May 6, 2012

Growth Optimal Portfolio VIII

Developing a Trading Philosophy

Usually, developers start by programming trading strategies based on some particular idea or concept they might have on market or price behavior. The objective is simply to design a better trading strategy. They will backtest over past market data to see if the trading procedures do generate profits or not. And from there will start an iterative process to improve the structural design of their new preferred trading strategy. But maybe they should also look at the trading environment and trading philosophy behind their trading strategies. What are the concepts that govern the methodology used? This research note tries to answer that very question. Not just to design a trading strategy but to design a trading methodology and a supporting long term investment philosophy.

I use a lot of equations to make my points as clear as possible, but in reality they are just there to express what should be considered as common sense or acceptable notions. The mathematical expressions are just representations of big blocks of information that can be processed and handled as single pieces of data. The very notion of a long term portfolio does not have the same meaning for everyone.

In the previous chapter, it was determined that an enhanced trading strategy H+ had to exceed the Buy & Hold. And the proposition was:

 Σ(H+ .* ΔPSPY)   >   Σ(HH .* ΔPSPY)  

What seems to be required is a holding matrix where: H+ > HH, and this enhanced trading strategy H+ would be a sufficient condition to out-perform.

H+ > HH, represents the set of all possible trading strategies that could exceed the Buy & Hold. It does not say what a particular trading strategy is; it only states that there is a set of trading strategies, if they exist, that can beat the Buy & Hold. This set of “enhanced” trading strategies could be of any size, over any number of assets, over any chosen portfolio ΔP?, over any time duration one would like to consider. The above expression is there also to state that the reverse: H- < HH,  would be the set of all trading strategies that do not achieve the simple objective of beating the Buy & Hold, and as such represent little interest, except in trying to avoid them.

The relation above is not an opinion, esoteric or metaphysical expression; it is a mathematical statement that says that to beat the Buy & Hold on whatever your chosen portfolio ΔP?, you will have to do better whatever the trading strategy H? you might wish to use. You will have to improve your trading methods until they can be part of H+; otherwise with H- you will under-perform the Buy & Hold.

Since an enhanced trading strategy H+ will have to operate on the same price data series, here on SPY or a portfolio ΔP? over its 5,000 trading days (20 years); what ever “enhancement” applied to the holding function would have to generate higher profits than the Buy & Hold, otherwise, once again, why bother; who needs, or would choose any H- as a desirable alternative?

SPY is an ETF, it represents the average performance of all its 500 listed stocks; and as an averaging process will tend to be less volatile than most of its constituents. But nonetheless representative of the average price movements of the 500 stocks.

Since SPY is representative of all 5 previously designed portfolios ΔP1, ..., ΔP5. Then the enhanced trading strategy designed for SPY should also apply to any one of the 5 portfolios, even if each stock in each portfolio was randomly selected as was pointed out earlier in the previous chapter. I would go as far as stating: ΔPn  →  ΔP?, that the 5 selected portfolios would tend, on average, to be about the same as any other 100 stocks chosen from the S&P500 as randomly generated portfolios.

Side note

The Berkshire Hathaway Case

No one doubts that Mr. Buffett over the past 45+ years has outperformed the general market. The enhanced Berkshire pay-off matrix H+ could be represented as:

 Σ(H+BRK .* ΔPBRK)   >   Σ(HH .* ΔPBRK)  

where HH is a Berkshire Buy & Hold strategy. Mr. Buffett outperformed this strategy by:   H+BRKHH > XBRK. With XBRK being the excess profit generated above the Buy & Hold. It would be useful to understand the reasons for this over-performance since then one could easily replicate the process. I think one thing that could explain a big part of what Mr. Buffett has achieved over the years is:

 Σ(H+BRK .* ΔPBRK)   →    Σ((HH + BBRK ) .* ΔPBRK)  

where BBRK is a progressive stock buying matrix and where Σ BBRK > 0. He simply accumulated shares over time; at times buying whole companies. Even if today his portfolio matrix: ΔPBRK  has some 30+ stocks and spans some 12,000+ days; it all started relatively small. It is with time that the number of stocks in his portfolio grew (adding columns), it is with time that he added rows (days) to his portfolio strategy matrix.

Always buying more and more, bigger and bigger, as if the result of an administrative procedure based on some excess cash reserve ratio. A procedure aimed at reinvesting  accumulating profits. This way, everything would be kept manageable with only a few employees required. All he had to do was manage his growing inventory one day at a time and decide if part of his growing cash reserves could be used for other stock purchases. He could take months to ease into a particular position or simply acquire a company to meet his reinvestment policy objectives. Very simple really, yet, how very astute. A profound understanding of the long term game at hand.

Not only was Mr. Buffett wired to succeed with his formula, I think he was almost forced to do so. At least, in hindsight, it is more than a reasonable assumption. As Mr. Buffett's portfolio grew, he had to make use of the dividends and the profits being accumulated in the Berkshire accounts. And their best use was to reinvest the proceeds, to acquire more stocks or companies. Leaving the money accumulate in the bank account would not have been enough to generate the displayed alpha. Nor would having issued dividends as those funds would not have been available for added future growth.

