Pricing Money Market Instruments

Money market instruments are shortterm debt securities with maturities of one year or less. Because of their high liquidity and low credit risk, they are fundamental building blocks in cashmanagement strategies, shortterm investment portfolios, and benchmark rate calculations. Accurately pricing these instruments is essential for investors, banks, and treasury departments. This page outlines the key concepts, formulas, and practical steps needed to price the most common moneymarket products.

Why Pricing Matters

• Performance measurement: Returns are expressed as yields; without a reliable price, yield calculations are meaningless.
• Risk management: Market value determines the exposure to interestrate movements.
• Regulatory compliance: Financial statements must reflect fair value for many moneymarket holdings.

Core Concepts

Discount Yield (Bank Discount Yield)

The discount yield is the most popular quoting convention for Treasury bills (Tbills) and similar discount instruments. It is based on the face value rather than the purchase price.

Formula:

Discount Yield = (Face Value  Purchase Price) / Face Value  (360 / Days to Maturity)

Key points:

• The denominator is the face value, not the price.
• 360 days is used for consistency with U.S. moneymarket conventions.

Bank (or Bond) Yield

Also called the investment yield, it measures the return relative to the amount actually invested.

Bank Yield = (Face Value  Purchase Price) / Purchase Price  (360 / Days to Maturity)

Effective Yield (Annualized Yield)

The effective yield converts a quoted yield into an annual rate that reflects compounding.

Effective Yield = ( (Face Value / Purchase Price)^(365/Days to Maturity) )  1

Pricing Specific Instruments

1. Treasury Bills (TBills)

Tbills are sold at a discount and redeemed at par. To find the price when the discount yield is known:

Price = Face Value  (1  Discount Yield  (Days to Maturity / 360))

Example: A 91day Tbill with a face value of $100,000 and a discount yield of 2.5% is priced at:

Price = 100,000  (1  0.025  91/360)  $99,368.06

2. Commercial Paper (CP)

Commercial paper is quoted on a bankdiscount basis similar to Tbills, but the market convention often uses a 360day year. The price formula is identical:

Price = Face Value  (1  Discount Yield  (Days to Maturity / 360))

Because CP may have maturities of 30, 60, or 90 days, the impact of the discount is more pronounced for shorter terms.

3. Repurchase Agreements (Repos)

A repo is a shortterm loan collateralized by securities. The price is expressed as a repo rate based on the amount borrowed.

Repo Rate = (Purchase Price  Sale Price) / Sale Price  (360 / Days to Maturity)

Reversing the formula gives the forward price:

Forward Price = Purchase Price  (1 + Repo Rate  (Days to Maturity / 360))

4. Certificates of Deposit (CDs)

CDs are typically quoted on a bankdiscount basis, but some are quoted using a simple interest rate (annualized on a 365day basis). The price for a discountquoted CD is:

Price = Face Value  (1  Discount Yield  (Days to Maturity / 360))

For an interestquoted CD:

Price = Face Value / (1 + Annual Rate  (Days to Maturity / 365))

StepbyStep Pricing Example

Suppose you are pricing a 180day Tbill with a face value of $1,000,000 and a quoted discount yield of 3.2%.

1. Convert the yield to a decimal: 3.2% 0.032.
2. Calculate the discount factor: 0.032 (180/360) = 0.016.
3. Subtract from 1: 1 0.016 = 0.984.
4. Multiply by the face value: $1,000,000 0.984 = $984,000.

The investor pays $984,000 today and receives $1,000,000 at maturity, earning a dollarreturn of $16,000.

Adjusting for DayCount Conventions

Most moneymarket pricing uses the 30/360 convention, but some markets (e.g., Europe) use actual/365. Always confirm the convention before applying a formula. The generic price equation can be written as:

Price = Face Value  (1  Yield  (DCF))

where DCF (daycount factor) = (Days to Maturity / Basis).

Yield Curve and Bootstrapping

Moneymarket yields are the foundation for constructing shortterm yield curves. By bootstrapping discount factors from a series of Tbill and CP prices, you can derive zerocoupon rates for any maturity up to one year. The process involves:

1. Collecting market quotes for instruments of increasing maturity.
2. Solving for the discount factor D_i using Di = Price / Face Value (for discountquoted instruments).
3. Deriving the implied zero rate: ri = (Di ^ (-1/ ti) 1) Basis.

Practical Tips

• Check the quotation convention: Some dealers quote bank discount, others quote investment yield. Misinterpreting the convention can cause pricing errors of several basis points.
• Use consistent daycount bases: Mixing 360day and 365day conventions in a single calculation leads to inaccurate results.
• Round appropriately: Moneymarket pricing is often quoted to four decimal places (e.g., 2.3750%). Use proper rounding to avoid cumulative errors in large portfolios.
• Monitor the repo market: Changes in repo rates directly affect the implied financing cost of holding securities, influencing the fair value of many shortterm instruments.
• Stay aware of credit spreads: While most moneymarket instruments are considered lowrisk, commercial paper and negotiable CDs may embed a credit spread over the riskfree rate. Adjust the discount yield accordingly.

Key Formulas Summary

Conclusion

Pricing moneymarket instruments is a straightforward exercise once you understand the prevailing quote conventions and daycount bases. The essential steps are:

1. Identify the instrument and its quoted yield type.
2. Apply the appropriate price formula using the correct daycount convention.
3. Convert the price to an effective or annualized yield if required for performance reporting.

By mastering these calculations, professionals can accurately assess shortterm investment opportunities, manage liquidity risk, and support the construction of reliable yield curves.

For deeper insight, explore topics such as moneymarket fundamentals, Federal Reserve repo operations, and the global CP market statistics.