- CFA Exams
- 2019 Level I > Study Session 2. Quantitative Methods: Basic Concepts > Reading 7. Discounted Cash Flow Applications
- 4. Different Yield Measures of a U.S. Treasury Bill

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

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

#### Practice Question 1

The price of a six-month (182-day) U.S. Treasury bill with a par value of $100,000 and a bank discount yield of 9.18 percent is ______.A. $90,720

B. $95,359

C. $97,680Correct Answer: B

#### Practice Question 2

A Treasury bill with 50 days till maturity is quoted with a bank discount rate of 3.50%. An investor purchasing $2,000,000 face value of this Treasury bill would pay ______.A. $1,965,221.84

B. $1,930,000.00

C. $1,990,277.78Correct Answer: C

F = $2,000,000

D = 0.035*(50/360)*$2,000,000 = $9,722.22

P = $2,000,000 - $9,722.22 = $1,990,277.78

#### Practice Question 3

Given a 30-day horizon, a money market yield of 4.0134% produces a holding period yield of ______.A. 0.33445%

B. 0.4213%

C. 0.3455%Correct Answer: A

MMY -> HPY

HPY = 0.040134 /(360/30) = 0.33445%

#### Practice Question 4

On June 1, 2008, the 12 3/8 May '14 Treasury bond is quoted at 134:05 bid and 134:09 asked. If Smedley buys a bond at the market rate and if the value of the bond on December 1, 2008 is 132:00, what will be her holding period return? (Do not take accrued interest, if any, into account in calculating the return)A. 1.0300

B. 2.91%

C. 1.0291Correct Answer: B

HPR = (Price_{1} + Interest - Price_{0}) /Price_{0}

One interest payment of 6.1875 will be received in November. This is 12.375/2.

Buying at the market, Smedley will pay the asked price of 134 9/32 or 134.28125.

HPR = (132 + 6.1875 - 134.28125)/134.28125 = 0.0291

#### Practice Question 5

A Treasury bill with 50 days till maturity is quoted with a bank discount rate of 3.50%. The holding period yield for this T-bill, if purchased and held to maturity, would be closest to ______.A. .4861%

B. .4885%

C. 3.50%Correct Answer: B

Holding period yield calculated:

F = $1,000

D = 0.035*(50/360)*$1,000 = $4.8611

P = $1,000 - $4.8611 = $995.1389

HPY = $4.8611/$995.1389 = 0.4885%

#### Practice Question 6

A 30-day T-bill is selling at a money market yield of 2.95%. What is its equivalent bank discount yield?A. 2.94%

B. 2.95%

C. 2.97%Correct Answer: A

Based on money market yield:

0.0295 = [(100,000 - P)/P] x (360/30) => P = 100,000/[1+0.0295/12] = 99,754.8

Bank discount yield = [(100,000 - 99,754.8)/100,000] x (360/30) = 0.0294, or 2.94%.

#### Practice Question 7

A 180-day U.S. Treasury bill has a holding period yield (HPY) of 2.375%. The bank discount yield (in %) is closest to ______.A. 4.640

B. 4.780

C. 7.850Correct Answer: A

First, use the HPY to find the money market yield: r_{MM} = (HPY) x (360/t) = .02375 x (360 / 180) = 0.0475. Then use the money market yield to find the bond discount yield: r_{MM} = (360 r_{BD}) / [(360 - (t) (r_{BD})]. In this case: 0.0475 = (360 r_{BD}) / [(360 - (180)( r_{BD})]. Now solve for r_{BD}.

0.0475 x ((360 - (180)( r

_{BD}) = (360 r

_{BD})

17.10 = (360 rBD) + 8.55 r

_{BD}

rBD = 17.10 / 368.55 = 0.046398

### Study notes from a previous year's CFA exam:

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