Sunday, September 8, 2013

Forecast-Error Insurance

Yale economists Mark Rosenzweig and Chris Udry have a new paper, "Forecasting Profitability." It's related to a project of theirs that examines the Indian Meteorological Department's annual monsoon rainfall forecasts and their effects on farmer profitability. (Farmers who rely on the forecast to guide their planting-stage investments, and many do, are exposed not only to rainfall risk, but also to "forecast-error risk.")

Mark raised an interesting related question in an email a few weeks ago, "Do you know of any insurance products for forecasts of any kind? Can one purchase insurance that indemnifies one against forecast errors, anywhere in the world for any forecasts?"

Hmm...quite fascinating! There are financial products insuring against rainfall events (e.g., see the discussion my 2005 JASA paper with Sean Campbell, "Weather Forecasting for Weather Derivatives"), but what about rainfall forecast-error events?

Of course the "forecast-error insurance" issue transcends rainfall. More generally, who might demand forecast-error insurance and why? Only users of forecasts? Perhaps also producers of forecasts (not unlike medical malpractice insurance)? Who might supply it, and how might it be priced (very tricky...)?

Here are some thoughts.

First, forecast object x and the associated forecast error e = x - x_f will generally be correlated, in which case insurance against x events is also partial insurance against e events. (Note well, however, that the implicit e insurance is only partial, and perhaps very partial, depending on the correlation strength).

Second, assuming that the relevant financial markets exist, one could construct an e hedge by holding an appropriate portfolio of x-sensitive stocks, which in an efficient market would reflect discounted x forecasts and hence move only due to "news" (e). Long or short positions in that portfolio would hedge against positive e or negative e. Better yet, one could implement the hedge using stock options rather than the underlying, going long a call or long a put (or both, a so-called "straddle," which would hedge against large e of either sign).

Maybe I've missed something? Are the questions well-posed, and if so, are there simpler or more obvious answers? In any event, many assumptions obviously lurk behind the thoughts / suggestions above, but nothing is impossible for the man who doesn't have to do it himself.