Investors can always choose between a six-month Treasury bill and tandem three-month bills. The yields on the three bills — the six-month bill, the three-month bill and the three-month bill three months hence — are presumably linked by the market forces generated by their choice. To examine the linkage, the authors use the concept of the forward rate — e.g., the rate that must prevail three months from now to equate the yields on tandem purchases of three-month bills (beginning with today’s spot rate) to the yield on the six-month bill.
If expectations accounted for the whole spread, the forward rate would be the interest rate forecast implicit in the current yield curve. If investors require a liquidity premium for extending the maturity of their holdings, however, the yield curve will point upward even when rates are expected to remain unchanged; in order to infer from the forward rate the market’s true forecast of future interest rates, we would have to subtract the liquidity premium. Historical yield spreads suggest that, other things equal, market participants require additional yield to extend the maturity of their holdings; three-month forward rates have, on average, exceeded subsequent spot rates by 58 basis points.
If liquidity premiums change more slowly over time than interest rate expectations, one can assume that most of the variation in yield spread is due to errors in expectations. Using this assumption to estimate forecasting errors implicit in market yield curves, the authors find that the average three-month error over the last decade has been 96 basis points.