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Treasury Bills 101

Treasury bills (“T-bills”) are offered in three maturities: three-months, six-months, and one-year. They are available with face values of $10,000+. Treasury bills are zero-coupon bonds which are purchased at a discount to face value. The discount is determined by bids at treasury auctions (Reference the tutorial, The Treasury Auction Process).

Annualized Discount Yield

Because T-bills are zero-coupon bonds, they are quoted and traded on an annualized discount yield basis rather than by dollar value. Yield is quoted for each $100 of face value over a 360 day period. A bond’s annualized discount yield is calculated as follows:

Annualized Discount Yield = (100 – MV)/100 x (360/t_M)

Where:

MV = Market Value
t_M = Length to Maturity

Consider the following example: A six-month T-bill is purchased for $98.50 per $100 of face value and held until maturity. What is the T-bill’s annualized discount yield?

Annualized Discount Yield = (100 - 98.50)/100) x (360/180) = .03 or 3%

Inversely, the T-bill’s market value, in dollars, can be derived using its annualized discount yield as shown below:

Market Value = 100 – r (t_M/360)

Where:

r = Annualized Discount Yield
t_M = Length to Maturity

Returning to the example above:

Market Value = 100 – .03 (180/360) = $98.50 per $100 Face Value

Evaluating T-Bills

Investors often need to compare the yields between T-bills and traditional coupon bonds. Because coupon bonds pay semi-annual interest that can be reinvested to compound income, investors must convert the annualized discount yield of a T-bill into its coupon equivalent yield for comparative purposes. The following formula is used to convert a T-bill’s annualized discount yield into its coupon equivalent yield:

Coupon Equivalent Yield = (365 x r) / [360 – (r )(t_M)]

Where:

r = Annualized Discount Yield
t_M = Length to Maturity

Consider the following example: If a T-bill has an annualized discount yield of 6% and 200 days until maturity, what is the T-bill’s coupon equivalent yield?

CEY = (365 x .06)/[360 - (.06)(200)] = .0629 or 6.29%

Summary

The Following chart details advantages and disadvantages of T-bills:

Treasury Bills

Advantages
     • Considered Free of Default Risk
     • Liquid. Little Liquidity Risk
     • Exempt from state taxation

Disadvantages
     • Low Yield
     • Vulnerable to Interest Rate Risk
     • Vulnerable to Inflation Risk
     • Minimum Face Value is $10,000

Questions:

1.    What is the minimum face value available for a T-bill?

    a. $10
    b. $100
    c. $1,000
    d. $10,000

2.    A six-month T-bill is purchased for $97 per $100 of face value. Calculate the T-bill’s annualized discount yield.

    a. 3%
    b. 6%
    c. 30%
    d. 0.6%

3.    A six-month T-bill has an annualized discount yield of 4.5%. Calculate the T-bill’s dollar value per $100 of face value.

    a. $100.00
    b. $95.00
    c. $97.75
    d. $95.75

4. A three-month T-bill has an annualized discount yield of 2%. Calculate the T-bill’s dollar value per $100 of face value.

    a. $99.50
    b. $100.00
    c. $98.50
    d. $99.95

5. A T-bill has an annualized discount yield of 4% and 180 days until maturity. Calculate the T-bill’s coupon equivalent Yield.

    a. 4.44%
    b. 4.14%
    c. 3.86%
    d. 3.56%

Answers:

1. D

2. C

3. C

4. A

5. B