On Optimal Portfolio II

October 26, 2011

I tried to show in my previous article that adopting a profit re-investment policy was not only possible but also a simple way to achieve an exponential Jensen ratio. The conclusion was that skill matters, and it grows with age. It's part of the very nature of an exponential time function. So the question becomes: why aren't most investors adopting such a winning strategy? Or better yet: are there ways to improve on this exponential Jensen ratio?

Just opening the door to exponential alpha may represent a major shift in modern portfolio theory. It says you are no longer bound by the efficient market frontier. That there is more out there and simple procedures can give you access to higher returns. Not only higher returns but returns increasing exponentially with time. This is almost heresy. Nobody has challenged the efficient market frontier for the past 60 years; no one has dared. All Modern Portfolio Theory is based on some form of the assumption of the efficient market hypothesis. And if markets are efficient, even under the weak form, then there is no long-term alpha generation and certainly no such thing as exponential alpha.

In my previous article, I tried to make the point that the exponential alpha was part of a reasonable explanation for Mr. Buffett's overperformance. If Mr. Buffett's alpha was just a number, then both performance lines (S&P and Mr. Buffett's) would not separate so fast or maintain a separate path for so long. The increasing separation is the result of a measurable power function. Has anyone looked at a long-term chart of KO or GE lately? Two major holdings in Mr. Buffett's portfolio which have been below their respective highs for the past decade.

Profit Re-investment Policy

The profit re-investment policy suggests that Mr. Buffett could have increased his Jensen ratio simply by re-investing more of his cash hoard in buying more companies and/or by adding more shares to his existing stock holdings. This, in turn, would raise another question: how high could an exponential alpha go?

In Part I, a simple minor change to Mr. Buffett's payoff matrix would be required to express his more aggressive stance:

Σ(H_p(1+g⁺)^(t-1).*ΔS⁺_p) Mr. Buffett's payoff matrix

where on his better stock selection process ΔS⁺_P he would have applied a higher re-investment rate (1+g⁺)^(t-1) using more of his generated profits to increase his holdings. And this would be sufficient to explain most of his added overperformance. Increasing his re-investment rate policy to g⁺ would indeed increase his overall performance.

Portfolio Control

Mr. Buffett's re-investment policy is under his control. He is the one to decide how and when to use his cash hoard. He is the one to determine at what rate it should be applied. It gives him the ability, in a way, to control where he wants to go, portfolio-wise. He knows how to control, within his portfolio size constraints, at which rate he can progress in his re-investment policies. He knows when to get his “elephant gun”.

In recent years, Mr. Buffett has declared that he might not be able to sustain his high-performance rate over the near future, mainly due to the size of his portfolio. Increasing his re-investment rate could be the answer to compensate for the increasing portfolio size since his increasing portfolio size will generate even more profits.

There is much to learn from Mr. Buffett's philosophy and investment procedures. If you want to improve on the best out there, it becomes a good thing to know first what they do. Re-investing part of his generated profits is not all Mr. Buffett does. He has other little “tricks” to improve his overall performance.

Part of the Whole Picture

I will try to give a different perspective and consider some of Mr. Buffett's investment procedures within the framework of my equations as if trying to explain his policies in my mathematical format or maybe explain mine. This way, it should provide a kind of explanation for the somewhat esoteric formulas I have given. There is nothing mysterious behind my equations; they are simply expressions of various investment policies and implementation procedures.

Mr. Buffett invests for the long term. That is his primary vision. As he says, his preferred holding period is: forever. Then, he should be doomed like the rest of us to reside close but under the efficient market frontier. If you Buy & Hold and diversify over many companies, you are bound over the long term by the same constraints as everyone else. You can't change the price data, and you have accepted not to change your holdings in an equation that has only two variables:

Σ(H_p.*ΔS_p)            Σ(H_D.*ΔS_D)             Σ(H_M.*ΔS_M) Profits
────────   →    ────────   →    ─────────    =   ────────
    H_Po*S_Po                 H_Do*S_Do                H_Mo*S_Mo Investment

As was stated in Part I, percentage-wise, performance will tend to the average secular market trend. You can make better stock selections, but it is not enough. The No Free Lunch theory will come right back to haunt you.

Investment Procedures

I'll jump right to the point. Mr. Buffett, in his arsenal of investment procedures, tries to see the whole picture. He'll re-invest some of his accumulating profits, will trade, even short-term, if he sees an opportunity, he will write covered calls, write long-term puts, and will increase his bet size as his portfolio grows.

