceable. There were other bad trades and, suddenly, massive collateral calls on all the "bookie bets" which were supposedly riskless because they offset one another. It did not take long for the notion of "systemic risk" to occur to various players as the hot potato of leverage got tossed around an ever more panicky throng of investment professionals. This fire drill has now become all too familiar. The New York Fed sat everyone down, a rescue fund was assembled and LTCM was wound up and wound down.

What is depressing is that the entire scenario - complete with excessive leverage, arrogant financiers, and panicky collateral calls - was repeated almost exactly ten years later. The Panic of 2008 - centered around mortgage backed securities - will probably go down as what should be called a Heisenberg Uncertainty Error. Elaborate mathematical models were developed of real estate markets and mortgage defaults and recovery rates based upon decades of data. These models revealed that mortgages are really not very risky so that money could be made by making progressively riskier loans and leveraged up by the use of tranches embodying varying levels of risk. Down payments could be reduced, appraisals could be dispensed with, and credit scores disregarded because risk could be mathematically determined to be limited. What the models ignored was that the very changes in the mortgage market generated by the aggressive use of the models to ease lending rules created an entirely new real estate market and an entirely new mortgage market which rendered data concerning past default rates and recovery rates totally irrelevant. By analyzing past data and aggressively applying that analysis, the financial community made the data no longer useful.

There is only so much you can do in one book. I wish Dunbar had suggested some solutions to these dilemmas but I am not sure that we are at the point at which any are available. I hope we are not damned to relive the same depressing scenario every ten years or so but I am not optimistic. This is a very important book for investors to read. As I have said before, be careful out there.