April 24, 2020

We often design stock trading strategy simulations by first programming them on some economic notion and then observing the outcome. As if the trading procedures, over the long term, would resolve the appreciation problem all by themselves, when a more global view should be taken. Where do you want to go, and how far will it take you?

Most of it could be determined beforehand. More planning and a better outlook as to what you really want to do.

You design something and wait for the outcome, or you design the desired outcome and then find ways to make it happen.

Most often, time will prove to be a major ingredient in that equation.

My previous article broke down a portfolio's payoff matrix to 3 numbers. They gave the final answer to the outcome of a stock trading portfolio, no matter its size or composition:

F(t) = F0 + Σ (H ∙ ΔP) = F0 + n ∙ u ∙ PT

A table with those numbers was provided to achieve different possible CAGR scenarios. They were not the only solutions; infinitely more are available, and in all cases, the equal sign will hold.

All the profits and losses, whatever their origin, were accounted for in the equation: Σ (H ∙ ΔP) = n ∙ xavg = n ∙ u ∙ PT where n, u, and PT were program variables which, technically, you can design to be whatever you want.

For instance, someone who bought Berkshire Hathaway some 50 years ago and maintained his position (about 30 did so) would have: 1 ∙ \$10,000 ∙ (1 + 0.20)50 = \$910,043,815. More than enough to pay for coffee and retire.

A single trade decision was enough, sitting down and waiting was the only thing required. That the market went up or down on a daily basis, you still had to just sit down and wait even in periods of market turmoil. Berkshire Hathaway has had 4 major drawdowns in excess of 50% over that period.

Then the question is: what was more important? Staying the course or getting out at the first sign of trouble? Shouldn't someone have introduced some capital preservation measures in the process in order to alleviate the drawdowns?

What Will You Do Going Forward?

The problem is not what others did but what you will do going forward.

I can say that whatever you do will have to comply with the above math. There is no escaping it.

You trade, you will generate a certain number of trades over the entire trading interval, no matter how long it is. You will generate profits and losses. Whether you win or lose, it can all be averaged out.

It does not make sense to build a portfolio for 20 years and see it all fail in a couple of months due to poor planning and poor execution. We cannot say that this thing is that complex. You have only 3 numbers to watch for. Only 3 questions to answer:

1) How many trades (n) can my program do over these 20 or 30 years?

2) What is its average bet size (u)? Hint: F(t) ÷ j.

3) What kind of average edge per trade (PT) can I get?

1) How can I increase (n) over the trading interval?

2) How can I increase the average bet size (u)?

3) What can I do to increase the strategy's average edge per trade (PT)?

It is not a matter of curve-fitting. It is doing what will increase those numbers while maintaining executability.

The 3 numbers mentioned become some kind of program pressure points. With all other things being equal, increasing any one of them will improve the final results. Since you have only those three numbers: n, u, and PT, you will have to find ways to increase the number of trades if you want to increase the final results. The same goes if you increase the trade unit u (the allocation). These are critical numbers to your trading strategy just as is PT, your program's average trading edge.

The trading game is not an instant lottery game. It is a long-standing endeavor, just as investing is. It is only that the rules of engagement are different. But, whatever trading methods you intend to use, those 3 numbers will prevail, whether you like it or not.

The initial stock allocation is rather easy to determine. If you intend to trade j stocks in your portfolio, then you have: F0 ÷ j. For a 400-stock portfolio, we have: \$10,000,000 ÷ 400 = \$25,000, or 0.25% of equity. This means a stock could drop to zero and only damage the total portfolio value by 0.25%! You could use any other kind of allocation as well. It depends on what you want to do and how you want to do it.

Should you opt to trade only 5 stocks in your portfolio? The math with change. The bet size will increase to \$10,000,000 ÷ 5 = \$2,000,000 and represent a 20.00% drop if a single stock goes to zero. Those are not nice odds. You are definitely better off to diversify and thereby reduce your market risk. Nevertheless, the market will take whatever bet size you want to put on the table. It does not care a bit that you win or lose, nor how much you bet.

You should be in control of what you do and not let emotions or the thrill of the game dictate what is to be done.

