Market Thermodynamics

[Dave M]

I had the thought of using thermodynamics to model the market. Has this been done?

The 1st Law of Thermo goes something like dQ=PdV+VdP. It says the change in total energy of a gas has two components, one each relating to change in pressure and volume. The market is kind of like a gas. If we let Q be the total $$ in the market, P be the average price per share and V be the total number (volume) of shares, then the equation still makes sense, i.e, the change in total wealth is the average price times the change in share-count plus the total shares times the change in price.

If prices are stable (dP=0) then dQ=PdV and is proportional to the number of new shares bought, dv. If dV=0, then dQ=VdP and is equal to the fixed number of shares outstanding times the change in price.

Since P and V are related, we need another equation relating them to one another, an "Equation of State" for the stock market, the function P=f(V).

Without that, we can still speculate. Q changes as money enters or leaves the market. The total share-count increases with increasing Q, and usually P increases, too, that virtuous cycle where we all keep buying and the price keeps rising, there being profits on all sides. If we are selling, dQ<0 and both shares and prices decline.

But here I ran up against a question I could not answer: What happens when we sell a share? Who buys it from us? Conversely, when we buy a share, who sells it to us? Since we are dealing with indices in the TSP rather than corporate shares, this simplifies the question but it is still out there -- is there a finite number of shares in the C-fund, for example? Are shares created out of nothing? Or, is there a fixed number of shares?

HELP?

Dave

 

[ChemEng]

The first law of thermodynamics only applies to closed systems. I wonder if the influx of money on a daily basis is small enough to assume it away. Even if not, its a cool way to approach the dynamics. Its much more interesting than the actual Thermo class that beat it in my head.

 

[Dave M]

Kinetic Theory

Now think of each individual stock as a molecule of gas. Its state (price) changes randomly. The sum over all N stocks available gives the net change in state (dQ) of the market.

This is like summing the momenta of the air molecules in this room. If heat (money) is added to the system, the total momentum M increases and we measure it as a rise in temperature (price).

Can prices rise in an adiabatic process? (dQ=0)

Is the gas confined or does it operate as does the free air?

Dave

 

[rokid]

DaveM,

It has been a long time for me since chemistry and physics. However, it is widely held that the underlying model of stock prices is Brownian motion.

http://www.nber.org/reporter/summer00/goetzmann.html

 

[Dave M]

Thanks!

I will study that paper and try to review some references.

I worked some last night with pencil and paper. In the end I obtained a circular result, that simply re-stated my assumptions. This was discouraging. Moreover, in order to make any sense at all, it was necessary to treat the subject in the largest possible coordinate, total market capitalization, which is of limited utility in TSP-land. So most of the above is rubbish.

And yet the idea still seems to have validity -- daily prices change may randomly but if money flows into the market, the average price ought to rise.

So here is another question: Is total market capitalization tracked? Can we say what has happened to the value of all stocks held, over time? How about capital flows? This seems to be the vital statistic.

Dave

Edit: Here is a quote from today by another poster, himself quoting the WSJ, that seems relevant -- "One method is to buy back shares from the market. Buybacks often result in higher share prices, as the company enters the market as a buyer, and the supply of available shares shrinks."

 

[SkyPilot]

I tend towards Newtonian physics as it relates to markets...

what goes up,

well,

you know...

 

[rokid]

The "total market" usually means:

1. S&P 500
2. Wilshire 5000 - S&P 500 plus cap weighted completion index, S Fund.
3. Wilshire 5000 plus bonds, i.e. F Fund
4. Wilshire 5000 plus MS EAFE, i.e. I Fund

Technically, the total market is defined as all invest-able assets, i.e. global stocks, bonds, real estate, commodities, and human capital. However, that's not really a definition that can be dealt with quantitatively.

It seems you should be able to discover the total capitalization for 1, 2, 3, or 4 over the last 30 years without too much trouble.

Finally, based on my reading, your assumption that stock prices rise based on the amount money injected into the market is correct - straight forward microeconomics. The recent tech bubble is one example, i.e. very high P/Es unrelated to the underlying, intrinsic value of the stocks. In addition, there is now some concern that the price of small value stocks is being bid up by the relatively recent discovery (Fama/French 3 factor model) that they have significantly outperformed the market and other market segments (large growth, large value, and small growth) over the last 80 years. If so, the future returns for small value could suffer.