Market Reaction and Portfolio Concentration

I was talking with my coworker the other day about the differences between arithmetic and geometric means. Arithmetic means are the averages that we are familiar with, whereas geometric means come into play in the compounding of returns. For example, let's say one of our stocks went up 2X in Year 1, and 4.5X in Year 2. The geometric return would be 3x ( square root [ 2 * 4.5 ] ). Equivalently, we could have had another stock with the same geometric returns and achieved the same results over two years (3 * 3 = 2 * 4.5).

With that being said, the differences between the two types of means differs greatly and changes with how we construct our portfolios. For the sake of simplification, let's assume that all financial assets consist of numerous fair independent coinflips that occur daily, with a 50% positive return for heads, and a 40% loss for tails. Although we can allocate our portfolio into any number of these assets, we must remain fully allocated and play everyday. What is the optimal strategy?

If we compute the two means, we see they differ greatly. The arithmetic mean is +5% ( [+50 - 40] / 2), whereas the geometric mean is -5.1% ( sqrt[ 1.5 * .6 ] ). To achieve the arithmetic mean, we would divide our bankroll into as many bets as possible, so that our sample means would converge to the population mean. This is the so-called "free lunch" of diversification. To achieve the geometric mean, we would place all of our bankroll on a single bet, and continually parlay the results of those coinflips into more coinflips, so that over a long enough series of days, our returns would approach the geometric mean. So is there ever a scenario where we would not want to diversify?

I got the idea that "it depends" from reading Bill Miller's Q4 2006 Letter to Investors. In it, he explains the reason why his streak of beating the S&P 500 was finally broken, and his mistakes of overly concentrating the portfolio at the wrong time.

If we go back to our earlier example, let us now assume that instead of numerous similar bets, there are different classes of coinflips we can make, and that they are limited in number. Class A coins offer +100% returns for heads, -60% returns for tails, and there are only 2 of them. Class B coins offer +20% returns for heads, -10% returns for tails, and there are 40 of them. Doing the math, we see that Class A has an arithmetic mean of +20% and a geometric mean of -10.6%. Class B has an arithmetic mean of +5% and a geometric mean of +3.9%. The arithmetic means of Class A clearly surpass those of Class B, but there aren't enough of them to properly achieve the population average.

So now the question of diversification / concentration is largely a function of opportunity diversity and becomes a conversation of tradeoffs between diversifying to achieve the geometric return, versus striving to achieve a higher arithmetic return through concentrating in rare "good bets". If your ideas are mostly similar and no ideas are clearly better than others, then diversify as much as possible.

The recent market events have introduced greater variability in the risk / returns profiles of my ideas, which has manifested in some positions being untouched whereas others have become hammered. Given an assumption of unchanged fundamental business value, I think now is the time to concentrate the portfolio, increasing positions in those ideas that seem 70+% undervalued (ie multi-bagger prospects) and exiting positions with only 30-40% undervaluations. Although this will almost necessarily introduce greater volatility in portfolio returns, I am confident that these actions will bear fruit 1-3 years hence.

Notable Quotes

"All life demands struggle. Those who have everything given to them become lazy, selfish, and insensitive to the real values of life. The very striving and hard work that we so constantly try to avoid is the major building block in the person we are today."
-- Ralph Ransom

"Restlessness and discontent are the first necessities of progress."
-- Thomas Edison

"All progress is based upon a universal, innate desire on the part of every organism to live beyond its income."
-- Samuel Butler

"Humanity has advanced, when it has advanced, not because it has been sober, responsible, and cautious, but because it has been playful, rebellious, and immature."
-- Tom Robbins

"Progress is made by lazy men looking for easier ways to do things."
-- Robert Heinlein

"Thinkin of a master plan, Cuz ain't nuthin but sweat inside my hand"
-- Rakim

"Ain't only three things to gambling: knowing the 60-40 end of the proposition, money management, and knowing yourself. Even a donkey knows that."
-- "Puggy" Pearson

"Things may come to those who wait, but only the things left by those who hustle."
-- Abraham Lincoln

"Go confidently in the direction of your dreams."
-- Henry David Thoreau

"Nothing focuses the mind better than the constant sight of a competitor who wants to wipe you off the map."
-- Wayne Calloway

"We are not here merely to make a living. We are here to enrich the world, and we impoverish ourselves if we forget this errand."
-- Woodrow Wilson

