August 18, 2013

When looking for a trading strategy, one usually starts with a search for methods and indicators that can identify trends, then proceeds to find triggers as decision surrogates to execute entries and exits. Looking at past stock data, trends of all lengths can be found with ease, even if one does not have a clear, precise, or universal definition of what a trend is.

And then again, maybe a trend definition might not be required to design profitable trading strategies. See, for instance, my note: **Trend or No Trend**.

The word trend is a very imprecise term. It can be applied to fashion, politics, culture, business, and surely much more. Someone could find trends in about anything and, at times, not be able to quantify in some way what the trend really is. Our brains have been trained since the dawn of time to search for and recognize patterns in almost anything we see.

Nonetheless, in financial time series, we only deal with a series of numbers. A trend is simply a regression line of a specified length summarizing the analyzed data. One could even push the definition further and say that a trend is whatever straight line that can be drawn between two endpoints. But even such a minimalist definition needs clarification. Even if a 10-day trend and a 10-year trend are both defined as trends, they are not that comparable. Each time a trend is defined, it needs to be analyzed within its context of data type, sampling size, duration, and distribution.

Stock time series are just series of numbers; any derivative of such series are in themselves series of numbers. A price within a price series is also just that: a number. It has no style, no color, no opinion, no belonging, no taste, no smell, no sound, no orientation, no memory, no shape, no inclination, no was or will be; it is just a number, and it has no trend. There are no fat or thin numbers either, nor do they speak. However, within a stock price series, all you can do is analyze a price within the relative context of the other prices in the series. If the variations are mostly governed by randomness, then even the context might not provide much additional information enabling us to determine what is coming next. The more stock price series are considered random-like, the more difficult it is to escape from its randomness attraction. For instance, if price variations (ΔP) of the stocks in the S&P100 over the next 20 years are purely random, then whatever trading strategy you want to implement will have for most expected outcome zero alpha generation: Σ(**H**.*Δ**P**) → Buy & Hold, or less due to frictional and other opportunity costs such as lower market exposure and/or lower market participation.

The graphic below represents some trend lines normalized to 50. This means that all the price series were made to equate 50 at time t=0. Those above 50 were divided by the factor necessary to bring them down to 50, while those below were multiplied by a factor so that they too, could be at 50 at time t=0. By normalizing in this way, you could look at the past as well as the future from one common point in time t=0: the now point.

**Trend Distribution**

(click to enlarge)

The chart shows the exponential regression lines that could best fit the three data points at times t=-500, t=0, and t=500. The color of each line has no significance. It is just that I was too lazy to color each line in black. I could have put more lines, but that too, was more work. What is of importance here is the shape of the lines in this chart. From any point in time, simply by setting t=0 to a specific date and then redrawing all normalized regression lines from that viewpoint (t=0), you would get about the same shape as the presented graph, with all lines converging to the normalized price at t=0.

The graphic shows the equivalent of 41 simulated stock price series trend lines, each with their respective compounded rate of return so they can fan out on each side of t=0. The graph shows past and future trend lines centered on the present. Of interest is the "now" point at t=0, where all data series converge, but it would be more precise if it was said that they joined at their "now" normalized value of 50.

**Strategy Design**

Before t=0 (t<0), all the data of the prices series are set in stone, they are part of history and whatever trading strategy that could be applied to those data series are mainly for research purposes. There is no real money to be made from past data. All you can do is design with hindsight what could have been successful trading strategies knowing what has happened. Designing profitable trading strategies for all data series prior to t=0 is relatively easy.

The problem is not: can you design a trading strategy that can profit from past data, but: can you design a trading strategy that can profit from future data? Technically, only one thing really matters, and it is how well you will handle the section on the chart where t>0. How well will your trading strategy handle the future? All you have as a guideline is all you have observed from past data.

Whereas everything was known for t<0 up to t=0, except for the "now"; everything for t>0 is unknown. You have the starting point at t=0 but nothing else. If you look at the future, you will see compounding return lines just as you saw them in the past, and you know that they have to develop in this fashion going forward, but you would not know which would go up or which would go down nor by how much. It is only in the vicinity of t=500, therefore after the fact, that you would know, but by that time, it would have become a new t=0 with again an unknown future. Had you waited the 500 time periods to see the trends define themselves, it would simply have been a waste of time as you would be back to square one, meaning a new t=0 and a whole new future t>0 to unfold. Extending the graph to t=1,000 or t=5,000 will not change the shape of the trend lines. You still won't know which stock will prosper or die trying. And looking at t>0, the future will not be straight lines but quasi-random paths to their unknown endpoints. However, the regression lines are an acceptable representation of the final outcome.

Delaying the implementation of your trading strategies can have high opportunity costs. I have a research note on this somewhere. But it is easy to figure out. Opportunity cost = (1+r)^{(t+x)} – (1+r)^{t} where x is the delay in years. As the rate of return grows and as t increases, the opportunity cost increases exponentially; the more you push out t=0, your starting point.

I have not seen anyone backtesting the future, all I have seen are simulations over past data. It does not mean that the future cannot be tested. It can. It says that if the future is simulated, it is a waste of time. And, if it is tested in real life, then there might be a price to pay, or more hopefully, rewards to reap. You trade in real-time, or you don't. The future will occur only once so you better pick the best trading strategy you may have. However, for sure, any trading strategy you design that does not outperform past market data has little chance to outperform going forward. It should be added that if you "fix" the numbers in your backtesting to show good results, the market might "refix" or remodel your live trading account to the downside due to your "misunderstanding" of "what if".

At whatever time, be it t<0, t=0, or t>0, only at t=0 can anyone take action. If you take action on historical data, it has no value; for sure, you cannot put any of those simulated gains in the bank. Your simulation over past data is just that: a simulation of what "could" have been. From your simulations, could you have found "some" trading procedures that could have been productive over past data and might also be profitable going forward? In a way, any backtesting might have the sole purpose of finding trading procedures that cannot only be applied to past data but, most importantly, would also be applicable to unknown future data.

Future data (t>0) has unique properties. You know trend lines will form; there is no escape from that, but you will know only after the fact what was the trend line. You can speculate, based on your unique point of view, that the future trend line might be up or down, but it still does not guarantee that future prices will be up or down. Also, t>0 is the only place where your trading strategy can make real money as well as lose it.

The beauty of the above chart is in its perspective, its viewpoint at t=0. Looking back (t<0) everything is preset, you simulate on past data in a few minutes to see if your intended working trading strategy has some merits; and then, if applied going forward (t>0) it could take years to find out if it was really worthwhile. I often see comments like, "Hey, if your trading strategy is that good, why don't you already own the planet?" Which, in essence, is quite a "stupid" question! It is like not understanding a basic equation like (1+r)^{t}, where t has to pan out over the years to achieve its goal, and where the initial capital will be a major scaling factor. The future is not an instantaneous response as in a backtest. If you backtest for strategies that can span 20+ years, you might have to wait over those 10 to 20+ years before you could say: I told you so.

... to be continued...

The next section will be on compounding trading strategies.

Created... August 1, 2013, © Guy R. Fleury. All rights reserved.