July 28, 2014

In the same vein as in previous articles, I'd like to present the following charts from a portfolio simulation done last weekend. It's huge, and I am still analyzing the details involved in such a big portfolio. Its payoff matrix has a size of 13,000 rows (days) by 985 columns (stocks); that's 12,805,000 data entries for each of the matrices involved.

I've opted to use the Elder Triple Screen (ETS) trading strategy as a backdrop and testing ground to learn and test my new possibilities using Wealth-Lab 6.6. Sorry, the ETS won't be strategy #5 to be tested and analyzed. I'll most probably use another one for that. The ETS modifications are too much of the chainsaw type of job for my taste at the moment. However, I do need to test and debug using something.

The first chart shows the overall portfolio performance from August 1964 to the present (50 years). The simulator's output is impressive:

**Portfolio Equity Curve: 50 Years**

(click to enlarge)

As before, the blue line at the bottom of the chart is the Buy&Hold. The general shape of the equity curve is similar to the Russell 1000 index. Note that it more than significantly departs from the Buy&Hold.

The ETS program was transformed to accumulate shares over the long term, thereby taking a buy-and-hold stance on many of its positions over this prolonged investment period. Yet, the average holding period was just slightly more than 5 years.

The performance summary report gives the portfolio's standing at the end of the test as:

**50-Year Performance Report**

(click to enlarge)

From the above, 389,586 trades were executed, with 81.48% of these showing a profit from closed and still-opened positions. There is no Machiavellian process at play here. What you see is simply the output of a trading script designed to accumulate shares for the long term. Notice the payoff ratio and profit factor: both are more than just high.

The following chart reveals even more:

**Portfolio Inventory Level (50 Years)**

(click to enlarge)

We can see the inventory buildup as time progresses. It does show the exponential nature seen in its governing equation:

A(t) = A(0) + Σ(**H**(1 + r + g + T)^{t}.*Δ**P**)

As was said in my 2007 **Alpha Power** paper (page 6):

"*it turns out that there is a whole family of procedures of the sub-martingale variety regulated by subordinators (as in a Lévy process) that can transform an expected zero alpha into an exponentially increasing one. ...In fact, when looking at the problem from a long-term perspective point of view, it is a whole philosophy of trading procedures with many variations on the same general theme that can be used not only to extract some alpha but, most importantly, to put it on steroids."*

From the equity chart above, any point in time shows the portfolio liquidation value. That is the net profit after closing all positions and quitting the game. You will suffer drawdowns but to a lesser extent than the Buy & Hold (percentage-wise).

The above test also revealed that much less capital would be required to achieve those goals than anticipated (I would venture from less than half to less than a third). Not all stocks came online at the same time; in fact, stocks were progressively added over the whole interval, and each one was treated differently. Each had its own signature.

Yet, all the stocks, as a group, would contribute and make you prosper over your long-term horizon as if by default. You might not be right on all your trades all the time, but in the end, it might not matter that much.

**Added: July 30, 2014**

Was anyone surprised by the results shown above?

I know I particularly liked the third chart. What I see in it is a direct consequence of the trading methodology used... Time, more precisely: doubling time, should be a core concept behind any portfolio construct. That you win, in the short term, from a trade here and there is almost totally insignificant when looking at the bigger picture, especially if your trading strategy does 389,586 trades over its 50-year time span.

It's the finish line that matters. The time when you will say: I quit and retire. But by then, you might also realize that quitting might not be that great an idea after all. Just letting your computer do its business might matter too... and based on the last 3 charts presented, it might matter quite a lot.

The third chart showed the net number of positions in the account as time progressed. The part in blue below the curve depicts the position of inventory accumulation over time. It spans 50 years and represents all the daily inventory adjustments done over the period. It resumes all the trading activity of the 985 stocks. Here is the third chart from the above.

The thing that's remarkable is the relative smoothness of this exponential curve. It started slowly and gradually grew in size. It showed, at a glance, the exponential part (1 + r + g + T)^t of its governing equation: A(t) = A(0) + Σ(**H**(1 + r + g + T)^t.*Δ**P**).

This equation says that the reinvestment policy g and the contribution from the trading activity T can help push performance to higher levels, all other things being equal. It will be, over time, how one will slice and dice trade size and trading decisions (13,000 trading days) on these 985 different price series, that will make a difference.

From all the chaos of having 985 price series meandering almost randomly over a 50-year period, the above chart still managed to generate quite a smooth exponential-looking curve. It also indirectly implied that one could "control" to a certain extent its long-term objectives. You could increase or decrease the aggregate value of (g + T) and thereby gain some control over its long-term CAGR and, consequently, its doubling time. Interesting prospects...

I had to provide that program with some steroids just to see and show one could "kind of" control this monster. Increasing the profitable trading activity, T would generate more funds that could be reinvested in more shares. So, without much comments on the procedures used, here are the results for this, run once, a 50-year test on steroids:

On the performance metrics I got:

**Summary Performance Report** (on Steroids)

(click to enlarge)

The equity line gave:

**Equity Curve** (on Steroids)

(click to enlarge)

And the inventory accumulation showed:

**Cumulative Inventory**

(click to enlarge)

These last 3 charts can easily be compared with the 3 first charts presented above. Putting just a little bit more pressure on the system added some $2B to this long-term trading scenario. In the process, it improved on all its metrics. More returns from less risk. I requested more trading activity, and the program complied. It generated 101,072 more trades and still improved its metrics.

Created... July 28, 2014, © Guy R. Fleury. All rights reserved.