"The Longer I live, the more I realize the impact of attitude on life. Attitude, to me, is more important than facts. It is more important than the past, than education, than money, than circumstances, than failures, than successes, than what other people think or say or do. It is more important than appearance, giftedness or skill. It will make or break a company, a church, a home, or a chorus. The remarkable thing is we have a choice everyday regarding the attitude we will embrace for that day. We cannot change our past, we cannot change the fact that people will act in a certain way. We cannot change the inevitable. The only thing we can do is play on the one string we have, and that is our attitude. I am conviced that life is 10% what happens to me and 90% how I react to it. And so it is with you, we are in charge of our attitudes."
-- Charles Swindol

"Empty pockets never held anyone back.
Only empty heads and empty hearts can do that."
-- Norman Vincent Peale

"Our deepest fear is not that we are inadequate. Our deepest fear is that we are powerful beyond measure. It is our light, not our darkness that most frightens us. We ask ourselves, Who am I to be brilliant, gorgeous, talented, fabulous? Actually, who are you not to be? You are a child of God. Your playing small does not serve the world. There is nothing enlightened about shrinking so that other people won't feel insecure around you. We are all meant to shine, as children do. We were born to make manifest the glory of God that is within us. It is not just in some of us; it is in everyone. And as we let our own light shine,we unconsciously give other people permission to do the same. As we are liberated from our own fear, our presence automatically liberates others."
-- Marianne Williamson

"I've never been poor, only broke. Being poor is a frame of mind.
Being broke is only a temporary situation."
-- Mike Todd

"Wait for a miracle and it will never come. Take responsibility and you'll invite a miracle."
-- Laura Berman Fortgang

"The mind once stretched by a new idea, never returns to its original dimension."
-- Oliver Wendell Holmes

"Making mistakes simply means you are learning faster."
--Weston H. Agor

"If you really want to do something, you'll find a way; if you don't, you'll find an excuse."
-- Unknown

"A gem cannot be polished without friction, nor a person perfected without trials."
-- Chinese proverb

"Ignorance is the night of the mind, but a night without moon and star."
-- Confuscious

"Better a diamond with a flaw than a pebble without."
-- Confucius

"You can't lose what you don't put in the middle...But you can't win much either."
-- Mike McDermott (Rounders)

"Circumstance does not make the man, it reveals him to himself. Men do not attract that which they want, but that which they are. Man is manacled only by himself."
-- James Allen

"The stock market is filled with individuals who know the price of everything, but the value of nothing."
-- Philip Fisher

"Conversation enriches the understanding, but solitude is the school of genius."
-- Edward Gibbon

"It is your work in life that is the ultimate seduction."
-- Pablo Picasso

"In my whole life, I have known no wise people (over a broad subject matter area) who didn't read all the time - none, zero."
-- Charlie Munger

"It had long since come to my attention that people of accomplishment rarely sat back and let things happen to them. They went out and happened to things."
--Elinor Smith

"High aims form high characters, and great objects bring out great minds."
--Tryon Edwards

"True happiness is not made in getting something. True happiness is becoming something. This can be done by being committed to lofty goals. We cannot become something without commitment."
--Marvin J. Ashton

"There is a close connection between getting up in the world and getting up in the morning."
--Anonymous

"The man who is born with a talent which he is meant to use finds his greatest happiness in using it."
--Johann von Goethe

"An individual who doesn't consciously select his goals is not really in control of his life. He is controlled. Without really knowing it, he is controlled by goals imposed by outside pressures (the expectation of other), or by habits (procrastination), or by desires (the longing to be honored and admired) and so on."
-- Anonymous

"Beaten paths are for beaten men."
--Eric Johnston

"The world turns aside to let any man pass who knows whither he is going."
--David Starr Jordan

"First, the only certainty is that there is no certainty. Second, every decision as a consequence is a matter of weighing probabilities. Third, despite uncertainty we must decide and we must act. And lastly we need to judge decisions not only on the results, but how those decisions were made."
-- Robert Rubin

"We cannot promise to beat the market or even to match the market. But we can promise that nobody will care more about your money and work harder than the team that we have assembled."
-- Bill Miller

"When we think about the future of the world, we always have in mind its being where it would be if it continued to move as we see it moving now. We do not realize that it moves not in a straight line… and that its direction changes constantly."
-- Ludwig Wittgenstein

"The thoughts of others
Were light and fleeting,
Of lovers' meeting
Or luck or fame.
Mine were of trouble,
And mine were steady,
So I was ready
When trouble came."
-- A.E. Housman

"Entrepreneurship is not a civilized joust. It is streetfighting."
-- James Hong

"Pray not for lighter burdens but for stronger backs."
--Theodore Roosevelt.

