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Department of Physical Models

Physics offers insights into market interrelations.

Victor Niederhoffer: The Physics of the Inclined Plane

The physics of the inclined plane provide a useful template for thinking about certain aspects of markets. As will be recalled, the basic law for all machines is that force times distance of input equals force times distance of output. The force necessary to send an object up the hypotenuse of the inclined plane is less than that required to send it up the vertical part

Input force * AB = Output force * BC

It is much easier to climb up a mountain when the ramp angle cab is low than when it is high. Problem is that a long ramp would require much expense and difficulty. But we can divide the ramp AB into many segments and wrap each segment around the side of the market and make it much easier.

Such a construction reduces the amount of force required to be applied by the cyclist or locomotive which solves the same problem with supporting trestles.

The market in going from a low price A to B has a similar difficulty to surmount. A big continuous sharp rise causes much disruption. Politicians might be thrown out of office. Vacations and girlfriends might be discommoded. Jobs might be lost. The volume of noise of the plucking of the goose might be increased. Worse yet, customers might lose too much too quick to meet their margin calls. Without customers, without hope of future gains, without the baking and filling necessary to create tremendous transactions costs and frictional upkeep, the markets would not be able to support their various trophic levels.

Thus the ascents and descents in the market take a winding path through the mountain of prices similar to the winding inclined planes in a market. The pyramids were built this way and so are major market moves.

P.S. I apologize for violating the law that physics should be left to the physicists. With a professor of physics 10 feet away from me at all times, a genius teacher of physics 5 feet away from me, an MIT engineer, the ultimate PhD, 2 feet away from me, and a college roommate/best friend in the Inventors Hall of Fame for co-inventing eye laser surgery, and my own knowledge so rudimentary I apologize doubly. The above post is a work in process. I solicit improvements, sharpening and augmentations. And I will be fooling with kidsí games of levers and gears so I can come up with the next applications of machines to markets.

Stefan Lewellen comments: I can't help but think back to my physics/mechanics classes. The professor would always lecture (and then prove) that there are three basic ways to climb a steep inclined plane and overcome the force of gravity: 1) Brute force (large amounts of capital moving in the same direction)
2) Leverage (no analogy needed)
3) A combination of brute force and leverage
Depending on the slope of the plane and available resources, the optimal solution was usually #3. As the plane became steeper, increased leverage was necessary in order to reach the top.

Jim Sogi comments: The physics of the inclined plane seem to me to provide a useful template for thinking about certain aspects of markets.

The other simple market machine is a set of stairs. That is what the market seems to do a lot, stair steps up and stair steps down. There is a step of a flat bar across time, and then a steep riser traveling a vertical in proportion to the length of the tread. Just the right height for the population to walk up and down on, not too steep. Random would not seem to have such regular stair step patterns so consistently. Itís really a convenience for humans for orderly price action. No one does it consciously, but an architect of the market that had the blueprint could do well to watch for the stair steps to wealth (or the steps into poverty). Every main market level has is a landing to take a short rest on before ascending or descending the next flight.

Typically the treads are not level but have a back slope to them both up and down. September and October 30-minute bars were real nice stair steppers. I'm sure there is a formula to graph an ideal stair step indicator, but I've never seen it. Remember the Slinky trick of walking Slinky down the steps? That's a good description of price action as each coil coils it appears to stay still with only a coiling action, then the end flips over end over end down the next set of stairs. The main thing to figure out is are the stairs going up or down.

Phil McDonnell comments:

The inclined plane has always struck me as an apt analogy for the use of options in the market. For example Intel closed at 21.45 today. The Jan 22.50 call last traded at .85 and the Jan 25 call closed at .25. One interesting way to evaluate options is based on rate of ascent required to break even. That is where the incline plane analogy comes in.

There are 92 days left until the January expiration. In order for the Jan 22.50 call to payoff Intel must be above the 22.50 strike price by expiration and it must be above by enough to recoup the .85 paid for the option (ignoring vig). So the break even price is 23.35 within 92 days. This naturally corresponds to a rate of ascent for Intel stock of 2.07 cents per day. Following are the numbers:

Option Price Breakeven Stock Move Rate of Ascent Needed
Jan 22.50 c .85 23.35 1.90 2.07 cents per day
Jan 25 c .25 25.25 3.80 4.13 cents per day
INTC   21.45    


Notice that as the inclined plane becomes steeper the price of the option falls dramatically. This is solid confirmation by the marketplace of the Chair's assertion. As the slope increases it becomes increasingly difficult for the market to supply the necessary force to lift the stock. Higher rates of ascent are increasingly less probable so the market prices them lower (.25 vs. .85 in the example above).

