# Re: forwarded message from William F. Hummel

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/

```