## Wednesday, January 4, 2017

### Stocks and k-states, part IV

I re-ran the analysis presented here (using a different random sample of 50 companies from the NYSE) for a longer period 1990-2010 and the distribution of stock market "k-states" (see previous link) is much more stable than the cumulative returns ‒ more evidence for the "statistical equilibrium" of k-states.

Here are the k-states:

Except for the Great Recession (2088-2009), the distribution is stable. And here are the cumulative returns alone:

In both figures, the blue distribution is more intended to guide the eye than a particular measure ‒ I eyeballed the parameters of a stable distribution to look a bit like the k-state distribution and scaled the parameters for the cumulative return space to give an "equivalent" distribution over the different domain.

1. In the dividend discount model or discounted cash flow/earnings models of stock valuation, book value does not determine the current price of a security. One would assume there must be a dividend/earnings model of information transfer stock valuation as well, no? After all, book value can be subjective, and many finance types have questioned whether book value even means anything for software companies, e.g.

1. Gregor Semieniuk did something similar with profit rates so I imagine there are many possible ways to frame it -- some that would work better than others.

The model above doesn't really use "book value" -- that was one way to bring up the idea of k-states (in terms of market cap and book value) but the main idea is that there is some fundamental variable X that grows at some rate ξ so that the market cap M grows at some rate μ = k ξ ... and the price p grows at some rate (k - 1) ξ.

In the graph above (and the ones like it) X is NGDP and ξ is the NGDP growth rate. Basically, I took the "book value" to grow proportionally to the economy. The graph above uses cumulative return to measure the growth rate μ for each company so that μ/ξ = k (for each company).

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Also, try to avoid the use of dollar signs as they interfere with my setup of mathjax. I left it set up that way because I think this is funny for an economics blog. You can use € or £ instead.