On Optimal Portfolio V

January 22, 2012

New Presentation: Alpha Power Trading Methods.

On Growth Optimal Portfolio IV ended with: “By adding a trading component to the above equation, one can push performance to an even higher level”.

A major feature of my Alpha Power Trading methodology resides in the fact that the excess equity buildup is used (instead of letting it go to waste), not to predict future prices, but simply to increase the inventory at a rate as close as possible to the price appreciation rate. This way, reaching exponential alpha using a profit reinvestment policy; similar to reinvesting dividends as they are received.

Now you say, adding a trading component to the mix should require additional capital. Not necessarily so. You can start your accumulation process using lower inventory levels leaving enough trading capital to make it worthwhile. Your intention in the first place is to Buy & Hold; and in the beginning, that is exactly what will happen.

The added procedures will differentiate themselves slowly as time progresses to finally make a huge difference at the finish line where it counts. But it will have been necessary to go through every step of the process in order to obtain the final results. There is no instant jumping to the end in 5 minutes. If the strategy is designed to run for 20 years, then it will take some 5,000 trading days at 250 trading days per year (some 7,305 days), to reach the end of the intended holding period. This should be considered a long time sitting on your butt.

I will often make references to the S&P 100 Index when elaborating on the payoff matrix. This means that the holding function and the price change matrices will be 100 stocks by 5,000 trading days. The S&P 100 Index will also serve as a benchmark for the portfolio.

Adding a Trading Component

Adding a trading component to the mix can improve overall performance. What is proposed is to trade over the share accumulation process and use the proceeds to buy more shares to hold for the long term. It's like saying: my primary intention is to Buy & Hold, but I am relatively flexible on the “hold” thing.

There is a need to convert the generated trading profits to its equivalent contribution rate to the share accumulation program which can be added to the increasing inventory level (see On Growth Optimal Portfolio IV article).

This would translate into the following expression for the payoff matrix:

Σ [ h_ioI(1 + g_i + T_i) ^t-1 .* P_io((1 + r_i)^t - 1)]

where g_i is the average reinvestment policy rate, and T_i is the average contribution rate from the profits generated by the trading component. The inventory of each stock would increase according to their respective delayed price appreciation functions. The trading component would add a path dependent inventory boost which would have for effect to also push the generated alpha to a higher exponential appreciation rate.

What the above expression would mean is that by reinvesting the accumulating profits in rising stocks and reinvesting the proceeds from the trading strategy, one could achieve returns above the Buy & Hold by this delayed exponential factor: (1 + g_i + T_i) ^t-1. It would be how the inventory is managed that would make a difference.

The average reinvestment policy rate g_i could be a fraction of the average price appreciation rate: r_i. In order to use most of the available excess equity buildup generated by the price appreciation, one could have the reinvestment policy rate approach the price appreciation rate: g_i → r_i.

The trading component is totally dependent on the trading strategy used. Any trading strategy having a positive expectancy would improve overall return.

The primary objective is not to trade; it is to accumulate shares while trading over the accumulative process. This would imply that at every significant price swings only part of the shares in inventory are sold, the other part being held for the longer term. It's more like having the trading profits finance the share acquisition program.

The whole process is a compromise. You balance your long-term portfolio objectives, which can be expressed mathematically, with the uncertainty of how stock prices might or will behave in the future. You are not predicting where prices are going, but you are predicting what you will do as prices evolve.

The Stop-Loss

You have a long-term stock accumulation portfolio, but this does not mean that the market is always going in your favor. You still need protective stops, even on the S&P 100 stock list. But in this kind of strategy, stop losses somehow need to be more flexible. You realize that the long-term accumulation process of the methodology can push your performance to really high levels supported by rising prices and that to reach your goals you should not exit the market at every wiggle in price. The stop loss needs more leeway.

With a 20 years time horizon to your trading strategy, a wiggle, a dip or a reaction to a price swing are viewed differently. Wiggles, dips are at most small blips on a 20 years chart. You are more concerned with trends that could last months, not minutes or days. And since you did, in the first place, select stocks for the long term, then short-term price gyrations should be of little concern. It is the major price dump that could be troubling or a feared phenomenon.

I would like to say that based on a long-term stock selection a major gap down will not happen but then I would be delusional. If the past is any guide, you know that somehow, sometime in the future you will hit one and most certainly more than one of those. It is part of the trading business.

Your real protection is in the numbers, and by this I mean over-diversification. Have no one single stock represent a big chunk of your portfolio holdings. And do have a final protective stop in place, a level which if reached sounds the alarm to get out of a losing position with no questions asked. Having the 100 stocks of the S&P 100 Index in your portfolio does qualify as being over-diversified.

It is the trading strategy used which most likely will generate the stop losses based on whatever the intended objectives were. Some trading strategies have and can maintain their edge only by executing short to mid-term stop losses. Often times, it is the execution of the stop loss on winning or losing trades that can save the trading edge.

The Game

The investment game is not to be right all the time, but if you have done your research properly, looking for long-term stocks to hold, you should find that long-term, you have been right most of the time. You do not want a perfect score, you only want a high score.

