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Unformatted text preview: Doomed to repeat it? November 2008 Christopher C. Finger email@example.com We can track the continuing deterioration of the fi- nancial markets by how far back we go to find com- parable events: we started with the bursting of the technology bubble in 2000, then moved to the LTCM crisis of 1998, to the Scandinavian banking crisis of the early 1990s, to the recession of the 1970s and finally to the Great Depression of the 1930s. It has kept raining, and a ten-year flood turned into a twenty-year flood and finally into a one hundred-year flood. Accompanying the economic arguments that go with these comparisons have been citations of the recent market movements in the context of those over the last hundred years. But what about risk? With all of the criticisms of models we have heard recently, we first need to establish that we can mean- ingfully quantify risk in the first place. Once we have done this, then we can start to ask questions about history. How volatile have markets actually gotten? How long do we have to wait, typically, for this level of volatility to abate? It may have stopped raining, but how long will it take the floodwaters to recede? Volatility matters We begin with an examination of the Dow Jones Industrial Average (DJIA). Though by no means a broad indicator of the market (as it contains only 30 US equities), it is attractive to examine for two rea- sons: first, it is the index most utilized by the popular press as representing the market; second, it has been calculated, mostly uninterrupted, for over one hun- dred years, and as such gives us the opportunity for a long historical perspective. The simplest risk models rely on three basic tenets: volatility is relevant; volatility changes; and changes in volatility are (at least somewhat) predictable. The framework for the model is that the return to come is the product of the volatility, which we forecast using the information available at the time, and the resid- ual , which we do not know, but which comes from a defined statistical distribution. Intuitively, each days return can be thought of as an n-sigma event, where sigma is the standard deviation, or volatility, that we have forecast, and n is the size of the residual. We work with a volatility forecast that is a simple weighted average of prior days squared returns, with the weighting scheme from one of our standard risk models. 1 Importantly, the volatility we consider on any given day is a forecast that a risk manager could have made (had the techniques been invented yet) at the time. We plot the DJIA along with its volatility in Figure 1. Here and for the remainder of this ar- ticle, we will refer to volatility in annualized terms....
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- Fall '09