**Subject 4. Different Yield Measures of a U.S. Treasury Bill**

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#### Money market instruments are low-risk, highly liquid debt instruments with a maturity of one year or less. There are two types of money market instruments: interest-bearing instruments (e.g., bank certificates of deposit), and pure discount instruments (e.g., U.S. Treasury bills).

Pure discount instruments such as T-bills are quoted differently than U.S. government bonds. They are quoted on a **bank discount basis** rather than on a price basis:

- r
_{BD} = the annualized yield on a bank discount basis - D = the dollar discount, which is equal to the difference between the face value of the bill, F, and its purchase price, P
- t = the number of days remaining to maturity
- 360 = the bank convention of the number of days in a year.

Bank discount yield is not a meaningful measure of the return on investment because:

- It is based on the face value, not on the purchase price. Instead, return on investment should be measured based on cost of investment.
- It is annualized using a 360-day year, not a 365-day year.
- It annualizes with simple interest and ignores the effect of interest on interest (compound interest).

**Holding period yield** (HPY) is the return earned by an investor if the money market instrument is held until maturity:

- P
_{0} = the initial price of the instrument - P
_{1} = the price received for the instrument at its maturity - D
_{1} = the cash distribution paid by the instrument at its maturity (that is, interest).

Since a pure discount instrument (e.g., a T-bill) makes no interest payment, its HPY is (P

_{1} - P

_{0})/P

_{0}.

Note that HPY is computed on the basis of purchase price, not face value. It is not an annualized yield.

The **effective annual yield** is the annualized HPY on the basis of a 365-day year. It incorporates the effect of compounding interest.

**Money market yield** (also known as **CD equivalent yield**) is the annualized HPY on the basis of a 360-day year using simple interest.

*Example*

An investor buys a $1,000 face-value T-bill due in 60 days at a price of $990.

- Bank discount yield: (1000 - 990)/1000 x 360/60 = 6%
- Holding period yield: (1000 - 990)/990 = 1.0101%
- Effective annual yield: (1 + 1.0101%)
^{365/60} - 1 = 6.3047% - Money market yield: (360 x 6%)/(360 - 60 x 6%) = 6.0606%

If we know HPY, then:

- EAY = (1 + HPY)
^{365/t} - 1 - r
_{MM} = HPY x 360/t

If we know EAY, then:

- HPY = ( 1 + EAY)
^{t/365} - 1 - r
_{MM} = [(1 + EAY)^{t/365} - 1] x (360/t)

If we know r

_{MM}, then:

- HPY = r
_{MM} x (t/360) - EAY = (1 + r
_{MM} x t/360)^{365/t} - 1

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