If you play the Buy & Hold, long-term, you get what the market has to offer: the expected secular market trend: 10% compounded (including dividends).

If you trade, long-term, you get what the market has to offer: the expected trader's secular trend: less than 10% compounded (need to account for commissions).

If you want to time the market, long-term, you get what the market has to offer: expected market timer's secular trend: less than 10% compounded (account for under-exposure).

If you play the Buy & Hold, long-term, and use some of the generated profits to buy more shares, you get what the market has to offer: more than the expected secular trend: more than the 10% compounded. The reinvested profits are also compounding over time. Mr. Buffett exceeds 20% compounded doing this, and it is quite reasonable, he is reinvesting most of the generated profits in buying more stocks, increasing his inventory which he intends to hold for the long term. He is, in fact, compounding on the generated profits. He does apply a reinvestment policy g_i to his portfolio.

But if you accumulate shares for the long haul and have an efficient trading system piggyback your stock accumulation program then you can reach much higher levels than the expected secular trend. You can even exceed Mr. Buffett's remarkable performance with ease.

The game is not about being right, it is about making money. And whatever trading strategy you may have devised, you might really be surprised by adding a stock accumulation process to the mix. However, if your trading strategy is only for the short term and using single positions at a time, then you will need to find your own compromise; because there I think you might need predictive abilities. And my trading methods do not use price predictions.

What Should Be The Trading Strategy?

Well, based on my research, just about anything goes. You can see in my own simulation section, on my web page, various strategies that have been modified to suit my trading purposes that have produced interesting results. The Trend or No Trend article summarizes the progression of my search for better and better trading strategies to be implemented. I particularly like my latest strategy which has a tendency to buy bottoms and sell tops while at the same time accumulate shares and cash, all without trying to predict future prices. (See latest simulations article and my presentation for an overview).

The whole point of trading over the accumulative process is to provide funds to accumulate more shares for the long term. It is this feedback loop that enables the trade acceleration as time progresses; a kind of positive reinforcement for good trading behavior.

The alpha generation will depend on the delayed exponential factor: (1 + g_i + T_i) ^t-1. And the trading component's contribution rate can have a major impact on the overall performance since it is also compounded over time. The higher the trading contribution rate, the higher the performance will be. And since this contribution rate is compounded, it does not have to change by much to amplify long-term results. Trading efficiency and the number of profitable trades become the main concern. You want the trading component to produce as much profits as possible.

Alpha Power Trading Method (20 years)

Even though about any profitable trading strategy would do, some are better suited than others. Strategies looking for rare events or having low market exposure, either in position size or time in the market are not the best choices. As given in the Alpha Power Trading presentation, or the Trade Acceleration article, the number of positive trades over the investment period counts, and looking for rare events is not the best way to increase substantially the number of trades.

The task is not to predict where prices are going, except in a long-term sense, but to profit from short, mid and long-term price movements and use the proceeds to accumulate shares for the long term. And since the methodology uses over-diversification as an equity protection measure, the dumpers or big gap down plays will have limited effect on the overall portfolio equity line. Especially when the methodology tends, as it progresses in time, to also accumulate cash.

Portfolio Stock Selection

Having used the S&P 100 stocks as a portfolio basis, a small part of the available equity is used to establish initial positions in each of the 100 stocks in the index. The over-diversification objective is met easily as about 30 stocks are considered sufficient for a 95% diversification level. The stock selection process (with a long-term horizon in mind) is also made easy by using all the stocks in the index which is composed of some of the top listed companies. Finding an appropriate benchmark will be extremely easy being already in hand.

For a 20 years time horizon, the price change matrix would be composed of the 100 stocks by some 5,000 trading days. And the holding matrix would be the same size containing the inventory level of each stock for each day of the trading interval. Whatever the trading strategy used, it won't change the price matrix which can serve as a benchmark, not only for stock comparison but for the whole group as well.

Adding a Covered Call Program

Adding a covered call program to the accumulation process would also result in higher performance levels. The profits generated by the covered call program could be used to increase the rate at which stocks are accumulating over time. Expressed as a contribution rate this would transform the above expression into:

Σ [ h_ioI(1 + g_i + T_i + CC_i) ^t-1 .* P_io((1 + r_i)^t - 1)]

where g_i is the average reinvestment policy rate, T_i is the average trading contribution rate, and CC_i is the covered call average contribution rate for each of the individual stocks ( i ).

Since the intention is to hold long term, all the shares in inventory at any one time could be used in a covered call program in order to add cash to the account where it can be used to acquire more long-term shares.

And if a number of shares are called, you simply repurchase the quantity delivered and sell new calls with a higher strike. This way maintaining your accumulating inventory level.

It would be more like renting out your stock inventory, for a little extra cash, as you progress in time than trying to speculate on options. You are aiming to hold on to your accumulating stock inventory for the long term so why not make a little more profits on the side.

With an exponentially rising inventory, the covered call program would contribute to raising the portfolio's alpha generation. It is a simple administrative procedure but would nonetheless contribute its share of portfolio profits.

