Jan. 20, 2019

The stock market is not homogeneous. Therefore, why even think of treating it as such? All sectors are not equal, then why invest in each one equally? All stocks are not equal, then again, why use equal weights? At any one time, you can not predict that 50% of stocks will be going up while the other 50% will be going down and know which will do what. So, why go 50% longs and 50% shorts?

It does not make that much sense, unless, you have other motives or constraints you have to adhere to. And even under those conditions, the game remains a compounding return game, even if you want to treat otherwise.

An automated trading strategy usually means a large number of trades will be taken over some extended period of time. This tends to shorten the average trade interval considerably. As a consequence, the more all this trading will resemble gambling. Therefore, why not accept straight out that part of what we will do will be gambling and deal with it?

If your automated "quasi-gambling" trading strategy does 50,000+ trades over the course of 5 years does it not start to tell you something? At a minimum, you should be able to put some averages on the table related to the outcome of the various procedures taken by your trading strategy.

It should be evident that anyone can design crap. And, in fact, a lot do. But, YOU do not have to.

A trading system can be described using a simple expression: Ʃ xi   where you sum up the outcome of all the trades taken. It says: here is the total profit generated. Averaging is as easy: Ʃ xi / n which will give the average profit or loss per trade. In Leo's tearsheet (referenced in Part II), this number was: \$36.24 with n = 44,467 trades.

The number of trades is big enough to declare it a large sample. A simple assumption would be to say: if the sample is representative of what was done and of what to expect, then you could extrapolate with some kind of confidence that your estimate might not be that far from what might be a future outcome. If that system was extended to have n = 100,000 trades, we should expect for it to reach about: \$36.24 ∙ 100,000 = \$3,624,000 in profits in (47 ∙ 100,000) / 44,467 = 106 months or 6.8 years, a little over twice as long. By then, its CAGR would have gone down from 3.9% to 3.6%. This, even when the average profit per trade remained constant. The strategy would appear as if it was breaking down.

Over time, however, the average profit per trade will actually decline. It will not remain stable or go up but decline and there are simple reasons for this. Even before designing a trading strategy, one should understand the math of the game and what is implied by all those equations. You put an equal sign on the table, that is a hard statement.

We need to go back to what makes a trading system profitable. If your trading strategy is designed in such a way as to see its CAGR decline over time, you have limited choices. Maybe compared to other trading methods it might remain acceptable due to its still positive CAGR as long as it is above a specific threshold for instance.

Part II showed that one could use a simple compensation technique (among others) not only to maintain a strategy's CAGR over time but also, most importantly, to make it rise with time. An expanding CAGR goes beyond the CAPM model. Is implied that the optimum portfolio resides outside and above the efficient frontier. It questions the very foundation of MPT which nonetheless might hold over the long term for the Buy & Holder. But simply because you are trading, you can jump over this line in the sand called the efficient frontier. Over the short term, a theory such as MPT might show itself to be like some Swiss cheese, full of holes.

The following chart has been presented before (over a year ago) and still holds.

You want to do more than the expected outcome (market portfolio), then you will have to do more. It is not by doing the same as everyone else that you will outperform them. All you will do is only get close to what they do. This means getting close the long-term market averages.

If it is what you want to do, then nobody can stop you, but also at the same time, you are not providing any kind of motivation or incentive to adopt your average CAGR when almost everybody else can already offer the same.