## The 4 Types of Yields Used to Value Money Market Instruments

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:

1. Bank discount yield
2. Holding period yield
3. Effective annual yield
4. 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:

RBD = 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.

RBD = (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 P1 as the face value/par value. The formula used is identical to that of the holding period return. Thus:

HPY = (P1 – P0 + D1)/P0

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 rBD, the money market yield is given by:

rMM = (360 * rBD)/{360 –(t*rBD)}

Example 4

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

rMM = (360 * 0.033)/{360 – (60 * 0.033)}

= 3.318%

## Question

A 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%

Solution

rMM = (360 * rBD)/{360 –(t*rBD)}

First, we need to calculate rBD

rBD = (Face value – price)/ {face value *(360/t)}

= (10,000 – 9955)/ {10,000 *(360/50)}

= 0.0324

Therefore, rMM = (360 * 0.0324) / {360 – (50 * 0.0324)

= 3.255%

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.

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