Adding a Naked Put Program

Just like the covered call, a naked put program could also be implemented to generate additional cash for the portfolio to use in acquiring additional shares for the long term. This would transform the inventory accumulation function into:

Σ [ h_ioI(1 + g_i + T_i + CC_i + NP_i) ^t-1 .* P_io((1 + r_i)^t - 1)]

where g_i is again the reinvestment policy rate, T_i the trading contribution rate, CC_i the covered call contribution rate for each of the individual stocks, and NP_i the naked put program contribution rate to the mix.

You wish to accumulate shares of rising stocks for the long term and the naked put offers you an immediate discount. Therefore, depending on the accumulation rate, which will fix the number of shares to be acquired in the near future, you can sell a naked put for a lower strike. What you will get is the premium if the stock continues to go up or you will be forced to buy at the lower strike what you intended to buy for the long term in the first place. Again, producing more money to accumulate even more shares.

Part Of A Total Solution

The object is not the trading, what is aimed for is the accumulation of shares for the long term. The reinvestment policy, the trading, covered call and naked put programs are just meant to pump cash into the account that can be used to acquire more shares. And as a byproduct increase the inventory level at an exponential rate while the average portfolio price is also increasing on average at an exponential rate.

You could even allow short sellers to borrow your stock inventory for a small fee. You are holding for the long term anyway, why not get the little extra return on your overall investment.

In my 2009 article: Total Solution the same arguments were presented in a different form but saying about the same thing. The one thing not included in this note are the additional trading procedures related to short selling.

Part of a Total Solution

The above chart shows what each trading component bring to the mix. On the far right, you find the contribution rate for each of the variables. For example, the Buy & Hold was put at 15% (to express a better stock selection than average), while the covered call and naked put programs were set to contribute 15% return to the overall performance. The reinvestment policy rate was set at 90% of the Buy & Hold accumulating profits.

Overall, each component contributes in its own way to increase performance and also depend indirectly on the performance of the others. Raising the reinvestment policy rate to 100% (meaning using all available excess equity) would have for result to push all other components higher except for the Buy & Hold which is not dependent on the reinvestment rate.

It is looking for a total solution, a compromise of a sort, but a total solution nonetheless. The above mathematical expression tries to do it all at the same time. And as such represents more than just a trading methodology, it represents an investment and trading philosophy. A different way of looking at portfolio management. It understands that portfolio management is not just guessing from one period to the next. But a multi-period, multi-asset and multi-objective endeavor that can span many years of market turmoil in a world filled with uncertainties. And it is by having an investment and trading strategy that spans the entire time spectrum that one can outperform traditional methods.

The last mathematical expression is the sum of investment policies and administrative procedures. It resumes what happens as time progresses. It does make a bold statement and that is: generating exponential alpha could be a rather simple task for any portfolio manager. It even goes further: it states that the efficient portfolio frontier is not even a line in the sand, nor a brick wall, but only an imaginary barrier that can easily be jumped over or totally ignored.

You may not be able to predict future stock prices that good, but then, it might not be necessary to do so.

Final Analysis

In final analysis, the trading game is all about compounding. That you start big or small, you take some market exposure in the expectation of reaching or exceeding the most expected outcome which is the secular market average compounded rate of return of about 10% per year (dividends included). To achieve alpha above this mark is most often left to forecasting future prices but the success rate is not that high since some 75% of professionals fail to generate real long-term alpha. It is also why there are so many indexed funds and portfolios, but there, all that can be hoped for is aiming for the average and almost making sure of reaching it; it might not be the best way to obtain alpha points.

On the other hand, you could use reinvestment policies and administrative procedures supporting your long-term stock accumulation program and see alpha generation at high levels and with ease. My trading methods are all about this alpha generation; not as a single number, but as an exponential function. And to achieve these commonly out of reach performance levels all that is required is to put the inventory on an exponential function as well. Compounding the inventory, accumulating more shares as time and excess equity buildup permits.

Your tools are simple and at hand. First, the reinvestment policy lets you use the excess equity buildup which otherwise would go to waste doing nothing. Even on a 10% compounded return over 20 years, it does represent 6.72 times your original investment, and 16.37 times on a 15% compounding rate. My recommendation is: use it to better your portfolio (see the above chart). It will provide instant exponential alpha generation.

Next, design a stock accumulation program to which you add a trading component. The primary purpose is not the trading, it is only a way to feed profits to the accumulation program. The better the trading strategy, the more funds can be injected into the share accumulative process which is the main long-term portfolio objective.

Having an exponentially increasing inventory, you can rent it out in the form of covered calls. And your naked put program could add a little extra by providing not only premiums but also discounts for shares that you intend to buy anyway.

Study the above payoff matrix expression as it provides a means to greatly improve your long-term portfolio performance. You can also get a summarized view from my latest presentation.

The property sought from all these administrative procedures is their ability to generate profits that can be used in the inventory accumulation program. That is where lies the exponential alpha generation.

Therefore, my best advice is again:

Accumulate, Trade and Hold more...