# Monty Hall and Door Number 1, 2, or 3

The Three Prisoners problem appeared in Martin Gardner’s “Mathematical Games” column in Scientific American in 1959. It is mathematically equivalent to the “Monty Hall problem” with the car and goat replaced with freedom and execution, respectively, and equivalent to, and presumably based on, Bertrand’s box paradox.

Three prisoners, A, B and C, are in separate cells and sentenced to death. The governor has selected one of them at random to be pardoned. The warden knows which one is pardoned but is not allowed to tell. Prisoner A begs the warden to let him know the identity of one of the others who is going to be executed. "If B is to be pardoned, give me C's name. If C is to be pardoned, give me B's name. And if I'm to be pardoned, flip a coin to decide whether to name B or C." The warden tells A that B is to be executed. Prisoner A is pleased because he believes that his probability of surviving has gone up from one third to one half, as it is now between him and C. Prisoner A secretly tells C the news, who is also pleased, because he reasons that A still has a chance of one in three to be the pardoned one, but his chance has gone up to two in three. What is the correct answer?

Similarly, like Monty Hall’s “Let’s Make a Deal,” investors have a choice between door number 1, 2, or 3. Door number 1 is that the equity markets are getting ready to trade out to new all-time highs. That view is shared by one of the best quantitative strategists on Wall Street, namely JP Morgan’s Marko Kolanovic whose recent report had this tag line, “Game theory implies low risk of trade wars; if equities follow 2015 flow patterns, new highs may come soon” (Chart 1 on page 2).

Door number 2 has it that the indices are likely to trade in consolidation mode over the next few months as they convalesce from last month’s heart attack that saw the S&P 500 (SPX/2752.01) surrender ~12% from intraday high to intraday low. However, door number 3 tells a different story, as predicted by our friend Dennis Gartman, who wrote, “This then is our WATERSHED comment; it is time to hold cash; it is time to sell rallies; it is time not to buy weakness. As T.S. Elliot said, ‘Hurry up now, it’s time.’ We can trade other things bullishly, but equities we’ll not and as the markets rally this morning we shall watch from the sidelines.”

Now Dennis is a lot smarter than we are, but we do not embrace his bearish “call.” We do, however, agree with his, “We can trade other things bullishly.” One of the areas we think you should position your portfolio for is a more inflationary environment. As our pal Rich Bernstein, of Richard Bernstein Advisors (I own his funds), writes:

Inflation expectations troughed in June 2016 (!), and have been gradually rising since then. It seems immaterial from an investment point of view whether this increase in inflation expectations is secular or merely cyclical because investors are largely ill-positioned for any increase in inflation. Chart 2 [page 3] shows that the 10-year T-note yield troughed roughly 3 weeks after inflation expectations troughed. The sizeable flows into fixed-income investments ran unabated until only recently despite the increase in yields.