# U to the Tenth Power, by Victor Niederhoffer

March 13, 2010 |

It is interesting to speculate about what happens when the market is up 10 days in a row and then again at the open, since this has never happened before so one can't do it. This is a quandary for frequentists and perhaps mysteries of the Bacons, Dave and our readers could shed light, as I can't.

## Alston Mabry writes:

I'm looking at SPY closes, only one peak higher than this, back in Sep 1995, 12 up days in a row. lt's like standing on K2 and being able to see Everest from there. But maybe I'm just tossing coins…

I found a funny rule in Statistical Rules of Thumb, by Gerald van Belle, called the Rule of Threes: "Given no observed events in n trials, a 95% upper bound on the rate of occurrence is 3/n." There is one very simple demonstration based on the Poisson distribution.

The van Belle rule would say that in 1000 repetitions, it would be 19 to 1, that a decline would occur less than 300 occasions (i.e. a probability of 3/10), a truly precise but completely misleading answer in this case, especially when the underlying base estimate is 0.5. Sort of the way people talk about Microsoft's answer to a help question. However, in this case I predict a decline of 0.25, just to make the people waiting for a reversal crazy and even poorer.

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1. Nick Pribus on March 12, 2010 12:27 pm

This speculation supposes that the appropriate unit of time over which to conjecture is a “day” and not an hour or a minute or a week or a month. Or semi-biweekly as I used to hold management meeting every Monday. It also recalls my utter amazement in high school that learning after flipping a coin heads 10 times in a row, the odds of the next individual flip being heads is still 50%. As are the odds of being up or down today, all other things being equal.

My second grade daughter has memorized Pi to the 50th digit in honor of Pi day coming up Sunday (3/14) – at 1: 59AM the real enthusiasts like to celebrate. Among other useless but nevertheless fascinating tasks like speculating the next flip of the market coin.

So sure we are up 10 days in a row, nearly 50 points, but then I went to look at the last two years and found a couple individual days up or down more than that in both nominal and percentage terms, and a handful of days both up AND down by that much, and even, one or two hours shifting nearly than much.

So I am still hunting an elusive secret from this data that will assist me to turn the dollar in my pocket into two by tomorrow, or next week, or next month, or in time for the next semi bi weekly report to my lovely household investment committee.

2. Nick Sont on March 12, 2010 2:33 pm

Perhaps of more insight would be to understand the hazards that the “mountaineers” (traders) have to endure as prices climb towards the summit.

1) Falling rocks/ice = Profit-taking periods. Does the mountaineer stay the course or not?
2) Avalanches = Unexpected price drops from news/events. Stop-losses getting hit.
3) Crevasses & Fall from rocks = Gap downs.
4) Altitude sickness = Greed. Leverage-up of gains and disregard for risk.
5) Weather/Solar radiation = Market changing cycles.
6) Volcanic activity = Margin call. Speculator sees the “lava” coming down his/her way, but altitude sickness will entice more risk taking and double downs.

How can one develop a systematic approach to reach the summit and avoid all the listed hazards?

3. Richard E Barsom on March 13, 2010 4:58 pm

Just seems like it wants to keep going up. You like when you walk outside it smells like Baseball.

4. Paul Marino on March 13, 2010 7:00 pm

Tennis Royalty?

Sampras and Agassi joking around at charity game until Andre goes a little too far regarding Pete's miserly ways in tipping as he also spoke of in his recent book. I feel embarrassed for Nadal and Federer.