From: John Conover <john@email.johncon.com>
Subject: Re: Optimal Stock Market Strategy Re: SGP versus Switching Campaigns; wisest strategy
Date: 5 May 1999 00:32:07 -0000
Archimedes Plutonium writes:
> In article <M_zX2.627$IE2.11532@news15.ispnews.com>
> conover@rahul.net writes:
>
> > Hi Archimedes. Since the entire history of the daily closes for all
> > stocks in the US for the century is available on CD, why not use that
> > data to simulate a diverse portfolio vs. a portfolio with a two stocks
> > in it and see which portfolio wins?
> >
> > That would settle the question.
>
> John, you are not a mathematician or scientist at heart or mind, are
> you. For if you were, you would immediately see the flaw in your above.
> I am talking about the Optimal Strategy of Stock Market with an
> investor possessing skill. Your ditty above is okay if you threw darts
> at the Wall Street J. for 10 picks compared to 2 picks.
> But, if you had a skilled stock market player, such as myself, 2
> picks will in most cases beat 10 picks.
>
Being as though you told me what stocks you picked, I know what you
were looking for in a stock-and these kinds of stocks have unique
characteristics that can be measured. As a lucky guess, I suspected
the following algorithm would pick the same stocks you picked:
For each day:
For each stock in the US exchanges:
Make a list of the count of consecutive up movements for
the stock:
Make a frequency histogram of the list for the stock:
Make a log-log plot of the histogram for the stock:
Buy the stocks with the steepest negative slope.
Although far from a production ready algorithm, running it on the
history of the US exchanges since 1980 through the present, results in
it picking almost exactly the same stocks you mentioned, (you also
mentioned the 20 years I used for the analysis.)
For two stocks, letting the investment in each stock ride, the
average portfolio gain per year was 38%.
However, for 10 stocks, and shuffling money around in the portfolio
such that there was an equal investment in each stock at all times,
the gain was 57% per year.
So, although you did well over the last 20 years-as most investors
have-you could have done better, with much less risk exposure.
Granted, such a simple algorithm did not address the more involved
issues of price arbitrage, transaction costs, taxes, nor dividend
re-investment, and assumed perfect market liquidity. So the numbers
are not representative of what could be attained in practice.
But it does show that a 2 stock portfolio is not optimum, since there
is a very simple algorithm that performs better, ie., there is an
exception to the premiss.
John
BTW, the algorithm does very poorly when confronted with markets that
are non-speculative, (it is designed to exploit speculative
markets-what it indirectly measures is the leptokurtotic distribution
of the marginal revenues for the stocks through skews in the positive
run lengths; the two quantities are related mathematically.) For
example, running it on the first third of the century results in
phenomenal gains through mid 1929, (during which time the market was
highly speculative.) Then, by late 1931, it lost all of its gains, and
its original investment, too-it was destitute. Note that if the
paradigm of the EMH were true over the past 20 years, this algorithm
would have done very poorly, ie., the EMT is not a good model-at least
for the last 20 years.
--
John Conover, john@email.johncon.com, http://www.johncon.com/