It was by reinvesting the profits that he was generating profits on what would have been wasted assets. He was getting a compounding return on his generated paper profits. With his added profits, he kept on buying more stocks. And as a result, a side effect so to speak, his trading strategy was generating some alpha.

 Σ((HH + BBRK) .* ΔPBRK) - Σ(HH .* ΔPBRK)      
 ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯      =  1 +  αBRK
         Σ(HH .* ΔPBRK)   

It was sufficient to continuously re-invest part of the accumulating profits to outperform the markets or its own chosen portfolio ΔPBRK. As crazy as it may seems, Mr. Buffett won based on his understanding of compounding returns which he learned from a very young age. A big part of Mr. Buffett's alpha generation could be a simple profit reinvestment policy.

Mr. Buffett's trading philosophy could be resumed to a single letter BBRK representing his trading history matrix:

Σ(H+BRK .* ΔPBRK)   →    Σ((HH + BBRK) .* ΔPBRK)

Buffett's investment philosophy is more complex that the model representation here, but nonetheless, the above relation does provide some insight into his trading methods. One thing is sure, there is no need to look very far to find a good reason for Mr. Buffett's alpha αBRK generation.

As was presented in my last October research note: On Optimal Portfolio, the long term Berkshire Hathaway vs S&P chart does show Mr. Buffett's alpha αBRK generation.

Berkshire Hathaway vs S&P

BRK vs S&P500

Should Mr. Buffett not add some alpha αBRK to Berkshire Hathaway, both lines in the above chart would simply almost superimpose on one another. It is by continuously reinvesting the generated profits that Mr. Buffett outperformed the Buy & Hold (here, the green line representing the S&P500).

Would this mean that anyone adopting a BBRK type matrix would be generating alpha? Well, yes, absolutely. All that seems required is to reinvest the accumulating profits into buying more shares in order to continuously increase the inventory on hand. And since the accumulating profits are of the compounding type, the accumulation matrix B? should also be one. And the most important, having a B? exponential matrix will lead to an exponential alpha. Any long term trading strategy over a Buffett type portfolio is bound to win over the Buy & Hold by default, as long as the B? matrix is increasing in time:

Σ((HH + B?) .* ΔP?)  >  Σ(HH  .* ΔP?)

Therefore, when setting up a long term portfolio, one should look closer at the reinvestment policy rate as more than just a simple administrative decision.

We often hear that over 75% of professional portfolio managers have a hard time beating the long term market averages, meaning that they do not succeed long term in beating the S&P500. Mr. Buffett is not doing market timing, he is simply reinvesting his accumulated profits and in doing so outperforms almost everyone else.

A Buffett style portfolio will outperform, but one can do even better.

Higher Performance Levels

To produce even higher enhanced trading strategies, one will have to work on the inventory levels held during the whole time horizon to see where stock inventories should be increased (by buying) or decreased (by selling). This inventory management task will require trading procedures, trading functions and decision surrogate matrices:

 H+ = HH + B - S   : another definition for an enhanced trading matrix

where B(uy) and S(ell) matrices will change the inventory on hand based on some “yet undetermined” decision process. It will be necessary to “control” inventory levels, meaning “trade” to change the quantity held over time. Otherwise, you would be left with only a better stock selection process to improve performance and that would be by finding a better ΔPn.

But even finding a better ΔPn will tend on average to any other ΔP?; or maybe more precisely ΔPμ, which would be more like the average 100 stocks portfolio chosen from the googols of available combinations. Your most expected stock selection ΔP? would tend on average to ΔPμ ; the most probable average selection.

All this to say that what ever the 100 stocks one could pick today from the S&P500, they will most probably 20 years from now look like an average selection, which in turn will resemble the S&P500. For the mathematically inclined, the average price of the 100 selected stocks will highly correlate to the index.

How could anyone select the best stocks to put in their portfolio 20 years in advance? All you can do today, is pick the best stock you can, based on what ever information is available to you today. For this very reason, what ever portfolio you pick will on average tend to any other ΔP?. How could someone guess which portfolio ΔP? will be the atlas portfolio ΔP*, the one with the highest possible return, when you have googols of choices and possibilities?

The above definition of an enhanced trading matrix is adding a S(ell) matrix to the Buffett enhanced matrix. But doing so, changes all the trading dynamics. It is not anymore only an inventory accumulation process, but a procedural differentiating function with exponential drift. You want the difference between the (B)uying and (S)elling matrices to grow exponentially; you still want to accumulate more shares over time as if saying:

 Σ( H+ .* ΔP?) ≥ Σ(( HH + B - S).* ΔP?>>  Σ(( HH + B).* ΔP?)  >  Σ(HH .* ΔP?

that the enhanced holding matrix (including buying and selling functions) must greatly exceed a Buffett style portfolio. It becomes not so much a portfolio selection problem ΔP? but a trading strategy H+ selection problem. Which strategy will push your performance levels higher than even a Buffett style portfolio?

What ever the portfolio ΔP? chosen, the set of trading procedures applied over the whole time horizon will represent the most crucial and critical elements in determining future performance results. It would be like answering the question even before you start any trading: will this new trading strategy, by design, be part of a future H+ or H- ?

Published ... May 6, 2012 © Guy R. Fleury. All rights reserved.

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