He tries to do everything at once as long as he sees, in probability, a profitable outcome. All these investment procedures add up to provide him with a sustainable high-performance level that could be considered the envy of many portfolio managers.

In my first paper in 2007 (Alpha Power), I summarized in a single formula a trading methodology (equation #16) that tried to do everything at the same time. This equation evolved and was simplified at first to:

Σ(1+L)(1+B)^(t-1)(H_p(1+g⁺+T)^(t-1).*ΔS⁺_p);

and then to the ITRADE formula. All three provide the same answer. The ITRADE formula is simply the matrix representation of the same thing.

In recent months, I've started making more parallels with Mr. Buffett's style of investing and my simplified formula. It is not that Mr. Buffett follows my equations; I don't think he is even aware of them; it is just that it does explain or provides, at least for me, a reasonable explanation for his over-achievement. And as a consequence, also serve as reasonable explanations for what the equations do. Mr. Buffett generates exponential alpha as a byproduct of his investment strategies. As such, it is all talent, skills, and know-how that is at work.

Procedure Analysis

The table and chart below show my interpretation of what I think Mr. Buffett's investment policies do for him within the scope of my simplified equation. He might or might not have these investment policies in force, but they do fit within my view of things, each contributing to the end results. I'll try to summarize each point as I see them:

I put his Buy & Hold long-term rate of return as 15%, 5 alpha points above average. This represents a 50% increase over the average portfolio manager's performance and should be considered as a lot. His stock selection needs to be above average since price series are the same for all.
I set his profit re-investment rate at 70%. This allows the use of the major part of all the cash, dividends, and proceeds from sales to be used in acquisitions while leaving enough for emergencies and unforeseen opportunities that may present themselves.
Mr. Buffett does a little trading here and there, even short-term trading. Look at the GS preferred stock deal. I think he still holds some of the warrants on that.
He should have a covered call program in place. With such a huge inventory of shares, he could earn additional income without that much risk since he is already ready to hold for the long term. He could even rent his shares to shorters for a small fee adding more income to his account.
His bet size grew all the time. From deals valued in the tens of millions to his latest 40 billion-plus. The bet size needs to grow with the portfolio size; otherwise, managing the acquisition process would require a small army. A 40 billion deal is much less work than 400 smaller deals of 100 million each. He only has a small staff of 22, I think.
I don't think Mr. Buffett uses much leverage. He looks more like a cash person to me; in the sense that he buys when the cash is in the bank, not before. But this does not mean he does not use other forms of leverage.

When we look at the chart, we see that each item contributes to the bottom line. Little by little, each policy contributes to the overall performance. And I think that that is how Mr. Buffett can achieve higher levels of performance and succeed in maintaining them over the years. It is all a byproduct of his methodology and his skills in managing his huge portfolio. I must say I greatly admire the man.

Berkshire Hathaway Study: Growth Scenario

Berkshire Hathaway Study: 20-Year Chart

In the first few years, it is hard to distinguish or separate the contribution of each of his investing procedures. But as time progresses, the picture becomes much clearer.

Improve on What?

That is the question.

In this note, I've presented my equation as an explanation for Mr. Buffett's style of investing. My equation does not describe all he does but covers enough to provide a relatively close representation of his investment philosophy in action. It is not that my equations are out of this world. They are merely a representation of trading procedures and their consequences over time. And I am not making any suggestion that Mr. Buffett follows my equations either. They only serve for me as an explanation of what he might do, currently does, or has done.

The ITRADE formula is simply a representation of trading policies in action, procedures that follow set rules of execution with a long-term view of their own objectives. The formula says that by the choice of investment policies and trading procedures, a portfolio manager cannot only achieve positive alpha, but he/she can aim for exponential alpha. And that is a major statement. You can set from day one your investment policies, what will be your trading rules and how you will monitor their progress over time. It is your knowledge of what you intend to do that will help you reach the higher levels of performance.

Based on the simplified equation, we know that a profit re-investment policy is a simple way to increase performance and can already start to generate some low exponential alpha. I think it is the first requirement and probably the easiest to implement. It has the advantage of using the equity buildup which otherwise would sit idle in the portfolio.

However, it is by adding a short-term trading procedure that a portfolio can achieve much higher performance levels. It becomes a way of pumping cash into the account that can be used to accumulate even more shares than the re-investment policy alone.

This can have a major impact on portfolio performance.