Daily Speculations

The Web Site of Victor Niederhoffer & Laurel Kenner

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Knot Theory and Markets by Victor Niederhoffer

Nobody asked me but the moves in the Dollar/Yen back and forth around the magic 110 level remind me of the turns in one of the advanced knots with many crossings, loops, and half hitches. Perhaps a 10-crossing knot. The mathematical theory of knots is applied all over physics (in such things as Feynman Diagrams and particle physics), chemistry, the structure of DNA, genetic engineering (the double helix structure of DNA can be modeled as an incredibly complex series of knots), number theory, statistical mechanics (see Vaughan Jones) as well as all the things we know about like fishing, sailing, logging, braiding, construction, and tying things on vehicles. But as far as I know, no one has applied it to stock market forecasting. (I do see some references on Google among the 7,000 items with "knots and stock market" to chaos theory. However, to not pretend to be something I am not, I must admit that I am probably the worst person in world to explore Knot Theory as my kids can do knots 100 times faster and more complex than I could ever conceive them. So I ask, I request, for others to explore this subject and see if any testable hypotheses or interesting insights can be developed from it.

J. T.  Responds:

When I was in high school my grandmother, aka "Nannie", retired from GE. She gave all of the grandchildren (12) each shares of GE. I was around 15 or 16 at the time. I immediately pleaded to my mother that GE was nothing more than a "dinosaur" of a company and that I would be better served selling it and buying Rock Climbing equipment. I won out with my mom and purchased two ropes, a harness, shoes, carabiners and webbing and began to learn the ways of climbing that my friends and I began to explore. Knots was something that came with the territory. In a nutshell two that I still remember and know because of their many uses is the "figure eight" and the single and double "Fisherman's" knots. The Figure 8 is to me probably the most important because it is easy to tie, easy to undo and also puts the least amount of stress on the rope. It is used mostly for its loop which allows clipping into and also is a good knot to tie into something such as a harness. The fisherman's knot is good to join to ends of separate ropes or to join the ends of same. Its kissing cousin is the double fisherman's which is almost impossible to untie once lots of pressure is asserted.

Now call me crazy but looking at the prices of the Yen over the days given you can mentally tie (starting on 4/19) the Figure 8 complete with the loop. Now as for that "Hitch Knot" you mentioned, you definitely don't want to tie that climbing! That is one knot that easily comes out, only good for horses, goats, and asses.

James Sogi on Knot Theory:

In sailing the simplest knot with the fewest turns that holds is best. It can be turned and undone the fastest, such as the bowline. One's life can depend on a simple bend of the line. More than 2 turns or crossings usually results in a knot that can't be undone after tensioning the line. In some circumstances this is the desired end, such as a braid bent in a permanent loop or two lines braided together for strength. The more turns, the greater the strength, and the harder to undo. Also the difference between an easily unbent square knot, or a tangled granny knot, ( which every child learning to to tie his shoe knows), is the lay of the bend....which way did the line cross first, over or under.

In Knot Theory, knots are classified by the number of crossings. Once more than two turns are bent, will the trading knot be harder to undo, in other words, is a range created? This year the most profitable trades have been the range trades. (Having said that, it will probably now breakout to change the cycles)

Mathematicians use + and - to count the crossings and the crossings up or down.  This same designation could be used to mark the number and direction of crossing across the pivot or round which seems similar to binomial distribution statistics.

One way of distinguishing knots is to use tricolors. Perhaps coloring the chart with the crossings across pivot or round with different colors might help with timing trade. Say on third color enter on assumption that third crossing with render knot hard to undo and result in further crossing, and extended range rather than breakout. Test needed.

Going a bit further afield to origami, one cannot fold a piece of paper more than seven times. No matter how big or thin the paper is. Try it. The energy stored up in the creases is too great: an entropy phenomenon. I theorize that the market, once it crosses itself more than seven time is building up quite a bit of energy and will be looking to break out.

6 crossings in the April/May quote on Chair's post. Looks like the yen continuous future crossed 9100 7 times in the last month.

One last point...Knot Theory appears to be a type of topology math and deals with three or more dimensions. This goes back to my idea that a three or more dimensional math or chart may reveal more than the flatlander sees now in x and y.

Its a knotty problem! The answer will "not" be in the dictionary!

James Sogi on Gordian Knots

As S&P wraps back and forth around the 1120 level for about the 20th time today , the following seemed apropos:

One day, according to ancient Greek legend, a poor peasant named Gordius arrived with his wife in a public square of Phrygia in an ox cart. As chance would have it, so the legend continues, an oracle had previously informed the populace that their future king would come into town riding in a wagon. Seeing Gordius, therefore, the people made him king. In gratitude, Gordius dedicated his ox cart to Zeus, tying it up with a highly intricate knot - - the Gordian knot. Another oracle -- or maybe the same one, the legend is not specific, but oracles are plentiful in Greek mythology -- foretold that the person who untied the knot would rule all of Asia.

The problem of untying the Gordian knot resisted all attempted solutions until the year 333 B.C., when Alexander the Great -- not known for his lack of ambition when it came to ruling Asia -- cut through it with a sword. "Cheat!" you might cry. And although you might have been unwise to have pointed it out in Alexander's presence, his method did seem to go against the spirit of the problem. Surely, the challenge was to solve the puzzle solely by manipulating the knot, not by cutting it.

Gordius used a bit of deception in the knot by splicing the ends together making it impossible to untie. Surely whoever figures out how to untie the market Gordian knot will be king of Asia. The answer seems to be: do as Al did and think outside the box to solve the problem. As long as S&P wraps back and forth across 1120, to mix metaphors, there is a knot to make your broker rich while the tiny mycelium breaks off tiny crumbs of the great oak, against the good advice not to get ground down by vig.

Scissors, Knots, and The Sage by George Criparacos

One has to note the easiness with which euro gained 150 pips against the dollar, during Greenspan's comments in Congress. As I was trying to flee from my long dollar position, trying to find in the dark the second hole to escape, the Congressman asks:

So you are saying there is a connection between the deficit and interest rates?
Wow! I think to myself. a meal for a lifetime in a Congressional hearing.
Yes. He replies.
Here we go, I thought, he is going to ask what the fed thinks about the other side of the scissors.
But no. Unfortunately, the congressman is not a speculator. The subject changes.
Lucky to find this morning that the yen is doing another 8 knot tie. It was my second hole out.

Victor Niederhoffer Responds:

If I live to be a hundred I will never forget how often I have been victimized by the Asians, all of whom can run rings around me in the areas of deception and intelligence.  Have I mentioned recently that they gave me and mine and my fund a death blow in 1997?  Thus having been burned once (nay, scarred for life with no skin left, permanent chest pain, and morbid, hypo-walletness) I eschew the Asian markets. Thus I was unable to participate in the dollar/yen's overnight advance against the yen (now 109.90 from 109.00 and the magic pole of 110.00 reasonably imminent) even though one has a predilection to be against the Sage at all times in all things. But regrettably one has noted that in his study of knots (may I recommend the clove hitch on a bight as a theoretical knot for bondage), the consecutive crossings are over and under and one has played the dollar for a crossing from above a pole to below at this very moment, thereby not having the second hole that Mr. Crisp alludes to and suffering the indignity of losing money at the expense of two old lions (Doc G. and the Sage) as they try to exclude younger lions from their share of resources and progeny), at this very moment.