# U.S. Treasury Discount Bond Database

# Frequently Asked Questions

- What is the day count convention in calculating monthly maturities?

For maturities from 1 to 12 months, the number of days in i month(s) are calculated as 365*i/12 rounded to the nearest integer. This results in yields for 1-12-month maturities being equivalent to yields for 30, 61, 91, 122, 152, 183, 213, 243, 274, 304, 335, 365-day maturities respectively. For maturities greater than one year, the same process is repeated. Given our data set for daily maturities it is straightforward adopt alternative day count conventions.

- Where do we obtain the Treasury bond data to estimate yields and discount bond returns?

For results prior to 2022, we obtained Treasury bond data (prices and features including maturity and coupon payments) from the CRSP Treasuries Time Series which is updated on an annual basis. Since 2022, we have switched to raw data from DataStream in order to offer a more timely and updated representation of our estimates. We cross-reference our new results with the annual CRSP data when it becomes available. This dual approach enables us to provide the most up-to-date and precise estimates of yields and discount bond returns.

- What is the day count convention used here?

We use the usual day count convention of 365 days in each year. Given our data set of estimates with daily maturities, it is straightforward to adopt the results to other conventions.

- How are the risk-free returns calculated?

First, one-day risk-free returns are obtained from the estimated discount curve for discount bonds with one day of maturity. Then, the one-business-day risk-free return at t is calculated by compounding the one-day risk-free return at t over s days, where s is the number of days between business day t and t+1.

The yield curve from the U.S. Department of Treasury is a par yield curve. The par yield curve is based on securities that pay interest on a semiannual basis and the yields are "bond-equivalent" yields. This means that the yields at a given point on the par yield curve are consistent with a semiannual coupon security with the same time remaining to maturity. We provide daily zero-coupon yield curve rates for the complete maturity spectrum, which are not created or published by the Treasury.