Let's Make a Deal

Let’s Make a Deal?

One of my favorite math problems or brain teasers is the Monty Hall Problem.  Named for the host of the game show, Let’s Make a Deal, this problem is interesting precisely because it is so counterintuitive.  It involves probabilities, which are by nature confusing to human beings, but it also involves re-evaluating decisions after new information emerges, which is fascinating to me.  The problem became famous after it was posed to Marilyn vos Savant in her “Ask Marilyn” column in Parade magazine in 1990.  Here is the question as it was posed to her:

Suppose you’re on a game show, and you’re given the choice of three doors:  Behind one door is a car; behind the others, goats.  You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat.  He then says to you, “Do you want to stay with Door No. 1, or switch to Door No. 2?”  Is it to your advantage to switch your choice?

Intuitively the probability of the car being behind door 1 or 2 is 50/50, but Marilyn told the reader that you should always switch.  She determined that there was only a 1 in 3 chance that the car was behind the door you originally chose, but a 2 in 3 chance it is behind the door you didn’t choose.  If that seems confusing to you, you wouldn’t be alone.  Her answer ruffled quite a lot of feathers.  It received numerous responses of incredulity and insult from some extremely well regarded mathematicians and university professors.  But intellectually Marilyn was no slouch herself.  From 1986 to 1989 she held the record for the highest recorded IQ ever.  So, yeah, maybe those guys who questioned her answer were out of their league.

Here is a simple illustration of the problem which helps clarify the answer:

 What changes the odds is the information revealed by the host, namely what is behind one of the doors not chosen.  At the outset, the odds were as presumed 1/3, but after the first door revealed a goat, the odds for the unchosen mystery door doubled.

The stock market seems to be in a similar position right now while waiting for word on a China/US Trade Deal and today’s hope for a “Brexit Deal.”  Tweets and reports of deals being hatched or made on both fronts has sent the market exploding higher by over 4.25% since the market intraday lows on October 3^rd –and this is just on talk and hope.  All this market enthusiasm for a deal seems to portend good things for the market if/when deals are made.  But could this be a similar scenario posed by the Monty Hall Problem?

Buy a Creeper Sell a Leaper?

Years ago, when I traded options at the Chicago Board Options Exchange a colleague of mine, Mark Westcott, was fond of saying “Buy a creeper sell a leaper.”  Usually he would announce this after the market had either grinded higher all day, or after it completely reversed early gains and finished lower for the day.  Now maybe it was the fact of him saying this only on days when events actually unfolded as such and not on days when it did not, but it did seem to ring true more times than not.  I mean it’s not guaranteed, but many times when markets gap substantially higher, or “run up” quickly, they fail to sustain the gains they acquired.  Maybe it’s not 100% of the time, but maybe it’s more like 66% of the time—like switching doors on Let’s Make a Deal. 

Until now I’d never considered the connection between markets mean reverting after explosive up moves and the Monty Hall Problem, but perhaps there is a connection because perhaps the two share similar driving factors.  And maybe the “buy the rumor, sell the news” market adage is also like Monty Hall revealing the goat behind Door No. 3 because they both involving the revealing of information.

Markets have now priced so much optimism into “Let’s Make a Deal” weekend, that perhaps the only reasonable assumption is that Deal or No Deal, once the dust settles from the endless trade war and Brexit drama, the market will be left to focus on the economic fundamentals of an aging expansion and the remaining tenure of the longest bull market in history. 

It may seem easy to say, “The market likes the prospects of a deal being made, so let’s bet that Trump makes a deal so the market goes higher.”  But therein lies the paradoxical scenario: 2 out of 3 possibilities lead to a market that may not go up any further.  Door 1 and 2 may hold goats, but of a different breed.  Door 1 has the no deal goat, which will most likely send markets lower, and door 2 holds the prospect of deal, but markets “taking profits.”  Either way, to me, expecting much further run up in the market on the back of trade deal or Brexit deal seems to by only 1 in 3.   

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