Money market rates: discount basis and add-on basis

What makes money market yields different from bond yields?

Money market instruments are debt securities with original maturities of one year or less. They include Treasury bills (government securities issued for a year or less), commercial paper , certificates of deposit (CDs), bankers’ acceptances , repurchase agreements and time deposits tied to market reference rates. Money market mutual funds hold these instruments and are sometimes used as an alternative to bank deposits.

A bond yield to maturity is annualized and compounded. Money market yields work differently in three ways.

Money market yield versus bond yieldthree differences

• Simple interest Memorize annualized, not compounded
• Periodicity varies Memorize Year ÷ Days, so it changes with maturity
• Non-standard quotes Memorize discount or add-on, with their own pricing formulas

1. Simple interest. The rate is annualized but not compounded.
2. Periodicity changes with maturity. A bond yield has one periodicity for every maturity, such as 2. A money market rate has periodicity $Year \div Days$, so a 30-day rate and a 180-day rate annualize differently.
3. Non-standard quotes. Many instruments are quoted as a discount rate or an add-on rate, and need their own pricing equations rather than the usual bond calculation.

Quoted rates are of two kinds, and the instrument tells you which.

Money market quoted ratesimple annual rate, not compounded

• Discount rate Memorize interest as a share of face value; the quoted amount is the face value at maturity
  • Treasury bills government, under one year
  • Commercial paper corporate
  • Bankers' acceptances bank-guaranteed trade paper
• Add-on rate Memorize interest as a share of the amount invested; the quoted amount is the price at issue
  • Certificates of deposit bank deposits
  • Repurchase agreements repos
  • Market reference rates the rate indexes

How does the discount basis work?

In the money market, the discount rate has a special meaning. The interest is built into the face value: you pay less than face value today and receive the face value at maturity. The rate is the interest as a share of the face value, annualized.

$$PV = FV \times \left(1 - \frac{Days}{Year} \times DR\right)$$

Here PV is the present value (the price you pay) and FV is the future value (the face value). The year is 360 or 365 days depending on the market, so always read it from the question.

Rearranging the formula gives the discount rate from a price. The first term, $Year \div Days$, is the periodicity. The second is the interest divided by the face value.

$$DR = \frac{Year}{Days} \times \frac{FV - PV}{FV}$$

Why a discount rate understates the return

The denominator is the face value, USD 5,000,000, and not the USD 4,930,000 the investor actually paid. Interest of USD 70,000 on the money invested is a bigger percentage than on the face value, so the quoted rate is too low. The same is true from the other side: for the issuer, a discount rate understates the cost of the money borrowed.

How does the add-on basis work?

An add-on rate is a simple interest rate on the amount invested. You put in the principal today and receive the principal plus interest at maturity.

$$FV = PV \times \left(1 + \frac{Days}{Year} \times AOR\right)$$

Rearranging gives the price of a deposit that pays a known amount, and the rate from a price.

$$PV = \frac{FV}{1 + \frac{Days}{Year} \times AOR}$$

$$AOR = \frac{Year}{Days} \times \frac{FV - PV}{PV}$$

The two quotes line up like this.

	Discount rate	Add-on rate
Formula	$\frac{Year}{Days} \times \frac{FV - PV}{FV}$	$\frac{Year}{Days} \times \frac{FV - PV}{PV}$
Interest is divided by	face value	amount invested
Quoted amount	face value at maturity	price at issue
Typical instruments	T-bills, commercial paper, bankers’ acceptances	CDs, repos, market reference rates

Exam tip Read the instrument first. Bill, paper or acceptance: discount formula. Deposit, repo or reference rate: add-on formula.

Go deeper Why 360-day years are still used

Many money market quotes use a 360-day year, a convention that began when calculations were done by hand and has stayed. Some markets use 365 days. The year in a question is part of the quote, so use the year given. The difference matters mostly when you compare instruments, which is why the next lesson restates everything on a 365-day basis.

Go deeper Money market funds as a deposit alternative

A money market mutual fund holds only eligible money market securities, so its return comes from the short-dated discount and add-on instruments above. Investors sometimes treat it as a substitute for a bank deposit.