Gadzooks.
Well played.
dlpicket Wrote: ------------------------------------------------------- > Isn’t the whole point of Black Swan that seemingly > impossible events do occur? > > Why then would he advocate going to mostly > treasuries? Seems like the default of the US > government is exactly the type of “impossible” > event he’s talking about. Yeah, I was thinking about that too… the ultimate black swan. I guess he figures that everyone will be screwed there, and so one is no better or worse off than everyone else.
I am interested in learning more about fractals etc. at this point I am not quite up to speed. yahoo exports daily and monthly data for the dow into excel. excel data analysis spits out a histogram in a few seconds. Here is a google doc of excel histograms for both daily and monthly Dow returns. http://spreadsheets.google.com/ccc?key=pvJzg_pK9jdYYvzcsvFiQGg&hl=en where are these “fat tails” I keep hearing about?
Take a Ln() of daily values Graph them
bchadwick Wrote: ------------------------------------------------------- > My problem is that Taleb doesn’t have many > suggestions to solving the problem. Basically > they amount to: > > 1) Stay out of the game. Translation: have > mostly treasuries. > 2) Buy some deep OTM options to spice things up. > Translation: buy some deep OTM options. > That, in a nutshell, sums up the entire book.
CFAchief Wrote: ------------------------------------------------------- > Take a Ln() of daily values > Graph them I had a few minutes over lunch to look at this again. Per your request, I took Ln(Dt/Dt-1) with daily values graphed them and… got similar looking results. avg, sd, and count functions gave the following outputs: number of observations: 1 sd - 1895 below -1 sd, 17259 between -1 and +1, and 943 above +1 sd 2 sd - 494 below, 19192 between, and 411 above 3 sd - 192 below, 19756 between, and 149 above 4 sd - 86 below, 19944 between, and 67 above 5 sd - 41 below, 20026 between, and 30 above So… 0.3% of the observations were outside of 5 sd, 0.7 outside 4 sd, 1.7% outside 3 sd, and 4.5% outside 2 sd. …normal would have what 4.4% outside 2 sd? I guess outside 4 and 5 sd is a little “plump” but there is also 86% between -1 and +1 sd? normal there is 68.2%?
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mwvt9 Wrote: ------------------------------------------------------- > . I agree.
So you had 71 observations outside 5 sds - that’s 0.35% If it was normal, you’d expect 0.00006% of observations to be outside 5 sds. So that’s 6100 times more observations than you’d expect in that region - which seems pretty fat tailed to me. 5 sd events should almost never happen in normally distributed world. “Fat tailed” distributions also have “peaked” middles which are evident here. Wikipedia has a decent entry on it: http://en.wikipedia.org/wiki/Kurtosis
Yeah, that’s the challenge. 0.35% sounds “pretty small,” so you figure “there’s not much difference from normal.” But 0.00006% is “incredibly small” If you end up assuming or optimizing things so that the chance of these outlying events is 6000x less than their real chance, then your chance of getting whacked by a large event is actually 6000 times too greater than you think, and your portfolio is not sufficiently protected, particularly on the downside. And if you are trading daily and have 0.35%, you can expect to be whacked by something like that about once a year on average, as opposed to once in the entire length of recorded history.
And if you want to learn something to help with your CFA studies, fit a basic ARCH model to the data and see how much better it fits.
Gotcha. The more I thought about it the more I recognized the scale. Initially, I thought “I guess the dow’s daily results outside 4 and 5 standard deviations were fat but the observations outside 3 sd was 4.5% which is about what normal would suggest.” I see how that is a poor first impression. Just because the probability outside 3 sd is similar, well, that clearly doesn’t mean that the probability of extreme outliers is similarly low. So thank you for helping me gain some clarity. As noted, the results clearly imply lepto. The peak, 86% within 1 sd, only 10% falling between 1 and 2 sd and then the fat tails past 4 and 5 sd. If an hour with excel leads to that conclusion, why did I ever accept normally distributed expectations?
JoeyDVivre Wrote: ------------------------------------------------------- > And if you want to learn something to help with > your CFA studies, fit a basic ARCH model to the > data and see how much better it fits. could be fun. The notion of volatility clustering has to play neatly into the variance of the error term as a function of the t-1 error term variance.
I actually sat by Prof Taleb this week before he spoke at a conference I was at. bchadwick explained his strategy well-80% bills, rest in OTM options. I found him to be not too friendly in person but delivered a good presentation. And to those quoting bell curve statistics and deviations, the point he was trying to make is very simply that “you dont know what you dont know”, and that modelling doesnt take into account these events. Interesting guy overall, I dont know that I walked out enamored with him but he has been able to swing a career out of telling people somethings that should be obvious…