Fish or Cut Bait

In light of recent events, this post seemed appropriate. I used to read the Motley Fool Message Boards (mostly Berkshire posts) everyday for a year or two, and it was instrumental in my education. They've reopened for free on an invitation-only basis. Let me know if you would like one by leaving a comment. There was mostly chatter on this board, but from time to time there were some really inspired posts. I've reposted it here for those without access. Special thanks to hartmanbirge, go here for the original post.

A lot has happened the last two months or so and at least to me the world is a far clearer, more exhilarating picture. I've had some time to do some thinking and I was struck by several themes. Bottom Line Up Front (or BLUF as we call it): An investor, an Army officer, a corporate CEO, a surgeon, a lawyer….you name the profession… if you're a professional then your purpose in life is not to manage – your purpose is to lead (people, change, emotions, whatever..). I've heard it said that a true professional is someone dedicated to their craft and someone who possesses a certain professional ethos. I think that should be taken one step further. Though professions vary greatly in what they represent I think it fair to say that all true professionals have a competitive drive (more with themselves than anything else) to prove themselves in great difficulty. They dedicate their lives to learning as much as they can about their circles of competence. And I also think it fair to say that the true professionals thrive best when chaos surrounds them… when “all others are losing their heads” as Buffett once said. I am convinced that there is a certain type who actually looks forward to chaos – it's where they're most comfortable. It's where they THRIVE. They've spent years and years studying and acquiring knowledge so that they can APPLY what they've learned and practiced upon a chaotic situation and get the exhilaration of a “win” - however “winning” is defined in their circle. They run with gusto to the sound of the guns. In order to do this there are several pre-conditions which must be met in order for our hero to do his or her thing:
1. They have to have a thirst to learn the craft and apply themselves to this quest voraciously – done during the “boring” times of status quo.
2. The above most likely requires an inner competitive drive – most likely with a high internalized set of standards
3. They need to have a “detached ego” which allows them to execute rationally rather than emotionally. (Recommend watching movie classic 12 O'Clock High with Gregory Peck)
4. They're beholden to none and have a personal center of gravity based on principles and values rather than external things
5. But ultimately they thirst for a set of external conditions that allow them to apply the above

In reading about George Marshall (the ultimate rational being) I note that he suffered in long obscure silence for decades (34 years) – plugging away…acting with integrity and honor…avoiding the limelight… doing the right thing. There was a time when he thought of leaving the Army. A Major at the time, his salary was just over the American average of $750. External opportunity arrived in the form of a job offer from a partner at JP Morgan – salary $30,000. Marshall was severely tempted. In the end of course he turned down the job offer that was pushing 40 times his pay. Why? I spent a few weeks mulling over that question. My only conclusion is that Marshall saw what was looming on the geo-political scene. He had already made a name for himself in WWI and had a wealth of knowledge and experience. He knew the craft so to speak. It is my conclusion that he thirsted for the chance to rationally apply it upon a chaotic scene and missing the chance would be the worst form of hell on earth. He had a deep sense of obligation and duty and due to his gifts to manage the chaos he had a duty. Because he had a grounding of values and principles, no amount of money or family riches could pry him from this. So he turned it down and waited patiently for opportunity – not financial – but the chance to apply his learned rationality upon chaos. Material possessions (to include money) as a central focus would have been a hollow outcome. Once given power as Army Chief of Staff he basically ripped the existing Army careerist culture to shreds and built a wartime Army full of mission oriented leaders who embraced extreme difficulty – (not at all unlike what's happening today I might add).

What's this have to do with investing? A lot I think. The above “rules” are the same no matter what the profession. Professionals are built for chaos, ambiguity, uncertainty, and extreme difficulty. Good times and relative “ease” though sometimes a welcome respite ultimately become the definition of a living HELL. Ask yourself if you ever felt any satisfaction getting an A on a test or a paper if the entire class did. No. Maximum satisfaction comes when you're the only one to get an A. There's a standard. There's a great difficulty that has been mastered and overcome. There is stratification. There are winners and losers. There is “justice” – those who took the easy way out and didn't study get “punished” by their poor grade. Grade inflation in a sophomore class or its stock market equivalent where all equities perform well (or fund managers) is the worst form of hell (Socialism might do well to learn this truth). To the master of the craft - There is a desperate NEED (and secret “want”) for external difficulty in order to apply the expertise acquired through internal drive. When Katrina hit New Orleans I noted two very distinct reactive differences. One type (with a need for external calm and status quo) was devastated (career bureaucrats). The second type I think saw the chaos as a challenge and call to perform (LTG Honore). The difference in response between the two was startling…

