by Calculated Risk on 1/18/2009 03:42:00 PM

## Sunday, January 18, 2009

### Intrade: Odds of a Depression

OK, this is amusing. Although there is no formal definition of an economic depression, the most common definition is a sustained recessionary period with at least a 10% decline in real GDP from peak to trough.

And that brings us to the odds of a depression from Intrade Prediction Markets. (hat tip Asymmetric). This graph shows that traders believe the odds of a depression in 2009 are about 55%.

And how does Intrade define a depression? Here are the rules:

This contract will settle (expire) at 100 ($10.00) if quarterly GDP figures show the US economy has gone into a depression in 2009.

The contract will settle (expire) at 0 ($0.00) if quarterly GDP figures DO NOT show the US economy has gone into a depression in 2009.

For expiry purposes a depression is defined as a cumulative decline in GDP of more than 10.0% over four consecutive quarters. This is calculated by adding together the published (annualized) Real GDP figures (as detailed below). If these annualised figures add up to more than -10.0% over four consecutive quarters then the contract will expire at 100.

Example 1:

In Q1 the Final Real GDP figure is -3.5%

In Q2 the Final Real GDP figure is -2.5%

In Q3 the Final Real GDP figure is -2.0%

In Q4 the Final Real GDP figure is -2.3%

The sum of these figures is -10.3% so the contract will be expired at 100.

...

Negative quarters in the preceding year will count towards the total GDP decline for expiration purposes. For example, if the total decline in GDP from Q3 2008 to Q2 2009 exceeds 10.0% then the contract will expire at 100.

**Quiz:**If the annualized real GDP declines 2.5% in each quarter of 2009, how much does real GDP decline in 2009?

A: -10% (as calculated by Intrade adding the four quarters together)

B: -2.5%

I'm not making this up. The answer is B. If GDP declines at an annualized rate of 2.5% each quarter, then the total decline in real GDP over four quarters is 2.5%.

So which is correct for Intrade? A a cumulative decline in GDP of more than 10.0% or "adding together the published (annualized) Real GDP figures"? ROFLOL. I think they might have a dispute coming!

I suspect this might actually come up if reported GDP declines 5% in Q4 2008 and another 5% in Q1 2009; some observers might claim GDP has declined 10% (adding the two together). Readers of this blog will know that real GDP would have

*only*declined about 2.5%! That is bad enough. (5% annual rate for half a year)