Frequently Asked Questions

For maturities from 1 to 12 months, the number of days in i month(s) is calculated as 365 × i / 12, rounded to the nearest integer - giving 30, 61, 91, 122, 152, 183, 213, 243, 274, 304, 335 and 365 days.

The usual convention of 365 days in each year. Because the data are provided at daily maturity resolution, users can apply an alternative convention if they prefer.

It depends on how densely the local bond market is observed at the maturities you care about. Where domestic bonds are plentiful, the two estimates agree closely and either can be used. Where the local cross-section is sparse, KR-T is the better choice, because it draws additional information from the U.S. reference market through FX spot and forward rates.

Both methods are compared out of sample against the Nelson-Siegel-Svensson (NSS) model, the parametric benchmark behind several official central bank curves. KR produces smaller out-of-sample yield errors than NSS in every market: the reduction is about 13% for the United States and ranges from roughly 26% to 47% across Germany, Japan, the United Kingdom, Canada, and Switzerland.

Under cross-validation designed to mimic real maturity gaps, KR-T reduces out-of-sample yield errors by up to a further 51% relative to standalone KR, and by 71-86% relative to NSS, while matching KR where local data are already sufficient.

One-day rates are taken from the estimated discount curve. The one-business-day risk-free return at t is calculated by compounding the one-day risk-free return at t over the number of days between consecutive business days.

The U.S. Department of the Treasury publishes a par yield curve based on semiannual coupon securities. This database provides daily zero-coupon yield curve rates across the complete maturity spectrum, which the Treasury does not create or publish.

Discount bond returns, term structure factors, and bond market condition measures.

The United States serves as the reference market in KR-T rather than a target market. KR-T files are provided for Germany, Japan, the United Kingdom, Canada, and Switzerland.

KR-T uses FX-hedged U.S. Treasuries as synthetic bonds, which can support maturities beyond the longest observed domestic bond. On each date, KR-T yields are published up to the last maturity supported by an observed domestic bond or a synthetic bond priced using FX forwards within the observed FX forward range.

min_observed_ttm to max_observed_ttm describes the maturity range of domestic bonds used in estimation on that date. Curve coverage is the range of maturities with reported yields on that date; its upper endpoint is max_curve_ttm. For international KR, the upper endpoint is the longest observed domestic bond, max_observed_ttm. For KR-T it is the longest observed domestic bond, or an FX-transformed U.S. Treasury where one reaches further.

KR-T additionally requires the U.S. reference market and foreign-exchange data, so its sample can begin later or contain fewer dates.

We additionally omit 23 dates (0.06% of the KR-T sample) because of insufficient FX coverage or quote inconsistencies.