Betting on El-Erian’s 25% Chance of Deflation

Mohamed El-Erian recently quantified the odds of deflation at 1 in 4, or 25%. His analogy to describe the dangers ahead seemed to be a recipe for inaction (and fear):

“…ask yourself the following question: would you accept a lift from a person who has a one-in-four chance of getting into a really bad car accident?”

Well, the answer depends on your intended destination. Are you trying to get to the grocery store or are you about to miss the deadline to claim some amazing, once-in-a-lifetime opportunity? I think implicit in El-Erian’s case is that there is nothing too enticing waiting for you on the other side of that trip.

The subtle irony of quantifying risks is that the process provides a structure and basis for action. The future remains uncertain, as it always does, but the response to current conditions becomes pretty clear. So, just for kicks, I decided to test El-Erian’s model on investing in the S&P 500.

Let’s assume that the really bad car accident is the equivalent of the index retesting its March 2009 lows at 666 within a year. That scenario seems pretty extreme to me; only very committed bears are still clinging to that case. Let’s also assume that the most likely case is that the market has a very modest gain within the next year to 1250. I picked this number because it is Goldman’s end-of-year target that was reiterated last week. As far back as December, 2009, perma-bull Abby Cohen placed a 1250-1300 range for the S&P 500, and many strategists pegged the S&P to hit 1200-1350 by the end of 2010. So I will give a nod to the bulls in the crowd by assigning a 5% chance to hitting 1350 within another year. We end up with the following (simplistic) decision tree:

25% chance of a 38% loss by August, 2011
70% chance of a 14% gain by August, 2011
5% chance of a 25% gain by August, 2011

These one-year gains may seem large but note that the S&P 500 is down 3% for the year, it is flat with the highs from last September, and the most likely case is a mere 3% gain above the highs for the year. Thus, I think my estimates for upside are very conservative.

Once we multiply this out we get an expected gain of 1% (=.25*.38 + .70*.14 + .05*.25). In other words, if someone presents us with this bet, we can expect for every dollar we put down, we will gain an extra penny at the end of a year. While the outcome is positive, it is hardly exciting enough to entice a nervous (aka risk-averse) investor to play along.

The potential upside increases the more optimistic you are, taking El-Erian’s model as a given. So, even with this 25% chance of deflation, the raging bulls should remain in a buying mood. Otherwise, El-Erian’s implicit case for inaction seems to work out pretty well.

Be careful out there!

Full disclosure: long SSO puts

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