Yield Spread Measures for Money Market Instruments

Money market instruments are short-term debt securities with original maturities of one year or less. They are a crucial part of the financial market and include a variety of instruments such as overnight sale and repurchase agreements (repos), bank certificates of deposit, commercial paper, Treasury bills, bankers’ acceptances, and time deposits based on market reference rates. For instance, a company might issue commercial paper to meet its short-term liquidity needs. Money market mutual funds, which invest solely in eligible money market securities, are sometimes considered as an alternative to bank deposits.

Yield measures for money market instruments differ from those for bonds in several ways.

Firstly, bond yields-to-maturity are annualized and compounded, while yield measures in the money market are annualized but not compounded. This means the return on a money market instrument is stated on a simple interest basis. For example, if you invest $1000 in a 90-day Treasury bill with a yield of 1%, you would earn $10 at the end of the period.

Secondly, bond yields-to-maturity are usually stated for a common periodicity for all times-to-maturity, while money market instruments with different times-to-maturity have different periodicities for the annual rate.

Lastly, bond yields-to-maturity can be calculated using standard time-value-of-money analysis, while money market instruments are often quoted using non-standard interest rates and require different pricing equations than those used for bonds.

Quoted money market rates are either discount rates or add-on rates. Commercial paper, Treasury bills, and bankers’ acceptances are often quoted on a discount rate basis, while bank certificates of deposit, repos, and market reference rate indexes are quoted on an add-on rate basis. In the money market, the discount rate involves an instrument for which interest is included in the face value of the instrument, while an add-on rate involves interest that is added to the principal or investment amount.

The pricing formula for money market instruments quoted on a discount rate basis is:

\[PV = FV \times \left( 1 – \frac{\text{Days}}{\text{Year}} \times DR \right)\]

Where:

PV = present value, or the price of the money market instrument

FV = the future value paid at maturity, or the face value of the money market instrument
Days \(=\) the number of days between settlement and maturity

Year \(=\) the number of days in the year

DR = the discount rate, stated as an annual percentage rate

\[DR = \frac{\text{Year}}{\text{Days}} \times \frac{(FV – PV)}{FV}\]

The pricing formula for money market instruments quoted on an add-on rate basis is:

\[PV = \frac{FV}{1 + \frac{\text{Days}}{\text{Year}} \times AOR}\]

Where:

PV = present value, the principal amount, or the price of the money market instrument

FV = the future value, or the redemption amount paid at maturity, including interest

Days \(=\) the number of days between settlement and maturity

Year \(=\) the number of days in the year

AOR = the add-on rate, stated as an annual percentage rate

\[AOR = \frac{\text{Year}}{\text{Days}} \times \frac{FV – PV}{PV}\]

Investment analysis is more challenging for money market securities because some instruments are quoted on a discount rate basis while others are on an add-on rate basis, and some assume a 360-day year, and others use a 365-day year. Furthermore, the “amount” of a money market instrument quoted by traders on a discount rate basis typically is the face value paid at maturity, while the “amount” when quoted on an add-on rate basis usually is the price at issuance.

Comparing Money Market Instruments on Bond Equivalent Yield Basis

The bond equivalent yield, often termed the investment yield, quantifies a money market rate using a 365-day add-on rate method.

Step 1:

For money market assets priced with a Discount Rate (DR), compute the Price for every 100 of Par (PV) as:

\[PV = FV \times \left( 1 – \frac{\text{Days}}{\text{Year}} \times DR \right)\]

Step 2:

From the PV obtained in Step 1, determine the Add-on Rate (AOR) for that specific money market asset:

\[AOR = \frac{\text{Year}}{\text{Days}} \times \left( \frac{FV – PV}{PV} \right)\]

Step 3:

The Bond Equivalent Yield (BEY) represents a money market rate defined using a 365-day AOR method.

With this, the asset can be evaluated alongside other money market assets that use the Bond Equivalent Yield as their standard.

Example: Determining the Bond Equivalent Yield

Suppose an investor is comparing the following two money market instruments:

1. A 60-day Treasury bill issued by the government, quoted at a discount rate of \(0.050\%\) for a 360-day year.
2. A 60-day bank certificate of deposit, quoted at an add-on rate of \(0.060\%\) for a 365-day year.

Which one offers the higher expected rate of return, assuming the same credit risk?

Solution

60-day Treasury bill:

• Days \(= 60\)
• Year \(= 360\)
• DR (Discount Rate \() = 0.050\%\) or 0.0005

Using the formula:

\[PV = FV \times \left( 1 – \frac{\text{Days}}{\text{Year}} \times DR \right)\]

\[PV = 100 \times \left( 1 – \frac{\text{60}}{\text{360}} \times 0.0005 \right) = 99.99 \]

\[AOR = \frac{\text{Year}}{\text{Days}} \times \left( \frac{FV – PV}{PV} \right)\]

\[ AOR = \frac{365}{60} \times \left( \frac{100 – 99.99}{99.99} \right) = 0.0608\% \]

The bond equivalent rate is, therefore, 0.0608%

The bond equivalent rate for the 60-day bank certificate of deposit is \(0.060\%\) or 0.0006.

The 60-day Treasury bill offers a higher annual return relative to the 60-day bank certificate of deposit.

Question

The bond equivalent yield of a 180-day Treasury bill quoted at a discount rate of 0.75% for a 360 -day year is closest to:

1. 0.750%
2. 0.753%
3. 0.763%

Solution

The correct answer is C.

Step 1:

For money market assets priced with a Discount Rate (DR), compute the Price for every 100 of Par (PV) as:

\[PV = FV \times \left( 1 – \frac{\text{Days}}{\text{Year}} \times DR \right)\]

\[PV = 100 \times \left( 1 – \frac{\text{}\text{180}}{\text{}\text{360}} \times 0.75\% \right) = \ 99.6250\ \]

Step 2:

From the PV obtained in Step 1, determine the Add-on Rate (AOR) for that specific money market asset:

\[AOR = \frac{\text{Year}}{\text{Days}} \times \left( \frac{FV – PV}{PV} \right)\]

\[AOR = \frac{\text{}\text{365}}{\text{}\text{180}\text{}} \times \left( \frac{100 – 99.6250}{99.6250} \right) = 0.763\%\]