Game Theory

Originally published 1/29/09

Remember the “battle of wits” between Vizzini and Westley in The Princess Bride?

Man in black:  [turning his back, and adding the poison to one of the goblets]  Alright, where is the poison?  The battle of wits has begun.  It ends when you decide and we both drink – and find out who is right, and who is dead.
:  But it’s so simple.  All I have to do is divine it from what I know of you.  Are you the sort of man who would put the poison into his own goblet or his enemy’s? Now, a clever man would put the poison into his own goblet because he would know that only a great fool would reach for what he was given.  I am not a great fool so I can clearly not choose the wine in front of you…But you must have known I was not a great fool; you would have counted on it, so I can clearly not choose the wine in front of me.
Man in black
:  You’ve made your decision then?
:  [happily] Not remotely!  Because Iocaine comes from Australia.  As everyone knows, Australia is entirely peopled with criminals.  And criminals are used to having people not  trust them, as you are not trusted by me.  So, I can clearly not choose the wine in front of you.
Man in black
:  Truly, you have a dizzying intellect.
:  Wait ’till I get going!!  …where was I?
Man in black
:  Australia.
:  Yes! Australia!  And you must have suspected I would have known the powder’s origin,so I can clearly not choose the wine in front of me.
Man in black
:  You’re just stalling now.
:  You’d like to think that, wouldn’t you!  You’ve beaten my giant, which means you’re exceptionally strong…so you could have put the poison in your own goblet trusting on your strength to save you, so I can clearly not choose the wine in front of you.  But, you’ve also bested my Spaniard, which means you must have studied…and in studying you must have learned that man is mortal so you would have put the poison as far from yourself as possible, so I can clearly not choose the wine in front of me!
Man in black
:  You’re trying to trick me into giving away something.  It won’t work.
:  It has worked!  You’ve given everything away! I know where the poison is!

The convoluted reasoning employed by Vizzini is an example of the type of projection that we all use whether playing a game of rock paper scissors or negotiating the price of a car or bidding for an item on Ebay.  Before taking action, we contemplate what action our adversary expects and how that expectation may counter our plans.  In the meantime, our adversary is going through the same process.  Or maybe not:

Man in black:  You’re trying to trick me into giving away something.  It won’t work.
Vizzini:  It has worked!  You’ve given everything away!  I know where the poison is!
Man in black:  Then make your choice.
Vizzini:  I will, and I choose…[pointing behind the man in black] What in the world can that be?
Man in black:  [turning around, while Vizzini switches goblets] What?! Where?! I don’t see anything.
Vizzini:  Oh, well, I…I could have sworn I saw something. No matter.  [Vizzini laughs] Man in black:  What’s so funny?
Vizzini:  I…I’ll tell you in a minute.  First, lets drink, me from my glass and you from yours.
[They both drink] Man in black:  You guessed wrong.
Vizzini:  You only think I guessed wrong!  That’s what’s so funny!  I switched glasses when your back was turned! Ha ha, you fool!!  You fell victim to one of the classic blunders.  The most famous is never get involved in a land war in Asia; and only slightly less well known is this:  Never go in against a Sicilian, when death is on the line!
[Vizzini continues to laugh hysterically.  Suddenly, he stops and falls over.  The Man in black removes the blindfold from the princess.] Buttercup:  Who are you?
Man in black:  I’m no one to be trifled with.  That is all you’ll ever need know.
Buttercup:  And to think, all that time it was your cup that was poisoned.
Man in black:  They were both poisoned.  I spent the last few years building up immunity to iocaine powder.

Vizzini’s fatal flaw was that he was fooled into playing a different game than Westley.  By accepting the challenge, he had already lost.

As investors, we do this too.  How many times have we been advised to buy ‘good’ companies and hold them forever?  But companies are not organic organisms, divinely imbued with good business sense, they are managed by people that have the same talents and flaws as other people.  Bank of America was a good, seemingly solid company until management made a series of astonishingly bad acquisitions.  Cisco and Intel and Microsoft are good companies, in the sense that they are profitable and dominant in their respective industries, but hold forever?  According to my calculations, over the last ten years, the best performer of the three has produced a total return of -37%.  Investors inclined to believe in the buy & hold philosophy should know that market indices like the S&P 500 or the Dow Jones Industrial Average do not necessarily reflect that same philosophy.

An interesting bit of research* was recently published that examined the substantial difference between the behavior of stocks and the behavior of a stock market as expressed by an index – in this case the Russell 3000 (the Russell 3000 is comprised of the 3000 largest publicly traded companies in the U.S.)  The research covered the period of 1983 – 2006 and examined every stock that traded on a major U.S. exchange during that period, including delisted stocks.  By using filters to find every stock that would have qualified for the index at some point during this period, they ended up with approximately 8,000 names.   Here are a few highlights from the study:

  • 39% had a negative lifetime total return
  • 18.5% of stocks lost at least 75% of their value
  • 64% of stocks underperformed the Russell 3000
  • 25% of stocks were responsible for all of the market’s gains
  • The average annualized return for all stocks was -1.06%

Now, 1983 – 2006 was a pretty good stretch for the market, so how could it be that the average annualized return for all stocks was negative?  The Russell 3000, like other well known stock indices, is weighted by market capitalization.  Meaning, a larger (more valuable) company makes up a larger percentage of the index than a smaller company.  For example, Exxon Mobil currently represents 4.41% of the index, while over 2500 of the remaining 3000 companies each represent less than 0.05%.  So as a stock declines in value, its impact on the index becomes less noticeable and, at some point, if it continues to decline, it is replaced in the index by another company.  This is in contrast to the roughly equal position sizes taken by most individual investors when they build a portfolio.  The result is a classic illustration of “survivorship bias” where the negative influence of the losers has a smaller impact than the positive influence of the winners.

The Dow Jones Industrial Average (DJIA) is a price weighted index comprised of 30 stocks.  According to the Dow Jones Co., the 30 components of the index are chosen, maintained and reviewed by editors of the Wall Street Journal.  There are no rules that govern when or why a company is removed from the index and why another company is added as a replacement.  A review of the history of the composition of the DJIA shows changes occurring with great regularity going back to it’s inception in 1896, most recently in September of 2008 when Kraft Foods replaced AIG.  In February of 2008, Altria and Honeywell were replaced by Bank of America and Chevron.  The rationale for removing Honeywell?  “Because it is the smallest company in the index by revenue and profit and because industrial companies have become less important to the stock market.”   This is obviously not a buy & hold strategy.

In addition, because the DJIA is price weighted, a $1 decline in GM (a 29% loss) has the same impact on the performance of the index as a $1 decline in the price of IBM (an 11% loss).  Currently, four of the thirty stocks in the index are priced below $10/share.  Due to the anachronistic way of measuring the Dow, if all four stocks (Citigroup, Bank of America, Alcoa & GM) went to zero, the net impact to the DJIA would be a rather meaningless loss of around 160 points.

It appears that those 100 year charts of the stock market with the pleasingly steady upward tilt may be more representative of a constantly changing selection of stocks with positive momentum than of stocks in general.  The question that investors must ask themselves is, “am I continuing to hold this particular company because the fundamentals demand it, or am I holding it because the market always comes back?”  If it is based on the macro effects of the market in general, then we have to wonder if we are playing the same game we thought we were.

*Crittenden, Eric & Wilcox, Cole (2008).  “The Capitalism Distribution: Observations of individual common stock returns, 1983-2006”  Electronic copy available here (link opens a .pdf file).