Estimating Yields on Treasury Securities

  • Computations of yields on Treasury securities depend on the face value, purchase price and maturity of the issue.

  • The yield on a Treasury bill varies, depending on its method of computation. The discount method relates the investor's return to the bill's face value; the investment method relates the investor's return to the bill's purchase price.

  • The discount method tends to understate yields relative to those computed by the investment method.

Treasury bills (T-bills), U.S. debt instruments with maturities of one year or less, play a central role in our nation's financial system. Backed by the full faith and credit of the U.S. government, Treasury bills are low-risk investments with a broad and liquid secondary market.

Unlike comparable corporate issues, the interest earned on Treasury securities is exempt from state and local taxes. However, because T-bills are free of default risk, they generally have lower yields than corporate issues of comparable maturities.

T-Bill Yields
T-bills are purchased by investors at a weekly auction at less than face value and are redeemed at maturity at face value. The difference between the purchase price and the face value of the T-bill is the investor's return.

The investor's return is used in mathematical formulas to determine the yield on T-bills. One formula, the discount yield method, takes into account the return as a percent of the face value of a T-bill, rather than its purchase price. Since the purchase price is typically less than face value, the discount method tends to understate the yield. An alternative formula, called the investment yield method, also can be used to calculate the yield. Unlike the discount yield formula, the investment yield method relates the investor's return to the purchase price of the bill.

Both the discount yield and the investment yield, as well as the high, low and average prices of the auctioned T-bills, are made public in an official Treasury report shortly after the auction.

The Treasury uses the discount and investment formulas for calculating yields on all T-bills, except the one-year bill. Yields reported by the Treasury are precise to several decimal places.

The Discount Yield Method
The following formula is used to determine the discount yield for T-bills that have three- or six-month maturities:

Discount yield = [(FV - PP)/FV] * [360/M]

FV = face value
PP = purchase price
M = maturity of bill. For a three-month T-bill (13 weeks) use 91, and for a six-month T-bill (26 weeks) use 182
360 = the number of days used by banks to determine short-term interest rates (the investment yield method is based on a calendar year: 365 days, or 366 in leap years).

Example

What is the discount yield for a 182-day T-bill, auctioned at an average price of $9,659.30 per $10,000 face value?

Discount yield = [(FV - PP)/FV] * [360/M]

FV = $10,000 PP = $9,659.30 M = 182

Discount yield = [(10,000) - (9,659.30)] / (10,000) * [360/182]
Discount yield = [340.7 / 10,000] * [1.978022]
Discount yield = .0673912 = 6.74%

For the 13-week bill, the same formula would be used, dividing 360 by a maturity of 91 days rather than 182 days.

The Investment Yield Method
When comparing the return on investment in T-bills to other short-term investment options, the investment yield method can be used. This yield is alternatively called the bond equivalent yield, the coupon equivalent rate, the effective yield and the interest yield.

The following formula is used to calculate the investment yield for T-bills that have three- or six-month maturities:

Investment yield = [(FV - PP)/PP] * [365 or 366/M]

Example

What is the investment yield of a 182-day T-bill, auctioned at an average price of $9,659.30 per $10,000 face value?

Investment yield = [(FV - PP)/PP] * [365/M]
FV = $10,000 PP = $9,659.30 M = 182

Investment yield = [(10,000 - 9,659.30) / (9,659.30)] * [365/182]
Investment yield = [340.70] / 9,659.30] * [2.0054945]
Investment yield = .0707372 = 7.07%

For the 13-week bill, the same formula can be used, dividing 365 (or 366) by a maturity of 91 days.

Yields on Treasury Notes and Bonds
Treasury notes and bonds, fully-backed U.S. debt instruments with maturities of more than one year, pay the investor a fixed annual rate of return or coupon (paid semi-annually). The return on a Treasury note or bond is equal to its face value times the coupon interest rate.

Formulas used by Treasury to calculate the investment yield on notes and bonds are complicated and vary, depending on the maturity of the issue.

However, the investment yield on a bond or note held to maturity can be approximated with the following formula:

{R + [(FV - PP)/M]}
Investment yield= __________________
[(FV + PP)/2]

R = coupon rate FV = face value
PP = purchase price M = years to maturity

Example

What is the investment yield of a seven-year Treasury note issued at a price of $99.709, with an annual Treasury announced coupon of 7 7/8, payable semi-annually?

R = 7 7/8 (7.875) FV = $100 PP = $99.709 M = 7

7.875 + [(100 - 99.709)/7]
Investment yield = ________________
(100 + 99.709)/2

Investment yield = (7.875 + .0415714) / (99.8545)
Investment yield = 7.9165714 / 99.8545
Investment yield = .0792810 = 7.93%