Path Dependence, by J.T. Holley

January 22, 2007 |

 Yes, there are two paths you can go by, but in the long run, there's still time to change the road you're on and it makes me wonder.          –Led Zeppelin's Stairway to Heaven

I've since felt that those lyrics were trading lyrics. What a song that has such sweet convergences and divergences. Many references to the Mistress, and yes, what a capitalistic ending that she's actually "buying" the Stairway.

James Sogi comments:

From a dialogue this weekend:
A: It was nice we met 35 years ago. It was like fate.
Q: What if you had a little GPS unit that told you where in life you were?
A: Well it wouldn't matter because things would be fated and you would go where you would go no matter what.

Well, there is no fate, but there is causation and timing, so the question always arises, "When is the best time to jump in and the best time to jump out of a trade?" Or in navigation, "what is the best course to take and when?"

While reading "Cake Cutting Algorithms" this weekend by Robertson and Welsh, I discovered that there were a few main methods of dividing a cake or object of desire among two or more fairly, which is applicable to markets as well. There is the basic cut and choose. The other is the moving knife. Variations include multiple cuts and choices. The parties yell stop when they feel their fair share has come, but if they wait too long, someone else will yell stop before them, leaving the waiter with less. The net result is to evenly divide the pie based on each person's self interest, but the individual's goal is to get the most cake. There is the trimming variation where one party goes away happy with a piece and the remaining trims up the remains. As in life and in the markets, the question is, when is it not in the abstract, but in competition with others? The path dependency would be simple in isolation, i.e. deciding when to eat dinner by yourself is easy, but with a group of eight is very hard. Try to arrange a meeting with six people.

When is the best time to buy a falling market? If you wait too long, others jump in before you and get a better price. Jump in too soon and you get inspired to write a haiku. When is the best time to sell your holding? If you wait too long, you might lose your profits. If you make too many cuts, then you end up with crumbs not a slice (i.e. vig. eats you up). The approach of the Bayesians takes into account the subjective, which is pertinent. The question on paths still is the following: Is there a sweet spot in each cycle that will maximize the trade? We want to know where the the right spot and the right amount is, but it is always in competition with others. In terms of counting a minimum number of cuts to fairly divide a cake, it takes at least two cuts to divide a cake three ways, and six cuts to divide it five ways. No wonder there are so many trades in a market to determine a price at the end of the day. If you take the situation where unequal portions are to be divided, different considerations are at play since the pieces are not interchangeable. Also, consider taking the benefit of disagreements that sometimes allows for fair division. In the market, if there were no disagreements, there would be no trades! Only the disagreement in value allows a trade to be made. At the moment of the trade, each trader is happy with the transaction. Only subsequent paths will lead to happiness or a haiku or both.

Kim Zussman offers:

Isn't this directly related to regression to the mean?

A student gets 100 on the first exam, but the next three are 80's and 90's, i.e. the first result was "luck" (good day, coincidental study with questions, etc.), but over many trials he approaches his true position in rank. This is discussed often with kids in school to help with setbacks and to point out how long it takes to become truly accomplished.

Life is like that. There is little you can do about who your parents are, where you live, who you meet; there are so many paths. But if you are consistently honest, hard working, and you try to get along, on average and in the long run, you will wind up approximately at the correct level.

Victor Niederhoffer adds:

Occasionally, I think back and forth in my life and everything that happened since is related to that. For example, Gail Niederhoffer, was a very good impersonator and used to call up people when she was nine and pretend she was someone famous. She did this with a reporter four times, and told him that he should investigate those people at NCZ who forecast stock prices with an accountant. Graham loves reading the article. He had traded for the palindrome. After we were introduced, I started trading bonds and currencies and stocks for him, and one of my jobs was to vet quant things there. And one such quant through the palindrome came to my office to discuss his sure thing for options. Ha. The rest of the story … but if Zeck wasn't my tutor at Quincy House, I wouldn't have met Gail at his wedding, nor would I have met Susan nor would any of my subsequent seven been born. It's like that for everyone and for every trade. But for causation, it's a very tricky thing. What's unseen is what would have happened without those forks. If I hadn't ever sent Doc Bo to visit the brothels of the SE Asian country with the PHD from northwestern in key posts, I might be still playing tennis with the Palindrome, and having a home in the Hamptons. Path dependence in markets is a key factor to consider and deserves to be modeled and systematized.

Stefan Jovanovich adds:

Morgan, a devout Episcopalian, believed that character was fate and that one's character was shaped by the people one knew and worked with and their characters, and in turn, by the people they knew and worked with. In that regard, he seems to have been like the man who believed that the cosmos rested on the back of a giant turtle. When asked what the turtle stood on, his reply was "It's turtles all the way down." Morgan thought it was character all the way down. His religious belief, IMNSHO, was formed most by the faith of his first wife.





Speak your mind


Resources & Links