And what of now? I think that any professional money manager (or dedicated individual investor who gets turned on by the game) who gets a sense of “fear” or trepidation or worry on what is I think shaping up to be a chaotic situation in the not too distant future is in the wrong profession or passionate hobby. I think there should almost be a CRAVING for financial chaos, markets run amok, and a slew of distraught Wall Street hedge fund narcissists searching for answers that never materialize. Finally, at long last…. After two decades where the whole damn class got A's on their term papers (individual stock analysis) there looks to be coming a day where the true craft and sound tested principles of rationality can be applied. Where the rising tide can't lift all the boats anymore. Perhaps it sounds callous to be seen as “cheering” for chaos but that's not it at all. The chaos is going to come with or without anyone's cheering. Equilibrium theory tells us that good times will be followed by bad (the longer and greater the good times then the inverse) – it's going to come. The only difference is in how it's rationally dealt with on a very individualized level.

This is no different to the “competitive destruction” thread – where the thesis that chaos affords an environment of stratification with winners and losers. And much to my satisfaction take a look at what's happening in the reinsurance market where others are running for the hills – leaving Berkshire almost alone to take on the risk and get enormous premiums (what was it? Half the potential insured loss? Amazing)… That's what Berkshire Hathaway was built and designed for. It wasn't built for the whole damn class getting an A…. it was built for a real bitch of a final exam… Higher inflation? Higher interest rates? Rapidly falling dollar? Dollar's precarious position as world's reserve currency? Crashing emerging markets? Exploding ARM debt servicing? Falling housing market? Automatized sell orders on market ETFs which bring everything down? Tons of conflicting “activity” in options and futures markets? Confused messages from new Fed Chairman? Threats by Iran to strangle global oil supply? Exploding oil prices? Mass restated earnings at Fannie Mae? Corporate corruption in executive suite and on the passive boards? Narcissistic CEO at Home Depot? Predictions of huge hurricane seasons for at least next decade? Trade deficits? Rising protectionism? Nationalization of oil infrastructures in South America? Rise of socialist and populist impulses (windfall oil tax anyone?) in America? American manufacturing sector on brink of destruction? Pension calamities across American industrial base? The tapped out and hyper-indebted American consumer who essentially is pulling the rest of the world on his shoulders? Things that are supposed to be non-correlated are all moving down? Alas…Derivatives meltdown potential? Al Qaida and their threat to our way of life, social harmony and stability (who would have thought that peaceful Canada would be major target)? I think that about covers it for the questions posed on this final exam taught in this hypothetical yet very real 401 class of reality that the world is teaching us. To put ourselves in the right frame of mind perhaps the movie Cinderella Man is a good primer….

Either the above and where it might lead turns one on…. or perhaps fills one with 1) serious doubts bordering on panic or 2) apathy bordering on denial (the most prone to actually panic if and when the time comes). Not at all unlike New Orleans - (You bet those levees will hold! Up to a CAT 3 for sure). Not a darn thing any of us can do to change the reality. All we can do is to properly define it and prepare as best we can. Perhaps this brewing storm never materializes – certainly that's possible – but then we probably muddle along an eternity with stagflation which may just be a worse outcome. A booming stock market? Heck we just had that – not very likely to happen again anytime soon. One might ask oneself how might you feel if your portfolio drops 50% and your purchasing power drops another 30%? Not possible? Hmmmmm… I think if one can come to real grips with that possibility now, or something even more dire – with a serious dose of self honesty – then you're built for leading through the worst of the potential chaos and in fact may even be looking forward to the “test.”

Farmers Capital Bank Corporation Tender Offer

I was scanning some of the SEC feeds that I receive and this notice caught my eye.
[SEC Filing]
[Press Release]

"Farmers Capital Bank Corporation (Nasdaq: FFKT; "Farmers Capital") announced today the commencement of a modified "Dutch Auction" tender offer, approved by its Board of Directors, to repurchase up to 550,000 shares of its common stock (representing approximately 6.97% of its outstanding common stock) at a price not greater than $35.00 and not less than $31.00 per share. ... The tender offer is expected to commence on July 19, 2007 and to expire, unless extended, at 12:01 a.m. (Eastern Daylight Savings Time) on August 16, 2007."

With shares available for approximately $29.90, this deal offers a return of 3.7-17.1% for an approximately 3 week holding period. Since this offer includes an odd-lot preference I purchased 99 shares today and immediately tendered them. This kind of arb provides some stability in today's volatile markets, although I did leave some money on the table with the EXPE deal ($29 tender price, exited for $27.70).