# Speculators Foresee No Catastrophe

In the latest *American Economic Journal*, Pindyck and Wang work out what financial prices and their fluctuations suggest about what speculators believe to be the chances of big economic catastrophes. *Bottom line*: [simple models that estimate the beliefs of] speculators see very low chances of really big disasters. (Quotes below.)

For example, they find that over fifty years speculators see a 57% chance of a sudden shock destroying at least 15% of capital. If I apply their estimated formula to questions they didn’t ask in the paper, I find that over two centuries, speculators see only a 1.6 in a hundred thousand chance of a shock that destroys over half of capital. And a shock destroying 80% or more of capital has only a one in a hundred trillion chance. Of course these would all be lamentable, and very newsworthy. But hardly existential risks.

The authors do note that others have estimated a thicker tail of bad events:

We obtain … a value for the [power] α of 23.17. … Barro and Jin (2009) … estimated α [emprically] for their sample of contractions. In our notation, their estimates of α were 6.27 for consumption contractions and 6.86 for GDP.

If I plug in the worst of these, I find that over two centuries there’s an 85% chance of a 50% shock, a 0.6% chance of an 80% shock, and one in a million chance of a shock that destroys 95% or more of capital. Much worse chances, but still nothing like an existential risk.

Of course speculative markets wouldn’t price in the risk of extinction, since all assets and investors are destroyed in those events. But how likely could extinction really be if there’s almost no chance of an event that destroys 95% of capital?

**Added 11a**: They use a power law to fit price changes, and so would miss ways in which very big disasters have a different distribution than small disasters. But to the extent that this does accurately model speculator beliefs, if you disagree you should expect to profit by buying options that pay off mainly in the case of huge disasters. So why aren’t you buying?

Those promised quotes:

An emerging literature has used historical data to estimate the likelihood and expected impact of catastrophic events. … We take a different approach from earlier studies and ask what event arrival rate and impact distribution are implied by the behavior of basic economic and financial variables. We do not try to estimate the characteristics of catastrophic events from historical data on drops in consumption or GDP, nor do we use the estimates of others. Instead, we develop an equilibrium model of the economy that incorporates catastrophic shocks to the capital stock, and that links the first four moments of equity returns, along with economic variables such as consumption, investment, interest rates, and Tobin’s q, to parameters describing the characteristics of shocks as well as behavioral parameters such as the coefficient of relative risk aversion and elasticity of inter-temporal substitution. We can then determine the characteristics of catastrophes as a calibration output of our analysis. …

We assume that discrete downward jumps to the capital stock (“shocks”) occur as Poisson arrivals with a mean arrival rate λ. …We therefore use data for the US economy from 1947 to 2008 to construct average values of the output-capital ratio, the consumption-investment ratio, the real risk-free rate, and the expected real growth rate. …

We obtain a mean arrival rate [of shocks] λ of 0.734 for the jump process and a value for the distributional parameter α of 23.17. These numbers imply that a shock occurs about every 1.4 years on average, with a mean loss … of only about 4 percent. …. [The] probability of one or more shocks with loss larger than L occurring over time span T is … 1 − exp [ −λT(1 − L )α] . For example, if we consider as catastrophic a shock for which the loss is 15 percent or greater, the annual likelihood of such an event is … 0.017. … The probability that at least one catastrophe (with a loss of 15 percent or greater) will occur over the next 50 years is … 0.57. …

Barro and Jin (2009) … estimated α [emprically] for their sample of contractions. In our notation, their estimates of α were 6.27 for consumption contractions and 6.86 for GDP. (more; ungated)