May 19, 2011

What is Alpha Power? Alpha Power is a trading methodology developed and refined over the years to become a total portfolio management solution. It was designed to meet several key objectives: 1- to greatly outperform the Buy & Hold strategy, 2- to accumulate shares over time while doing so, 3- to trade market swings over its accumulative functions, 4- to accept other features that can boost performance.

Its outstanding feature is that it is based on predefined trading procedures; mathematical functions that trigger entry and exit points. This is not a system responding to usual market indicators. It makes no price predictions and yet it’s a portfolio level trading system.

It's a trading methodology and a trading philosophy backed by a mathematical model. My current working model looks like this:

There is a lot of power built into the above equation which operates at the portfolio level (say 50 stocks or more). It can raise portfolio performance to new heights; way beyond the Buy & Hold strategy.

## The Buy & Hold Needs a Boost

The basic tenet is that the old Buy & Hold strategy of investing is not dead; it only needs a boost. The primary objective of the **Alpha Power** trading method is to accumulate more shares over time than what would have been put in the Buy & Hold. The reasoning is simple and as a trivial example; consider that if at the end of a trading interval you have 2 times more shares than in the Buy & Hold, then you have 2 times more equity in your portfolio.

It all starts with the Buy & Hold equation: in its simplest form, an initial capital is invested in *i* selected stocks growing at their respective compounded rate of return over a long-term horizon.

Buy & Hold wealth equation

Trivial Alpha Power equation

The above two equations resume the situation. You can not change the price; it is the same for everyone. You can not change the time, it is just there and also the same for everyone. Ah! The rate of return can be different for everyone: yes. But Modern Portfolio Theory states that the most likely outcome for the expected long-term rate of return is simply the market average; which translates to close to the same for about everyone.

If you want twice as many shares in your portfolio twenty years from now, you will have to buy them sometime over the investment period. To make things simple, say we start with 1,000 shares as initial stake, you would need to buy 50 shares per year to reach your goal. And you would have to compensate for the fact that those purchases are done at a different price than the initial price. Where would the money come from? From the excess equity buildup; as price rises, you use the paper profits to buy more shares. For example, take $100,000 invested in the Buy & Hold and having 10% compounded return over the 20 year investment period (the secular market average). This will grow your portfolio to $ 672,750; of this total, $ 572,750 is in paper profits that have gone unused. The Alpha Power methodology will use part of this excess equity to buy more shares and thereby achieve a higher return than the Buy & Hold. It will even find boosters, enhancers, and accelerators to improve performance even further. The main idea is to use the excess equity buildup instead of letting it go to waste.

## The Original Paper

The original **Alpha Power paper** provides the basic understanding of the method in action. The first objective was to accumulate shares long-term at a compounded rate using the profits generated by the rise in the stock price. The accumulation process itself could be controlled to a great extent using mathematical equations.

My first attempts at controlling functions were of the linear type. They represented an increase in performance but it was not enough. I wanted more and on the principle that if it could be done using linear equations, it was just a small step to start using quadratic or exponential equations. Going exponential was a better idea, at least in the beginning it surely sounded more profitable.

## Going Exponential

From linear, I went exponential! And from there, the method progressed to the point where it became a whole trading system in itself, a process that could be controlled, automated, and which could produce results that would very easily outperform the Buy & Hold. The original method was generating alpha.

The idea was to increase the inventory on hand at a delayed growth rate: using part of the accumulating profits to acquire more shares. This way, the terminal wealth would grow as the product of two exponentials and part of the excess equity buildup would be put to more productive use.

Then, by adding a short-term trading component you could push performance higher.

And having the stock inventory building up over time, you could overlay a covered call program which would also have the ability to push returns higher.

Here in this last equation, the accumulation, trading, and covered call programs have been converted to their respective rate of return contribution to the wealth function.

## Is This The Limit?

I do not think so. You could add leverage and incremental position sizing which would increase the bet size as the portfolio increases in value.

The above equation, the improved Alpha Power trading equation, has quite a few components contributing to the overall performance. All of which when taken separately can boost performance. When taken all at once, they have an exponential multiplicative effect except for the leverage factor which is linear.

