Pascal’s Wager for the Market

As we start 2015 with a market swoon and the prospect of a zero interest rate policy out to 2016, we find ourselves stuck in a state of cognitive dissonance.

On the one hand, economic indicators are signalling a strong state to the US economy. The unemployment rate has fallen while GDP has marched higher. Despite recent stock market volatility, the S&P 500 index is up over 200% since the low in March 2009 when the Fed first embarked on QE. These are indicators of a booming economy.

On the other hand, inflation is getting crushed everywhere. Government bonds are surging. The price of oil is plummeting. Markets are speculating on whether the ECB will signal the beginning of its own QE program in its January 22nd meeting. These are indicators of a market in crisis.

These events do not normally occur near one another, let alone simultaneously. Investors are right to be confused. Diverging evidence explains the current high level of volatility of volatility (VVIX). Vol of vol is an important higher dimension market which measures traders’ certainty in their own collective perceptions. The VVIX is currently at levels last seen in October 2014, when stock markets experienced a violent decline and we saw the Treasury Flash Crash. This suggests a high degree of uncertainty within the market as to the future.

Vol of Vol is an important higher dimension market which measures traders' certainty in their own collective perceptions

Vol of Vol is an important higher dimension market which measures traders’ certainty in their own collective perceptions

The decision traders face now is which reality to believe. Should they embrace the belief in a rising economy? Should they worry about all the negative signs and the fact that the S&P 500 hasn’t had a daily decline of more than 3% in almost 800 days?

In many ways this decision is very similar to one posed by Blaise Pascal in his famous wager some 350 years ago. The French mathematician broke new ground in probability theory by asking whether or not a person should believe in God (this was the subject in philosophy back in the day, so you will have to forgive our foray into religious territory, we are not endorsing any particular religion here).

In Pascal’s view, belief has a positive expected value because the upside is infinite, whereas the downside is finite. In this model, humans bet with their lives. If your were a believer and it turned out God didn’t exist, you lost only a finite amount of material wealth (tithings) and personal enjoyment (opportunity cost of not being a hedonist, for example). If you were right, however, you had an infinite payout of eternal bliss. As probabilities can only range between 0 and 1, the math is glaringly simple: the expected value of believing was always greater than not. When balanced against an infinite upside, no probability was too small.

Swinging back around to finance, we think immediately of a bet with similarly lopsided payout: options. Buyers of options face a finite cost with (while not exactly infinite) extremely high payouts relative to their downside. Moreover, in a market typified by persistently high vol of vol, the manufacturers of options (market makers) will be systematically underpricing the value of an option. 

Like Pascal’s Wager, we face two choices: to believe or not to believe. However, we enjoy a luxury that Pascal could not envision. We have the ability to bet on God’s existence and absence at the same time. Plain vanilla Options actually come in two flavors, calls and puts. This means you can bet on both belief and disbelief and retain an asymmetric payout in your favor.

A high VVIX doesn’t just imply wild moves in the stock market. It means that the VIX itself will be highly volatile. Some days we will experience wild volatility, while others will be so calm you will wonder if you lost your internet connection. In this environment, spot volatility exposure should be purchased on the extreme dips. A high VVIX implies an assymetric payoff: the VIX can’t decline past 0 (its lowest value since 1991 was 8.89) but it can rally higher than we can imagine.

Given the backdrop, it is highly likely that the market will go vertical, up or down. With global interest rates near zero and a looming pension crisis, it would be insane to discount the prospect of a “melt-up” or a parabolic move higher in stock and bond prices. The current skew is to the downside, and market makers could be very surprised by a price rise as they realize they hedged the wrong tail.

At the same time, with the prospect of deflation in Europe and Japan and a hard landing for China, it would be equally mad to think that we couldn’t enter a spiral of lower prices and deleveraging. Moreover, the simultaneous proliferation of algorithmic trading could lead to a 1987-style crash of blistering speed.

There is a binary regime to the current market: every second we are not booming, we are crashing. Every second we are not crashing we are booming. Within this environment, the best bet to believe in the unknown unknowns of the market. Scalp cheap volatility and the world is yours to inherit.

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