The table in my previous post showed the case for long-term 5%, 10%, 15%, and 20% CAGRs. The 5% case is about the long-term average for individual traders trying to make it on their own (refer to academic papers on the subject). The 10% is about what one could expect using index funds over the long term. Usually a little less due to all the expenses and management fees.

To reach the 15% CAGR level, you need to add some alpha to the game. This can be achieved using better timing methods, better stock selections, and better trading techniques. What you want to see is: (1+ gm + α) = 1.15, which would require an alpha of about 0.05, which is not that much but is still hard to get.

The majority of fund managers, over the long term, have failed to even achieve this. And with all their resources in manpower and equipment, not to include the best minds out there, what could make you think that you can outperform these guys without designing better methods than theirs? You have to innovate and re-engineer your trading methods for where you want to go and not just hope that somehow, over the long term, by some kind of luck, you will get there.

Everywhere in this trading game, you need to be reasonable. Everything needs to make sense. The big question: is this kind of trading methodology feasible or not? It should always be asked.

However you trade, the money has to come from somewhere. If you want to make it in a one-shot deal, then you better be right! I agree; nothing beats the biggest bet on the biggest move. But the question should be: can you support the risk? Can you find this big bet? Can you predict that "black swan", that outlier that might appear once a generation, or once in a thousand years? That kind of bet is not for everyone. Your goal should not be to bet on those things but to make sure that, over the long haul, you win and win big. If you want to build your retirement fund, that is your objective.

Already, with a 20% CAGR over the long term, you could mimic Mr. Buffett's portfolio return. That is 10% in alpha points which few have realized over the past 50 years. You know it is reasonable, you have Mr. Buffett's example that it has been done (and there are others that have done it too).

There are advantages to trading that are not found in investing. This is where you should concentrate the efforts to increase this alpha even further. Go for 15% or 20% alpha points to jack your CAGR to 25% or 30%. This will make quite a difference over the long term. It is a compounding game, after all, and time is a major ingredient in the solution to the payoff matrix.

Doing More

In the following table, which is an extension to the previous one, I raised the CAGR up to a 30% level with an example of the number of stocks and trading units that could be required to do the job.

The Payoff Matrix Projections Extended

(click to enlarge)

We should notice that to increase performance, the strategy traded more as we got along, just as the trade unit u was increased. However, the requested average profit target was not increased that much. It was gradually increased from 2.0% to about 3.2%. This is looking for, on average, an average 2.0% to 3.2% price change on a weekly basis. The bet size was also gradually increased.

It is all about your trading methods and your choices. Millions of other number combinations could have been used to reach the same objectives.

You Can Do It

The point is: can you force your trading strategy to do such things? And the answer is: definitely yes. It is your planning that matters here. The how you look at the game and the math behind it.

For instance, from the above, you know that you have to increase the bet size as you go along. That is not difficult. It can be incorporated into your trading strategy design simply by adding to the number of stocks you are going to trade. Or, simply increase the trading frequency or use some leverage.

Your initial bet size is proportional to F0 ÷ j, as stated earlier, for an equally weighted scenario. As the portfolio grows, the bet size will grow proportionally since the trade unit will remain proportional, on a continuous basis, to the number of stocks traded u(t) = F(t) ÷ j. You can fix the allocation to a fraction of equity as: 1 ÷ j.

So, yes, the trading unit will vary with time, following in locksteps with the portfolio's equity line. But this should not be surprising since, at the start of the trading strategy, the number of stocks to be traded was fixed.

It is why in each CAGR scenario, the number of stocks to be traded was increased as the estimated CAGR level increased. This is done in order not to accelerate the bet sizing too much and to maintain a lower estimated average profit target to do the job. Evidently, increasing the average profit target will produce even more.

This is quite a different structure for a trading strategy setup that we usually see in academic papers, or in practice, for that matter. But, nonetheless, everything holds. If you want to achieve more out of your trading strategy, you will have to provide more time and trade more with the preset notion of where you are going. One thing is sure, you will not be able to escape the above equation no matter what you do. And ignoring those 3 numbers will not make them go away either.

See recent articles for more on this subject.