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

Subject: Re: forwarded message from William F. Hummel

Date: Fri, 14 Aug 1998 23:10:28 -0700

John Conover writes: > > To illustrate, I will build a very simplified model of an equity > market, that has a growth that is dependent on T-Bill rates-ie., can > be manipulated through monetary policy. An investment portfolio > strategy will be optimized, and verified through simulation. Finally, > the equity market model will be compared with the New York Stock > Exchange Composite. The idea being that if the optimizations work on > the model, and the NYSE behaves like the model, the optimizations > would be valid for the NYSE. > As an interesting little aside, when I used tsinvestsim(1) and tsinvest(1) to simulate the equity exchange market, I also let tsinvest run a wagering strategy to pick the 10 best stocks from the 300 in the exchange and invest in them. The way the -d1 option works on tsinvest is that it maintains a complete set of dynamic statistics on every stock in the exchange. It then assembles a dynamic portfolio, based on the stocks which are instantaneously growing the fastest, and then optimizes and balances the portfolio, ie., it does portfolio management as described previously. Here is what its portfolio did over the 100,000 day simulation: avg = 0.000535 rms = 0.007314 Giving: P = ((0.000535/0.007314) + 1) / 2 = 0.5365737 and: Q = 11.537930152E21 or: G^100000 = 11.537930152E21 which is: G = 1.000508 Did pretty well, huh? Not really. Here's why. Computing G', rms', avg', and P' from the equations for n = 10: avg' = 0.00053361 rms' = 0.007304861 P' = 0.5365243 and: G' = 1.000507 exactly what the tsinvest program did with a lot of sweat. Note that it could have done just as well by randomly picking 10 stocks at the beginning of the simulation, and sticking with them to the end. Or, it could have done just as well letting a chimpanzee pick the socks, or a random number generator, or a dart at the WSJ, etc. (Just like the real NYSE.) Of interest, the value of the 300 stocks at the end of the simulation varied between a loss of 50X, and a gain of 10E18X, with the mode and mean at about where G said they should be. The distribution of the value of the stocks is a Gaussian distribution at the end of the simulation. So, why didn't tsinvest buy into the high rollers at the end of the simulation? It did. Each and every one of them. So, why didn't it make more money? Because if you look at the wagering strategy used, half of the time it will be a buy low sell high strategy, and the remaining half of the time it will be a buy high sell low strategy, perfectly offsetting each other. John BTW, the -d1 option to tsinvest is a close approximation to what graphologists, (ie., those using the efficient market hypothesis with P/E ratios,) do. There are 5 other options which can get very aggressive with portfolio management. It turns out that it is very difficult to make money off of the exchange model described previously, above what it will give anyone and everyone, using any method. Why? There is no strategic advantage of one stock over the other-they are all the same. And what happens next, at every step of the simulation, is independent from the entire history of the simulation. The simulation is a good "zoo" case to test any strategy you want to apply to the market, and is frequently used for that by the programmed traders where it is used to verify strategies. Making lots'a money off of this model is the "holy grail" of programmed trading. If you slant the growth values in the simulation (ie., make them all different-like a real exchange,) tsinvest will go after the hot stocks with a vengeance, frequently overflowing the coprocessor before the 100,000 day end of the simulation-the -d2 and -d4 options are what most use in this scenario. The program has done a 10X portfolio growth in 18 months, but this was done by exploiting certain characteristics of the NASDAQ that were available only in 1995 through 1996. It was, also, a high risk operation-the program uses adaptive computation, and could go unstable. The option that was used has been removed from the public version at http://www.johncon.com/ntropix/archive/tsinvest.tar.gz. -- John Conover, john@email.johncon.com, http://www.johncon.com/

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