When looked as a whole, the last equation represents the new Alpha Power trading method which is designed to do the following:

- Accumulate shares over the long term at an exponential rate
- Trade short to mid-term market cycles over its inventory accumulation program
- Scale in and out of positions as a way to average in and out
- Increase its scaled position sizing as a function of portfolio growth
- Run a covered call program over its increasing inventory
- Increase its incremental bet size over time according to portfolio size
- Add leverage to boost performance
- Reinvest part of the profits generated by the accumulation, short-term trading, and covered call programs into accumulating more shares which in turn generate more profits to be reinvested in accumulating more shares…
- The more a stock rise in price, the more all these functions push performance higher.

Each programmed function can contribute to the overall performance as compared to the Buy & Hold. Should the price of a stock not rise, its inventory stays the same or declines. All this will result in having the biggest positions in the highest rising stocks in the portfolio while having the smallest bets on the worst performers. The whole process acts as a portfolio asset allocation function.

## The Jensen Modified Sharpe

The **Jensen Modified Sharpe paper** provides the mathematical backdrop for the accumulation program and part of the position sizing functions. On pages 30 to 33 is provided the equation set needed to determine the required capital, the quantity that will be purchased, and the profit that will be generated based on the price differential. The first derivative of the required capital equation will even give at what price the maximum capital requirement will be.

Based on the equations, the method starts by taking a small initial bet. If the price increases, other small bets may be triggered. Should the price not rise, no additional bets are made, and should the price fall; a stop loss might be generated on the small bet.

In the beginning, because of the small initial bets, portfolio volatility is greatly reduced as the majority of the portfolio is still in cash. With a rising price, more shares can be bought since your position already shows a profit. With time stocks will get to a point where the inventory on hand is the same as the initial quantity invested in the Buy & Hold strategy. Both methods have the same equity on hand. But the game does not stop there. While the Buy & Hold might stand still (quantity-wise), you keep on accumulating shares as prices continue to rise. You even get to a point where the added profit generated by the ongoing increasing inventory is more than enough to pay for the shares being added to the portfolio as if the market was paying for your accumulation program. Again see the **Jensen Modified Sharpe** paper for a more elaborate view.

## Alpha Power Trading Methodology

Using the **Alpha Power** trading methodology, you pre-set what you want to get out of the market from the start. You put it in mathematical form, equations that govern your trading behavior. Should the price behave in such a fashion as to run the course of your preset equations then you would have known in advance the sum of profits that would have been generated. When prices behave at a lesser price differential, they see their portfolio weight decline. The method rewards the best performers the most.

You want more profits; you raise your objective functions knowing beforehand how much more capital will be required to accomplish the task as well as how much profits might be generated. Again, the **Jensen Modified Sharpe** paper provides the governing equations on pages 30 to 33.

When considering all this from the point of view of my last paper: The Trading Game, any asset could be chosen to be part of the portfolio. In fact any asset at all that can be bought using the portfolio equity buildup, that can be sold when you want to and that can appreciate in time could do the job.

## Trading Philosophy

It becomes a trading philosophy where instead of trying to predict every market move, you sit back and wait for the market to respond to your pre-set request. Your participation in the market is on your terms. You have designed your own game within the game. When a price triggers a stock purchase you know it is based on your holdings increasing valuation and you know that passed a certain price, it’s the market itself that will be footing the bill.

Your equations govern your trading behavior. Non-performers are eliminated as a side effect as they represent only small bets on losing trades. Whereas, the best portfolio performers have their positions size increase in proportion to their advance. This is not just buying low and selling high. It is: buy low. No, it is: just buy), buy higher and higher and higher. But first, let the market prove that it has reached the higher price level.

So, how high can you push your long-term portfolio return? I would say, quite high and on your own terms. I am still in the implementation phase. All the tables presented thus far only deal with the accumulation and position sizing algorithms. In all the tests provided, there was no leverage, no incremental bet sizing (all trades were for 5k), and no covered call program implemented. Only the rudiments of a short-term trading method were applied.

This implies that, based on the improved Alpha Power equation, higher performance levels can be reached, and from my current tests, I definitely have to say yes.

Created on ... May 19, 2011, © Guy R. Fleury. All rights reserved.