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.

  1. 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.

  2. 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.

  3. Now you multiply the result of step 1 by that of step 2. $0.00062 times 12.8571 equals 0.8%.

Look Out!
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?

  1. 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.

  2. 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.

  3. Subtract the result of step 2 from 1. Following along, 1 minus 0.00662 would be 0.9993778.

  4. Multiply the result of step 3 by 1,000. This gives you the final figure of $999.38 (1,000 times 0.0003778).
Accrued Interest
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