The FRED database (maintained by the St. Louis Federal Reserve Bank) has added 40 series that are the output of the arbitrage free term structure model based on the paper by Kim and Wright. These data are used by Fed researchers to try to explain away what is happening in the bond market.
The chart above shows model outputs for the 10-year maturity: the 10-year zero coupon yield, and the term premium. (This primer explains what a zero coupon yield represents.) Please note that the data end as of March 2016, and so we can only use these data for historical analysis, and not to see what the market is pricing "right now."
Zero Rates Vs. Instantaneous Forwards
The FRED database also has series of instantaneous forward rates. The zero rates that I am discussing here are constructed using the curve of instantaneous forward rates. The difference between them is straightforward (using the 1-year maturity as an example):
- The 1-year instantaneous forward rate is the forward level of the overnight rate, one year from now.
- The 1-year zero coupon rate is approximately equal to the average of the instantaneous forward rate over the next year. (The calculation technically uses compounding, not averaging.)Since the zero rates are an average of instantaneous rates, they are less extreme. For example, the 10-year instantaneous term premium could be much larger than the term premium embedded in the 10-year zero rate.
Why Would We Want To Use These Data?
The rate expectations view of interest rates states that observed bond yields are equal to the expected average of the overnight rate over the lifetime of the bond. (Link to a primer on rate expectations.) This is why bond market participants appear to obsess over central bank watching: policy trends at the central bank determine the fair value for bond prices....MORE