June 22, 2020

My last article, **Stock Trading Game - Gambling It Out**, made the point that stock prices could be considered as having the number of up and down days close to the equivalent of a coin toss. There was no need to look at thousands of stocks to validate this hypothesis. Even a small sample over an extended period of time would be more than sufficient to make that point. Nonetheless, some 21 years of data (5,473 trading days) were used to assess the general direction of the daily price movements and their long-term outcomes.

It was easy to acknowledge how close to a 50/50 proposition the data was. The numbers on that chart even corroborated that there was a small upward drift present in the data, just as numerous academic papers have done over the past decades. Therefore, nothing outside usual expectations.

Still, the data was within one standard deviation from the expected mean for these tests. We could not state, for instance, that at a 95% confidence level that those price series were not random-like.

Before designing a trading strategy, we need to understand how stock prices move around individually and collectively. It will be from that understanding that we can then make profitable trading strategies that will exploit what we have found as inherently structured market dynamics, even if a lot of it is chaotic and random-like.

What did that chart say? That taking a bet that tomorrow's close will be an up day was very close to a coin toss, thereby, making that bet a gambling proposition. And this gave the process of predicting what will happen tomorrow a very low correlated value. Meaning that those estimated predictive powers were approaching a zero information ratio and thereby tending to make it a zero-sum game.

Notwithstanding, there was a slight edge to the upside in the data, but not by much. It is as if playing with a slightly biased coin with an up-day probability of 0.51. This said, on 100,000 trades, you might be right, on average, an expected 51,000 times versus being wrong 49,000 times. Making 98,000 trades out of 100,000 technically canceling each other out. You could add or subtract zeros from the number of trades; the biased upward percent trend, even if small, would prevail.

It is sufficient to look at a long-term chart of the market and draw a simple trend line to see this secular upward trend in action. Furthermore, no one is denying it either.

Here is one such chart. It is a little dated. Still, from it, you can extrapolate to today which would also make this secular trend thing very clear.

**Dow Jones Industrial Average**

Over the years, you are technically playing the black line which could be viewed as the expected average upward drift on the average stock in the above log-scaled chart. You could have taken a position almost at any time over a 20 to 30-year period and still come out ahead just for having participated in the game, without even having had to predict where the general market was going.

You could have picked the same stocks as in the DJIA with the same weights and rebalanced any time when one of the 30 stocks was replaced. That was not, and is not, complicated for anyone to do. All you needed was to be persistent and adapt as the composition of the DJIA's 30 stocks changed.

Your long-term general prediction would have been the same as Mr. Buffett's bet on America. And you would have prospered. However, we can see that there is a limit to the upward slope of that black line in the above chart. That secular trend is close to a 10% CAGR, dividends included.

If you wanted more, then you would have to do more, otherwise, your expectation and your probable long-term outcome would also tend to that 10% CAGR or close to it.

**So, How Are You Going To Do It**?

If you buy KO (or some other stock) and hold it for 30 years, you get the exact same percentage return as anybody else who has done the same thing, that you buy 1,000 shares or 400,000,000. The size of the bet matters a lot since the amount involved will be compounding for 30^{+} years.

In an interview, Mr. Charlie Munger was asked: What was your best investment ever? He replied without hesitation: “KO”, even though KO was at the same price level as some 20 years ago. Berkshire Hathaway has 400,000,000 shares of KO and last year made 640 million in dividends from their KO position alone on an initial investment of 1.4 billion. That was a 45.71% return on investment on a stock that has almost gone nowhere. So, yes, it was a very good investment. And furthermore, all that Berkshire Hathaway had to do was wait and do nothing else.

However, a trader, by moving in and out of stocks, cannot reach those dividend levels without some outstanding effort, and certainly not by flipping that many shares on a weekly basis.

**In Need Of A Long-Term Perspective**

One has to design a trading strategy in such a way that it survives over the long term. That design must also allow the portfolio to grow big starting with whatever it has as initial capital. One thing is sure, the initial capital will play a major role in the equation. Simply look at the future value formula: F(t) = F_{0} ∙ (1 + **E**[g])^{t}. Another thing is that the trading strategy has to generate all the profits from its available and limited cash resources as it goes forward.

A single trade can be expressed as: q ∙ (p_{out} - p_{in}) = q ∙ Δp = $X, where the profit or loss $X comes from the difference in price. If, on average, Δp = 0, you have no profit, no loss, no return. No value whatsoever in doing such trades or playing such a game.

The problem does not change if you do more trades, it is the same math: Σ qi ∙ (p_{out} - p_{in}) = Σ (qi ∙ Δip) = $X. You simply add up the result of all executed trades. This is where it might get complicated, but it remains so simple.

If you want a better return on KO for 30^{+} years, your trading profits need to exceed what you could have had just holding it. That too, can be represented using an equation: F(t) = F_{0} + Σ_{n} (q_{i} ∙ Δ_{i}p) > F_{0} + q_{KO} ∙ (p_{t} – p_{0}), which says that no matter the number of KO trades (n) taken over those 30^{+} years, the sum of their respective profits and losses need to be more than the profits from just holding KO. It should be evident that if your trading on KO does not generate more profits than holding KO, you are underperforming. And therefore, the better solution would have been to hold KO for the duration. This will apply to any stock you want to trade in your portfolio.

Using the same payoff matrix equation as in my recent articles, you can express the outcome of a whole portfolio on the same simple math.

F(t) = F_{0} + $X = F_{0} + Σ (**H** ∙ Δ**P**) = F_{0} + **E**[n] ∙ x_{avg} = F_{0} ∙ (1 + **E**[r_{m}]+ α)^{t} ≥ F_{0} ∙ (1 + **E**[r_{spy}])t

The above equation says that whatever the amount of trading you do in your portfolio, it should at least outperform holding a market surrogate such as SPY over the trading interval. That too, is relatively simple to state. It is another thing to make it a reality. Especially in light of my previous article, **Stock Trading Game - Gambling It Out**, where it is stated that randomness plays a major role in daily stock price fluctuations.

**Related Recent Articles**:

**Stock Trading Game - Gambling It Out**

**Trading Is Not That Simple, But**

**Winning The Stock Trading Game**

**Books**:

**Stock Trading Strategy Mechanics**

June 22, 2020, © Guy R. Fleury. All rights reserved.