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 http://www.johncon.com/ntropix/archive/tsinvest.tar.gz. Traditional 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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