Aug. 24, 2019

We can design our stock trading strategies to do whatever we want. However, most often, it just turns out to be whatever we can. These strategies could be based on about anything as long as they remain relevant to our intended objectives. Also, they actually have to be feasible in the real world and be able to survive over the long term.

What is the use of a stock trading strategy that will blow up in your face
at some time in the near future and completely destroy your portfolio?
How about if it is not even designed to outperform market averages?

In my previous post, it was shown that if the engineered alpha is spread out over time, it might not take that much to double or even triple a strategy's outcome. The formula is simple enough: 2 ∙ Cap. ∙ (1 + r)t = Cap. ∙ (1 + r + g)t. Even if the base return (r) was 20%, as with Mr. Buffett's long-term CAGR, for instance, an added g = 2.80% would be sufficient to double the outcome, while adding g = 4.48% would triple it. It is not a question of doubling the 20% CAGR, it is simply increasing it by 14% to double the outcome, or by 24% to triple it over those same 30 years.

To keep (r) as the market's average return and secular trend, I will use alpha for the above-average return. And from there, add this manufactured g to the formula: 2 ∙ Cap. ∙ (1 + r + α)t = Cap. ∙ (1 + r + α + g)t. In Mr. Buffett's case, both the alpha (α) and the average market return (r) would be at 10%. And therefore, r + α = 0.20.

Money-Wise, It Makes Quite A Difference

The $10,000,000 Quantopian initial capital scenario would grow to $2,373,763,138 without the added g. Doubling would generate $4,747,526,276, while tripling the outcome would produce $7,121,289,414. Almost $5 billion more from the added and self-engineered g = 4.48% (refer to A Long-Term Perspective II for the r = 10% base return scenario).

This is on the assumption of having a long-term view of the portfolio management problem. First, you must have the objective of lasting that long, meaning that your trading strategy will not blow up before reaching its destination. And second, you need to achieve this 20% ( r + α) long-term average CAGR over the period before adding g.

Let's start by saying that you might not be Mr. Buffett. On the other hand, adding some g to Mr. Buffett's alpha scenario would definitely produce more.

This growth factor g is just another way of expressing some added alpha. Here, this alpha is being engineered from within based on the structure of the trading strategy and its trading behavior. We are trying to extract manufactured alpha from the trading mechanics, the very process by which we are building our long-term portfolio.

This is to show how little is required to jack up performance. It might not even require being better at predicting what is coming next. You could set up functions designed to control what you want to see and how your trading strategy should behave depending on what is thrown at it.

The CVXOPT Optimizer

The above trading strategy relies on the CVXOPT optimizer to make its trades. It is a “black box” you feed with your portfolio weights. After CVXOPT's optimization routine, it will execute its trades and rebalance as closely as possible to your provided weights.

Should the optimizer see nothing that is actionable, it will do nothing. In fact, should all price series provided be random, it will answer with a zero-return portfolio (this has been demonstrated in detail in other notes and in my previous book).

We would have to conclude that price series are not totally random (they do have trends), but nonetheless, remain random-like to a great extent. The optimizer will detect and rebalance its stock weights on any trend of some duration within a price series, no matter its origin.

So, Where Do You Get This Extra g?

Evidently, from the trading strategy itself.

In this case, I opted to literally force-feed the optimizer with my special diet of mathematical functions (refer to Reengineering For More III for a description).

This is not optimizing the optimizer, trying to make better predictions, or trying to find better factors or alphas. This does not fit the over-fitting or curve-fitting conundrum either. It is force-feeding the optimizer with what you want to see using mathematical functions based on administrative procedures that can be independent of technical indicators, fundamentals, pattern recognition, or alpha generation factor analysis.

You simply tell the optimizer: follow this mathematically fabricated trend the best you can! That is: follow this new payoff matrix: Σ(H ∙ (1 + g(t))t. ∙ΔP) where g(t) is this intricate function applied over the life of the portfolio (again see Reengineering For More III for its description).

Having g(t) positive is sufficient to elevate the outcome of the whole payoff matrix from start to finish. This outcome will depend on how strong you want g(t) to be and how much capital is at your disposal over the life of your portfolio. The above expression will also force an exponential equity line, as illustrated in the 15-year equity line snapshot in Reengineering For More.

Some think that the above trading strategy is total BS. Well, it is not. It is, however, an innovative trading methodology with a long-term perspective. It is simply different from what you usually see.

Force-Feeding The Optimizer

This trading strategy is just the outcome of force-feeding equations to the mathematical contraption called the CVXOPT optimizer. The equations, being something you designed, can evidently be put under your control. This is what makes this trading strategy so remarkable. It uses the same tools as everybody else designing trading systems on Quantopian, yet it displays a much higher payoff matrix.

At the very least, it is a demonstration that it can be done.

BTW, what was shown is just the preliminary phase, the exploration phase of the possibilities and potential of having this long-term vision of the portfolio management problem. It leads to designing even better systems made to respond to other considerations if need be (read by adding more equations).

I see this as just the beginning of a different and innovative approach to building a long-term portfolio.


Related articles:

A Long-Term Perspective

A Long-Term Perspective II 

Aug. 24, 2019, © Guy R. Fleury. All rights reserved.