Money market instruments are those financial instruments that mature in less than a year, e.g. Treasury Bills, commercial papers or municipal notes. Most T-bills have a maturity of either 91 days or 180 days. The yield on these instruments can be measured using 4 key conventions, namely:

- Bank discount yield
- Holding period yield
- Effective annual yield
- Money market yield

We now look into each type of yield individually and note their key features:

**Bank discount yield**

It is used to calculate the yield on T-Bills, which are quoted purely on a discount basis. The money to be paid at maturity is agreed upon in advance, and the investor pays a lower amount. The difference between these two figures represents the discount, denoted by letter D. Thus:

R_{BD} = D/F (360/t) = (Face value – price)/ {face value *(360/t)}

Where D = face value – price, F is the face value, and t is the time to maturity in days. 360 is the bank’s conventional number of days in a year.

**Example 1**

Consider a T-Bill with $100,000 face value, trading at $99,450 with 60 days to maturity.

R_{BD }= (100,000 – 99,450)/ {100,000 *(360/60)}

= 0.092%

Problems: It’s a percentage of face value instead of trading price, uses 360 days instead of 365, and also ignores compounding.

**Holding period yield**

It measures the annualized return on a money market investment, considering the remaining life and P_{1} as the face value/par value. The formula used is identical to that of the holding period return. Thus:

HPY = (P_{1} – P_{0} + D_{1})/P_{0}

**Example 2**

For a T-Bill with $100,000 face value, trading at $99,450 with 60 days to maturity;

HPY = (100,000 – 99,450)/99,450 = 0.55%

Note: Any interest must be included as ‘D’. T-Bills, however, are offered purely on a discount basis.

**Effective annual yield**

EAY = (1 + HPY)^{ 365/t} – 1

**Example 3**

For a T-Bill with $100,000 face value, trading at $99,450 with 60 days to maturity;

EAY = (1 + 0.0055)^{365/60} – 1

= 3.393%

**Money market yield**

Given r_{BD}, the money market yield is given by:

r_{MM} = (360 * r_{BD})/{360 –(t*r_{BD})}

**Example 4**

For a T-Bill with $100,000 face value, trading at $99,450 with 60 days to maturity:

r_{MM} = (360 * 0.033)/{360 – (60 * 0.033)}

= 3.318%

QuestionA United States T-Bill with $10,000 face value, trading at $9,955 has 50 days to maturity. Calculate the money market yield;

A. 0.03255%

B. 3.255%

C. 0.35%

SolutionThe correct answer is B.

r

_{MM}= (360 * r_{BD})/{360 –(t*r_{BD})}First, we need to calculate r

_{BD}r

_{BD}= (Face value – price)/ {face value *(360/t)}= (10,000 – 9955)/ {10,000 *(360/50)}

= 0.0324

Therefore, r

_{MM }= (360 * 0.0324) / {360 – (50 * 0.0324)= 3.255%

*Reading 7 LOS 7e*

*Calculate and interpret the bank discount yields, holding period yields, effective annual yields, and money market yields for U.S Treasury bills and other money market instruments.*