Comments on: Yesterday Was a Four Standard Deviation Event

By: Aaron Street

Aaron Street — Wed, 15 Oct 2008 03:18:10 +0000

Kyle, by your calculations, what has been the standard deviation of the past two weeks?

It’s got to be close to 1:1,000,000,000,000 at this point.

It’s still not time to panic, but the market is definitely not random.

By: John

John — Mon, 13 Oct 2008 01:49:50 +0000

Anyone wish to update their comments? We’re now experiencing fat tail events daily………thoughts??

By: Hanks Weekly Hangouts #50 (September 20, 2008) | MiB Smarter Money

Hanks Weekly Hangouts #50 (September 20, 2008) | MiB Smarter Money — Sat, 20 Sep 2008 08:02:49 +0000

[...] 6. AmateurAssetAllocator tells us that Yesterday Was a Four Standard Deviation Event [...]

By: Kyle

Kyle — Fri, 19 Sep 2008 18:59:42 +0000

Extremely unlikely events happen every day. That they happened in close sequence does not imply it’s not random. Similarly, that daily market returns are not strictly normally distributed (as the above simplistic explanation assumes) does not significantly alter the results. Even taking the flared tails into account, the stated probabilities are relatively close. For your hypothesis to be valid, you’d have to assume causation where there’s no evidence of any being present, which is a logical fallacy of the highest order.

By: Luke

Luke — Fri, 19 Sep 2008 17:10:47 +0000

Perhaps in absolute value terms it passed today…? FTSE100 had a 8.4 standard deviation event today! Aaron Street is perfectly correct – you fail statistics… perhap “The (Mis)behaviour of Markets” by B. Mandelbrot might help.

By: Andy

Andy — Tue, 16 Sep 2008 16:45:37 +0000

this too, shall pass….Good words for troubled times. The only question when?

By: Aaron Street

Aaron Street — Tue, 16 Sep 2008 15:31:30 +0000

Of course the market could react to an AIG failure – or some other major event that might occur in the near future – by going up or down. I’ll concede that market reactions aren’t perfectly predictable.

But your analysis implies that they are perfectly random, which is also not the case.

I’m arguing that the market has never moved by four standard deviations up or down on a day when there weren’t acute crises/successes.

My point is not that people need to panic, just that you should concede that major market declines are more likely to occur in the face of the acute issues of this season, than they are at a time when there are no underlying major financial crises.

By: Kyle

Kyle — Tue, 16 Sep 2008 14:29:27 +0000

True, the conclusion depends on the data points being normally distributed. Historically, daily market returns HAVE been normally distributed even in the face of acute events (like the 1987 crash or 9/11 or yesterday’s failures). Company failures actually aren’t all that rare, so yesterday’s events weren’t exactly abnormal. Furthermore, daily returns are usually if not always completely divorced of the reality of the underlying market fundamentals. Even if there were more bailouts or large bank failures, there’s no reason to believe the market would drop by four standard deviations again in response. It could quite possibly move higher.

By: Aaron Street

Aaron Street — Tue, 16 Sep 2008 13:58:59 +0000

Your math seems sound, but your conclusion from the data has a serious flaw.

By saying that a 4.71% decline only has a 0.0006% chance of happening on a day, assumes that these data points are randomly distributed along a curve. However, our current situation – and yesterday’s decline – weren’t random events along a distribution curve, they were symptoms of acute events (bank failures, bailouts, etc.) that are much more than 0.0006% likely to happen again today and tomorrow.

Put another way, your analysis works if you were to throw a dart at a calendar: then there would be a 0.0006% chance that the date the dart hit would have had a 4.71% decline.

The odds of a 4.71% decline today, tomorrow, or anytime in the near future until these underlying financial problems are solved is much, much greater than your analysis implies.

My two cents.