June 15, 2020

If you knew that if you played the stock market game and that you would win no matter what, even if it took a long time, would you not find the time and resources to play your expected winning game if you could?

All you can do going forward is to look at history and extrapolate from there. Doing so would show that over the long term (20^{+} years), the average expected portfolio growth rate **E**[g] fluctuated near 10% dividends included. It is not because this has prevailed over the last 200^{+} years that it will also prevail going forward. What will turn out to be the value of your E[g] twenty-plus years from now? How could you make that estimate, and on what basis? How accurate, really, could that estimate be? Of note, it is said that 75% of portfolio managers have fallen short of this 10% long-term goal.

The future remains uncertain. But, at the very least, you have history as a guide on your side. It says that if you can make a reasonable stock selection and hold on for 20^{+} years, your portfolio is expected to grow at this 10% rate with a probability approaching 1. That is a statistical probability that is often expressed with an added “almost surely”.

Playing the stock market game by trading is quite different from long-term investing in stocks. Speculating over the short term, or on a daily basis for that matter, is not the same as investing in the long-term prosperity of a nation. And this distinction needs to be made.

The trading process is still investing in the markets, but it also brings with it its own set of problems. One of which is that short-term price variations appear almost random-like, meaning that the accuracy of predictive trading methods is relatively low. It might even have a hard time being on the positive side of luck.

One way to test for randomness is simply to count the up and down days over an extended period of time. If a price time series is close to random, it should show something close to a 50/50 bet. If you take 10,000 price series over 10,000 trading days (≈ 39.68 years), and still get an average outcome close to 50/50, you should definitely start to consider that there is a lot of randomness in those price series.

Your predictive powers increase as you move away from the expected long-term positive side of 50/50. Those powers certainly do not increase as you move closer and closer to the 50% probability of tossing a coin.

However, in price series, what is observed is that the hit rate is more like 51% to 53%. This indicates that, on average, there is a slight upward bias in those price series. Historically, the market is operating as if tossing a biased coin with a probability for an up-day in the vicinity of 0.52.

The following chart is a little dated (see article: **Where is the Alpha**?), but the principles would still apply. The list of stocks shown is just a list I was working with at the time, with no particular fundamental reason for their selection. The chart shows the count of up and down days over a 21-year interval (5,473 trading days). The expected 50/50 random distribution would give 2,736.5 for up and down days. One standard deviation is 37. We should find 68% of the data between 2,699.5 and 2,773.5. A not random hypothesis, at a 95% confidence level, could not even be considered since all the stock data was within 1 standard deviation.

**Up And Down Runs Test** (21 years)

Another interesting observation from the above chart is the percent number of days above the last recorded price. For instance, ABT has had 5,395 trading days out of 5,473 that were lower than its last price. Taking a position in any of those 5,395 trading days would have resulted in a profit if you had sold at the last price. While FDX, to reach a 0.00% higher than the last price, required that FDX was at a historic high. Making it that if you had bought FDX any time over those past 5,473 trading days (21 years), you would have had a profitable trade as of the last recorded price. And this, even if the up days were 49.35% of the total.

What is the solution if you have to play in such a game? It should be quite simple to demonstrate that an optimal solution would be to bet in the same direction as the bias and at the same level. Should the bias be 52/48, then you should bet to the upside 52% of the time. This is the same as admitting the bias and the underlying random nature of price movements.

If your trading strategy is designed to be 50/50 while the game is 52/48, it is simple too: you are shooting yourself in the foot. It is not the market that is out to get you. It is you who designed yourself to fail. And that is quite different than having a positive expectancy.

When I see someone doing a simulation and has a 51% hit rate, I have to classify it as a random outcome, meaning that whatever trading method was used, it had no predictive powers since it was no better than having tossed a biased coin. There is no talent required in tossing a coin and getting the same bias as the coin. However, it is detrimental to your portfolio if you play a 50/50 strategy in a game that is already biased to the upside at 52/48.

**Related Recent Articles**:

**Trading Is Not That Simple, But**

**Winning The Stock Trading Game**

June 15, 2020, © Guy R. Fleury. All rights reserved.