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Department of Physical Models

Physics offers insights into market interrelations.

1/29/2005
The S&P as a Wedge, by Victor Niederhoffer

A wedge is a machine that may be thought of as an inclined plane standing on its narrow end. It works like an inclined plane to reduce the amount of force required to travel a given distance, by multiplying the distance that it travels through an object.

The inclined plane works because it splits the force of gravity into a horizontal and a vertical component. It's only the sloping part parallel to the plane that has to be overcome. The wedge moves through an object and separates the output force into these same two components which varies directly with the length of the sloping side and inversely with the angle it makes the object it's slicing through.

While I knew that the wedge was used for joining, splitting, and cutting in such common tools as the fork, knife, saw blade, chisel, file and ax, I was surprised to learn that almost all power tools Ė such as the lathe, miller, shaper, drill and chain saw -- receive their mechanical advantage from the wedge.

The wide range of applications led me to an initial study of the influence of one market in holding, splitting and cutting through two other markets. The force applied to the wedge corresponds to the magnitude of the move in one market, like stocks, and its market value And I envisioned the cutting angle it makes with two markets, such as bonds and the dollar, as the coterminous move in the other two markets. I envisioned the output force as the subsequent move in the two markets.

I thought it best to start with three markets commonly working with and against each other: stocks, bonds and the euro. For simplification I divided the moves in each market into three equal categories: large decline, medium move, large rise.

Letís start with coterminous one-day moves -- a useful descriptive base, but like most things fed to us, useless for prediction unless youíre a triples trader or related risk-reducer destined to be ground into oblivion.

The results for one-day moves in S&P over the past five years are as follows. The number of coterminous moves the same day is listed and then the expected move the next day for S&P is given in parentheses.

MarketMoveMarketMoveMarketMove# of ObsS&P Point Chg
Next Day
S&P-Bond-Euro-56-4
S&P-Bond-Euro+412
S&P-Bond+Euro-442
S&P+Bond+Euro+1150.25
S&P+Bond-Euro-940.0
S&P+-Bond-Euro+334
S&P+Bond+Euro-573
S&P+Bond+Euro+34-2

For example, there were 56 occasions when in the same single day, the S&P, bonds and the euro each declined. The average S&P move the next day was a 4-point decline.

Several interesting findings emerge from this study of the wedging effect of the S&P on itself as it cuts through the bonds and euro. To start with, when the S&P and bonds decline, it is about 3 to 2 that the euro will decline in that period. However, when the S&P declines and bonds rise, it is almost 3 to 1 that the euro will have risen during that period. Thus, when the S&P declines, the euro follows the bonds.

When the S&P rises, and bonds decline, it's 3 to 1 that the euro will have declined. But when S&P and bonds both rise, itís less than 2 to 1 that the euro will have declined.

Thus, when the S&P rises, the euro tends to decline in either case but more so when the bonds have declined.

The expectations the next day speak for themselves, with the moves the day after those rare occurrences when all three market decline -- something that happens less than once a month -- being something that one should always watch out for.

NB: When the euro goes from 120 to 125, that is an increase in the value of the euro against the dollar.

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