Debt Securities - Computing T-bill Discount Yield
The imputed interest rate on a T-bill. As discussed earlier, T-bills are issued at a discount off their $1,000 par value, not quoted as a yield. To determine that yield, you need to know the price and the number of days to maturity. For simplicity's sake, a year is considered to be 360 days long, which assumes there are 30 days in a month. (This day-count convention may actually make things more complicated, but the 360-day year is now a tradition for calculating T-bill rates).
Computing a T-bill's discount yield is a three-step process. For these purposes, carry all computations out to six digits to the right of the decimal point. Treasury's mainframe carries it out 15 digits.
- Subtract the price you paid for the bond from $1,000. Take the difference and divide it by 1,000. Let's say you are buying the bond for $999.38. Subtract $999.38 from $1,000 and divide the resulting $0.62 by 1,000, and you end up with $0.000622.
- Now you take 360 - the number of days in a year, by convention - and divide that by the days to maturity. Let's assume it is a one-month bill, which usually matures more precisely in 28 days. Now divide 360 days by 28 days for a result of 12.857143.
- Now you multiply the result of step 1 by that of step 2. $0.00062 times 12.8571 equals 0.8%.
Do not get thrown off by orders of magnitude. A percentage is a number divided by 100. Do not think of 0.8% as 0.8%, but rather as 0.008. Sometimes bond traders refer to "basis points" or "BPs" or "beeps". A BP is a hundredth of a percent, or a percent of a percent. Maybe it will help you to think of 0.8% as "80 beeps".
You also need to be able to do this backwards. Given the rate, can you figure out the price?
- Multiply the rate by the number of days to maturity. In this case, multiply 0.008 times 28 days, and your result is 0.224.
- Divide the result of step 1 by the conventional number of days in a year. In this example, that would be 0.224 divided by 360, which gives you 0.0006222.
- Subtract the result of step 2 from 1. Following along, 1 minus 0.00662 would be 0.9993778.
- Multiply the result of step 3 by 1,000. This gives you the final figure of $999.38 (1,000 times 0.0003778).