An Explanation of the Forward Premium 'Puzzle'

Posted: 2 Jun 2000

See all articles by Shu Yan

Shu Yan

Oklahoma State University - Stillwater - Department of Finance

Richard Roll

California Institute of Technology


Existing literature reports an empirical puzzle about the foreign exchange forward premium, the spread between the forward rate and the concurrently-observed spot exchange rate. The premium is often negatively correlated with subsequent changes in the spot rate. This defies economic intuition and possibly violates market efficiency. Various explanations have been offered, ranging from non-stationary risk premia through econometric mis-specifications. Some researchers have accepted the puzzle as a fact of inefficient foreign exchange markets, a phenomenon that provides profitable trading opportunities. We suggest there is really no puzzle at all. The simplest conceivable model adequately fits the data; forward exchange rates are unbiased predictors of subsequent spot rates. The puzzle has arisen because (a) the forward rate, the spot rate, and the forward premium all follow non-stationary (or nearly so) time series processes, and (b) the forward rate is a noisy predictor. We document these features with an extended sample and show how they can give the delusion of a puzzle.

Keywords: Foreign Exchange, Anomalies, Non-stationary Time Series

JEL Classification: F31, G15, G13

Suggested Citation

Yan, Shu and Roll, Richard W., An Explanation of the Forward Premium 'Puzzle'. Available at SSRN:

Shu Yan

Oklahoma State University - Stillwater - Department of Finance ( email )

Spears School of Business
Stillwater, OK 74078-4011
United States

Richard W. Roll (Contact Author)

California Institute of Technology ( email )

1200 East California Blvd
Mail Code: 228-77
Pasadena, CA 91125
United States
626-395-3890 (Phone)
310-836-3532 (Fax)

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