In the above discussion nothing beyond elementary arithmetic is required. In particular the famous Black-Scholes is not even required. However for those who prefer an standard option model approach the corresponding rate of ascent is given by the simple formula:

Break even rate of ascent (for the stock) = theta / delta

This formula gives the daily rate of ascent required and will differ from the elementary formula given above on any given day. However over the full time frame of the option the average of the daily rates will converge to the simple calculation. In either case the market will offer lower prices on options which require improbable high rates of ascent.

Charles Pennington adds:

A surprising aspect of the Chair's post is that he suggests that the market eyes a target, the top of the mountain, but that it doesn't move there instantaneously, rather with fits and starts. Even with the fits and starts, though, on average it has to be going up in order to make progress toward the mountain top. So the recent direction, averaged over fits and starts, betrays the ultimate destination. So isn't the Chair's post an argument for some kind of Red Soxian t**** f******** approach? I suspect not! I hope the Chair can explain. His overall approach is interesting. In optics, if you know where light starts (A) and ends (B), then you can use the "principle of least time" to determine the pathway from A to B that is taken. The pathway is the one that gets the light from A to B fastest, in the least amount of time. What is the analogy for markets? Suppose we think we know where the market will be one year from now, perhaps by using the fed model. Leave aside that if we knew even this we'd be rich, and go a step further to ask what the the pathway will be from now to then. What determines this pathway? I think the chair is suggesting that the pathway chosen will be the one that leaves the most money in the pockets of brokers, market makers, spam-faxers of promotions for bulletin board stocks, and the like. Unfortunately I haven't figured out a way to code this criterion into my PC, but I will keep trying.

Jeremy offers:

If you drop an apple like Newton, it will fall straight to earth because of gravity
If you throw an apple it will make a trajectory
One apple, two kinds of physics
One market, an infinite variety to choose from
But don't tell Renaissance T

George Zachar was Inclined to respond:

NOT "two kinds of physics"!

Different forces acting on the same object, but obeying the same laws/principles/rules:

Force = Mass * Acceleration

Momentum = Mass * Velocity

Sorry for the brief post outside my core expertise of obsessing over 1)interest rates 2)tradesports.com and 3)the press, but there are precious few things I actually remember from high school physics, and this is the bulk of it.

J.T. switches topics:

Your descriptions and applications made me visualize the many mountain switchbacks I have hiked up. Each switchback is an inclined plane, and each advances you higher going up or lower going down, but they move in opposite directions and the scenery changes during ascent and descent. One wouldnít want to climb a mountain without them. The burn in oneís muscles would be similar to "goose feathers being plucked." Switchbacks are also preferable to a direct path down the mountain; rolling and tumbling may result as the loss of control and the muscular burn causes the knees to give out. Your post also brings to mind that it takes longer to go up a mountain than to come down. So true with markets as well.  

James Sogi: Contango and Backwardation/Inclined Planes

Yield curve theory fits in with the Honorable Chair's Inclined Plane theory. The slope of the curve is the angle of the incline plane that the market expects to have to push up or pulley up. Some yield curve models use only the initial angle to do the computations. Following up on E and Bud Conrad's discussions, the relationship of forward future contract prices to spot prices forms a yield curve, which provides information as Steve demonstrated today. The commodity and bond yield curves give information about the risk premium needed for speculators to assume risks. The angle shows the steepness of the plane of risk up which the speculator toils, or in the case of backwardation the height the speculator must lift the burden of risk until the end of the contract. "Contango" refers to commodity future forward prices being higher than spot. "Backwardation" refers to commodity future forward prices below spot. The forward price must converge to the spot price, like a bond due to the "convenience yield" John Maynard Keynes proposed in the early 1930s The Theory of Normal Backwardation. Keynes believed that hedgers and speculators in the futures markets are both risk-adverse. Keynes argued that speculators are also risk-adverse in the commodity futures markets. He argued that since natural hedgers owned commodities and sold futures to hedge their price risk, this left speculators as the net owners of the same futures contracts and the ultimate bearers of the price risk in the spot market. According to this view, the convenience yield represented the risk premium demanded by speculators for accepting this price risk. Dr. John Hull. in Futures, Options and Other Derivatives, explains: "Convenience yield reflects the market's expectations concerning the future availability of the commodity. The greater the possibility that shortages will occur during the life of the futures contract, the higher the convenience yield. Convenience yields are like implied volatilities with stock options. They can be estimated- imputed from today's observed market pricing of futures contracts; but, as an expectations-based variable, they can never be known ex-ante . And like the term structure of interest rates, a term structure of convenience yields can be estimated by looking at the pricing of commodity futures with differing expiration dates. http://tinyurl.com/52c5z

Commodity futures prices can serve as a mechanism for price discovery either for the present price or for determining expected future prices. There is information in the commodity yield or price curve. Given how all the markets are correlated with oil now, this yield curve merits study. Corrections always welcomed.