From: John Conover <firstname.lastname@example.org>
Subject: Re: script that does the same thing as tsinvest?
Date: 14 Dec 2000 20:52:53 -0000
And, the same techniques of measuring how well the executive suite is operating can be used to forecast how long a company will last, too. Since a company's stock price has fractal dynamics, the price can go on excursions that vary from its fundamental value by orders of magnitude, for literally years. Suppose we want to invest in a stock of a new company that looks like it is really taking off. The question is whether the company is a durable investment, or not, (i.e., has some durable fundamental value, or is a fad-like a company producing pet rocks.) The question is, how long would we have to measure, (i.e., what's the data set size requirements,) so that we would have a good probability, or confidence, in investing in a durable company. Using the tsshannoneffective program, with the -c option, and the values of a "typical" company on the American exchanges, (avg = 0.000949, rms = 0.0308058436,) we would have to have 8971 trading days of data, (about 35 years of 255 trading days per year.) What this says is that you can not tell whether a company is a good long term investment, or not, without 35 years of daily data. Meaning that a company can last, on average, 35 years, on luck alone, (or, by serendipity, half the companies will last less than 35 years, half more-if everything is assumed to be a fad; or, in other words, in 35 years, half the companies will fail.) And, what's the empiricals? Of those companies that were listed on the US stock exchanges in 1965, about half are gone. John BTW, in case you are curious as to what the tsshannoneffective program does, it calculates the error function, erf. The probability of a "bubble" in a stock's price continuing past n many days is erf (1 / sqrt (n)), which is about 1 / sqrt (n) for n >> 1. So, there are two "forces" that "push" against each other in the durability of a company, the Shannon Entropy, (which is the likelihood that a stock's price will move up, i.e., the company's value to the society will increase,) and the chances that the Shannon Entropy is a "bubble," (i.e., the likelihood that the Shannon Entropy will crash.) Since both are probabilities, they can be multiplied together, to get the combined chance of a company lasting at least n many days. The Shannon Entropy, P, for the "typical" stock is: P = ((avg / rms) + 1) / 2 = ((0.000949 / 0.027238) + 1) / 2 = 0.517420515 What value, when multiplied by that, is 0.5, (i.e., solving for the number of days where the chances are 50%/50%,)? Iterating the number of days in the tsshannoneffective program gives: john@john:~ 675% tsshannoneffective -c 0.000949 0.027238 8971 For P = (sqrt (avg) + 1) / 2: P = 0.515403 Pcomp = 0.502670 For P = (rms + 1) / 2: P = 0.513619 Pcomp = 0.506885 For P = (avg / rms + 1) / 2: P = 0.517421 Pcomp = 0.499989 or, 8,971 trading days. Note that our assumption that "everything is assumed to be a fad [or bubble]" seems justified by the empiricals. If you think about it, its not as far fetched as it seems. The "bubble" for flint tools, vacuum tubes, pet rocks, and dot-coms, has long passed-even though some were essential technologies. But what about the essential inelastic industrial markets, (like table salt, healthcare, etc.,) which will be purchased, regardless of cost? What the empericals say is that the companies that deal in the inelastic markets are subject to competitive pressures, too, (which manifests itself in capitalization "bubbles.") (As an example, consider table salt. Although it is essential for life-and will demand any price-a company that delivers it better-using better technology, distribution, cost structure, or packaging-will have an advantage, for a while; only to be out done by a competitor, e.g., the company's value was a "bubble," even though the unit shipments of salt remained constant.) John Conover writes: > As kind of an aside, it is fairly easy to show that most stocks on the > American exchanges have optimal growth in value, and have optimal > risk for investors. > > The rms, (root mean square of a stock's price fluctuations,) is the > volatility, which is, also, the risk of investing in the stock. > > The avg, (average of the stock's price fluctuations,) is the gain in > value of a stock, which is what one gets for taking the risk and > investing in the stock. > > It can be shown, (using information-theoretic methodologies,) that > optimal, (meaning maximum,) growth in the price of a stock occurs when > avg = rms^2. If rms > sqrt (avg), the growth will be less, and if avg > < rms^2 it will be less, too. > > And where do stocks run on the American exchanges? > > Using the -r option to tsinvest, the "typical" stock's avg is > 0.000949, (I just averaged them up, for all stocks.) The average rms > for all stocks, (again, just averaging them all up,) is 0.027238. > > What is the optimal rms for an avg of 0.000949? Taking the square root > of the avg, the optimal rms = 0.0308058436, which is within 10% of > perfection. > > What does this mean? > > It means, that on the average, the typical American company's > executive suites are mitigating the risk of doing business almost > perfectly, and growing the company's market capitalization almost > perfectly, (it is best to err for avg to be ever so slightly greater > than the square root of rms-there is never any reason for rms > sqrt > (avg), which is the hallmark signature of a naive executive suite-it > is the signature of throwing caution to the wind.) > > John > > BTW, throwing caution to the wind can be a valid strategy in the short > run, sometimes with huge run ups in market capitalization-for a > while. Unfortunately, an executive suite can not remain a fugitive > from the laws of probability forever, and the inevitable eventually > happens when the humbling experience of a stock price crash occurs. > > The dot-com companies are a notable example. > > John Conover writes: > > > > Note that the model used is very close to compound interest in a > > savings account, with variable rates-you just don't know what the > > interest rate, (which can be negative,) will be tomorrow, or the next > > day. > > > > If there are no fluctuations, (i.e., avg = rms,) then: > > > > P = ((avg / rms) + 1) / 2 = 1 > > > > (i.e., the likelihood of an up movement is 100%, or a certainty,) and: > > > > G = ((1 + rms)^P) * ((1 - rms)^(1 - P)) = 1 + avg > > > > which is the formula for compound interest, i.e., after n many days, > > the value of the investment would be (1 + avg)^n. > > > > John > > > > BTW, note that the interpretation of the root mean square of the > > fluctuations, rms, is slightly different than that of Black-Scholes. > > > > The Black-Scholes model uses the rms to be the square root of the sum > > of the square of the fluctuations minus the average, avg, (i.e., the > > variance.) This is the risk of investing, and if it is zero, (i.e., > > avg = rms,) there is zero risk. This method of computing rms is the > > "standard" from probability theory, and larger rms means more risk. > > > > The method of computing rms in tsinvest is not to subtract the avg > > from the square of each fluctuation since tsinvest is based on finding > > the probability of an up movement, i.e., the Shannon Entropy. The > > value avg is the offset of the median of the fluctuations, which are > > assumed to have a normal distribution, with a standard deviation of > > rms. > > > > Although different methods, in reality, they are very close to being > > the same since rms >> avg by several orders of magnitude for equity > > prices. > > > > John Conover writes: > > > > > > The numerical methods used in tsinvest are quite straight forward, and > > > most can be done in a spread sheet. > > > > > > There is, also, a set of 60 some programs that can be used for general > > > fractal analysis at http://www.johncon.com/ndustrix/utilities.html, or > > > they can be downloaded as a tape archive from > > > http://www.johncon.com/ndustrix/archive/fractal.tar.gz. > > > > > > The tsinvest sources were, largely, cut-and-stick from the sources to > > > these programs. > > > > > > A possible scenario to automatically pick stocks might be: > > > > > > To find the marginal increments, (i.e., the fluctuations,) of a > > > stock's price, use the tsfraction program. > > > > > > To find the average increase in value, use the tsavg program. > > > > > > To find the risk of the investing in a stock, (i.e., the root mean > > > square of the fluctuations,) use the tsrms program. > > > > > > which is the two values used by tsinvest. > > > > > > So, if sprice is the name of a file containing the price of a stock > > > over time: > > > > > > tsfraction sprice | tsavg -p > > > > > > would print the average increase in value of the stock, avg, and: > > > > > > tsfraction sprice | tsrms -p > > > > > > would print the risk of investing in the stock, rms. > > > > > > Then, the Shannon Entropy, (or Shannon Probability, i.e., the > > > likelihood of an up movement,) P, would be: > > > > > > P = ((avg / rms) + 1) / 2 > > > > > . > > . > > . > > > To calculate the gain, G, in value of a stock, use the tsgain program: > > > > > > tsgain -a avg -r rms > > > > > > which, as a stock picker, bigger values are better. All it does is > > > solve the equation: > > > > > > G = ((1 + rms)^P) * ((1 - rms)^(1 - P)) > > -- John Conover, email@example.com, http://www.johncon.com/