From: John Conover <john@email.johncon.com>

Subject: Re: forwarded message from William F. Hummel

Date: Fri, 14 Aug 1998 23:47:30 -0700

John Conover writes: > > or about an 11% growth per year, which is reasonable in comparison > with the 14% predicted, above, (depending on one's point of view, of > course.) > So, could we improve our model? Maybe. If you look at the model, there are too many stocks. Why? Because, for the NYSE: avg = 0.00437 rms = 0.00874 We can compute what rms' is by: rms = 0.00874 = rms' / sqrt (n) or, n = 5.720824, which is about 6. But how can we justify that when there are over 3,000 stocks in the NYSE composite. Easy, a little work on the SEC corporate database at http://www.sec.gov/edgarhp.htm, looking at the form 10Q's for the NYSE, we find that the NYSE is dominated by about a half a dozen companies. (Look at GM's market valuation which is directly reflected in the NYSE Composite index.) So, the average stock would be: avg = 0.00437 rms = 0.02090454 giving: P = 0.5104523 And, recalculating the characteristics of the exchange: P' = ((sqrt (6) * (0.000437 / 0.02090454)) + 1) / 2 = 0.5256027 avg' = 0.000437 rms' = 0.02090454 / sqrt (6) = 0.008534243 G' = 1.000401 The simulation with these values gives: avg = 0.000452 rms = 0.008590 P = 0.5263097 G = 1.000415 which is in very close agreement with the metrics of the NYSE. What these numbers mean is that, for an average stock on the NYSE, there is a 2% volatility, (ie., for 68.3% of the time, the daily movements of the stock will be less than +/- 2% of its value,) and that over the course of a calendar year, the average stock's maximum value divided by its minimum value will be a factor of 2. Some will be less for a short time, some more, but on the average, these numbers will represent the stock's movement. Also, any portfolio's volatility will be greater than the volatility of the index, and its growth will be less than the growth of the index-at least in the long run. So, bottom line, you can flee to quality and buy T-Bills, but, on average, your portfolio will only grow half as fast, in the long run, as if you bought equities. But if you buy a few equities, your portfolio value will vary by +/- 50% over a year, in getting a long term growth that is somewhat less than twice what T-Bills give you. The magic solution, (actually, optimal,) would be to have 10 stocks, (but not many more,) comprising 40% of your portfolio value, the remainder of your portfolio being T-Bills-at least in our simple equity exchange model. That would make your portfolio grow the maximum possible, with the minimum volatility and risk. This optimal solution maximizes your gain, while, simultaneously, minimizing your risk exposure. You get the best of both worlds. John BTW, if you talk to an institutional fund manager, or a really good broker, he knows these numbers. There were known, intuitively, for many decades. One of the triumphs of applying information-theoretic means to the equity markets were formal proofs of such things. The proofs were offered between 1956 and 1989. See the tsinvest(1) manual page for particulars and bibliography. -- John Conover, john@email.johncon.com, http://www.johncon.com/

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