May 3, 2020

Whatever your automated stock trading strategy, it needs a purpose, an objective. You need to plan for where you want to go and how you will get there. From my previous article, you can estimate how many trades will be executed without even writing a single line of code, knowing you will be scheduling a periodic rebalancing procedure over your portfolio's life cycle.

This article continues in the same direction as the preceding ones (see related articles below), going from the endpoints and designing a trading strategy backward from the perspective of its long-term objectives. And then redesign the trading strategy for going forward. All in the process of trying to answer the question:

What does my trading strategy have to do to reach its long-term objectives?

As expressed in previous related articles (see below), the following equation still holds:

Σ (H ∙ ΔP) = E[nt] ∙ xavg = y ∙ rb ∙ j ∙ E[tr] ∙ xavg = \$X

where y is the number of years the rebalancing is applied, rb is the number of rebalances per year, j is the number of stocks in the portfolio, and tr is the expected turnover rate. We could set the cumulative number of trades at time t as: nt = y ∙ rb ∙ j ∙ E[tr]. We can see from the formula that the turnover rate tr has a major role to play. Nonetheless, in these examples, I will limit its range to: 0.00 < tr ≤ 1.00.

Determining y, rb, and j are portfolio-level settings. They are not predictions but states under which the portfolio will have to operate. If you set the number of years to y = 20, using a monthly rebalance rb = 12, and using j = 400 as the number of stocks traded, then those are certainly not predictions but just initial portfolio settings.

You are left with finding the expected turnover rate E[tr]. This can be solved with ease. Do a simulation on your trading strategy, and it should give you this approximation, whatever that trading strategy may be. That same simulation should give you an estimate of the average net profit per trade as well: E[xavg].

The Return Space

The following chart displays daily portfolio returns over a 17.16-year period (chart taken from a recent simulation). At first glance, we could say it is, at least, erratic. In signal processing, it would be classified mainly as market noise. When you take such a chart over one year, 5, 10, or 20, it always resembles noise. Hard to predict with any accuracy.

Returns Distribution

(click to enlarge)

However, you might not need price predictions that much after all.

For instance, the two black lines on that chart could represent a percent threshold, which, if crossed, would execute a trade. The price goes up by 2 or 3%, and chop-chop, you sell, take the profit, and put the money back into the trading account. You do not need to predict that the price will go up, only that when it does, you cash in on part of the inventory.

Evidently, such a thing would need to be corroborated by the equation. For example, making: E[PT] ≈ 0.02 would do the job. Nothing exaggerated and based on the black lines, something that happens more than often.

It's a trading system, and you are playing averages. It does not look like that when we look at each individual trade, but when you deal with 100,000+ trades, you simply average things out. It becomes the averages that matter and not the individual trade.

When looking at the averages, the price variance alone might be sufficient to profit. There are a lot of 2% moves in the market, either daily, weekly, monthly, or yearly. You might not need to predict those price moves but just cash in when they occur.

In essence, saying that you can play on market noise and win simply by cashing in those paper profits.

Does it come down to the control of those 2 black lines in the above chart, as some functions, and simply profit from the price variations in this ocean of variance? It does appear so. The two black lines might be crude, but they should nonetheless make the point. I expect they too, are stochastic in nature and erratic, but I also expect them to average out over the long term.

This is making profits by systematic trading a lot easier than anticipated.

It would appear that all you need is to let your program do its job. This is where trading is different from long-term investing. On a monthly basis, you can make 12 successive trades that can produce 2 to 3% on the month, making the equivalent of one yearly trade that would have produced 24 to 36%, even if that stock finished flat for the year. And, 2 to 3% moves over a month's time in the stock market happen really, really often.

You still need to design something worthwhile and, most of all, doable to achieve your objectives. You have the above equations to guide you. You can set those objectives yourself based on how you want to set up your portfolio. It also appears that the control of your bet sizing is a key.

It is how your trading strategy will behave in all that market noise that will make the difference. Not that you predict it, but just use it to your advantage. The number of trades you prescheduled is going to do it for you and remain under your control, as demonstrated by the above equation.

What you have to do is design something that is consistent will your objectives. If with one million as a bankroll, you make net, on average, \$2 per trade, and you want \$10 million in profits out of it. Your strategy better be able to do 5,000,000 trades! Can I suggest you design something better?

The question remains: where is the money? To be answered in Part III.

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The Portfolio Rebalancing Gambit I

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