Re: portfolio management

From: John Conover <john@email.johncon.com>
Subject: Re: portfolio management
Date: Sat, 19 Sep 1998 18:08:41 -0700

```John Conover writes:
>
> But if you could time the market, you could do better, right? Yes, you
> certainly could-if you could time the market, that is. Unfortunately,
> no one in the history of civilization has ever done that-except by
> luck. For awhile. I will disprove that the market can be timed by
> showing an exception. What a likelihood of P = 0.51 means is that by
> lottery, one would expect to pick a stock from the NYSE (or NASDAQ,
> AMEX, etc.,) that went up on any given day, 51% of the time. Anyone
> can do that, and most people do. Let's suppose that someone can do
> better, by say, 9% and do it 60% of the time. Only 9% better than you
> and me. P = 0.6, so:
>

For some reason, folks are having a lot of trouble comprehending why
one should not try to time the market. The problem is that everyone
has tried, and succeeded-sometimes. So, you loose a few every now and
then-wouldn't the gains offset the losses? The answer is no.

Here's why. If we look at our typical stock, with a likelihood of an
up movement, P, of 0.51, and a root mean square of the marginal
returns, rms, of 0.02, with an average of the marginal returns of
0.0004, and calculate the gain:

0.51            (1 - 0.51)
G = (1 + 0.02)    * (1 - 0.02)           = 1.0002

per day, and 1.0002^253 = 1.051905597 per year. This would make the
indices of a stock market, made up of such typical stocks, increase in
value at about double that value, or about 10% per year, which is very
close to what the DJIA, NYSE, and S&P 500 have done since 1966. What's
the chances of one of these typical stocks more than doubling in value
in a calendar year?

It turns out that it is easy to calculate. Here's how. We know that
the day-to-day fluctuations in every stock's value add root mean
square, over time-and for one day, rms = 0.02. So, at the end of a
year, the distribution for the entire exchange would be 0.02 * sqrt
(253), (since there are 253 trading days in a year,) which is
0.318119474. Lets suppose that we are watching a stock that just
IPO'ed at 18 bucks. We would expect such a stock's value, a calendar
year from now, to be between 18 - (18 * 0.318119474) and 18 + (18 *
0.318119474) dollars, (ie., between 12.27384946 and 23.72615054
dollars,) 68.2689492% of the time. All I did here was to calculate the
standard deviation of the possible values for the stock a year from
now, based on the standard deviation of the stock's day-to-day
fluctuations. I then found out how many dollars were in a standard
deviation, and added and subtracted it from the stock's current
price. What's the chances of the stock more than doubling in a year?
Easy. 18 / (18 * 0.318119474) = 3.143473067 standard deviations, which
is 0.000834778894826007, or about one in 1,198, or about one in a
thousand. There are about 10,000 stocks in the US equity markets, so
we would expect to find about 10 that more than double every
year. One, or so, every several years, will increase about 10X, like
Netscape did right after its IPO. (These probabilities agree fairly
well with the historical data from the NYSE, BTW.)

So, lets look at Netscape. During the escalated increase in its stock
value, it was running, short term, a P of 0.57, an rms of 0.14, and an
avg of 0.0196, for an annual increase in value of 12.031925 fold in a
calendar year.

Intuitively, you know these measurements are not sustainable, and it
is in the high end tail of the distribution calculated above. Why?
because if Netscape could have sustained such stock performance for a
decade, then one share of Netscape would be worth 1.14452074 trillion
dollars, about a 5'th of the US GDP! Hardly plausible. What went
wrong? The time interval for the measurement was too short. We were
mislead by the random probability of a stock increasing 10X in a year.

Computing how long we have to measure the statistics of a stock so
that we will not be misled is not trivial, (it can not be calculated,
but it can be computed-there is a difference,) and one of the programs
in the tsinvest distribution does exactly that. The name of the
program is tsshannoneffective, which gives 635 days, (about two and a
half calendar years,) as the minimum interval over which we should
have measured Netscape's stock performance to make an investment
decision.  If we measure the statistics of Netscape's stock
performance for the first 2.5 years after its IPO, then we end up
with, approximately, P = 0.51, rms = 0.02, and avg = 0.0004. Very
close to the statistics of all the other stocks in the US equity
markets.

But we still have not answered the question what would happen if we
tried to time the market and get out of Netscape while it was still a
fugitive from the laws of probability. That's really what the
tsshannoneffective program does. Suppose we measured Netscape's stock
performance for exactly one year, and then made an investment
decision. What's the chances of success, (ie., being able to get out
in time,)? There is a 51.7217% chance of loosing 90% of the
investment, and a 48.2783% of increasing the investment by a factor of
10. So, if an attempt is made to time the market, it will be
successful a little less than half the time-a very bad investment
strategy. (To put it in perspective, you would be slightly better off
investing in the slot machines in Las Vegas, than attempting to time
the market.)

John

BTW, the tsinvest program uses the algorithms out of the
tsshannoneffective program to avoid making bad investment
recommendations when searching the ticker for the best set of stocks
for an optimal growth portfolio. The algorithms used are general, and
can be included in any program. The sources are in
statistical estimate is only one method that it uses-it turns out that
statistical estimate is grossly optimistic with fractal data sets.
For example, using only statistical estimation, one would expect to be
able to time the market 51.9635% of the time-what would seem to be a
very workable agenda, with a significant pay off. Not so, however. If
one attempts such an agenda with only a 48.2783% likelihood of
succeeding, one will win sometimes, but in the long run, loose the
entire portfolio, (at a rate of 0.999406857 per day, on average.) The
tsinvest program can be programmed to attempt to do market timing, and
then simulations can be run using the NYSE historical data CDs of
every stock in the NYSE since 1966. The simulations verify that the
48.3% number is, indeed, valid. (That's the main use of the tsinvest
program-to simulate trading strategies, before its turned loose with
live data.) The 48.2783% number is, also, fairly close to empirical
market metrics from formal studies run in the mutual fund industry.

--

John Conover, john@email.johncon.com, http://www.johncon.com/

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