Example: Money market yields

A $1,000 90-day T-bill is priced with an annualized discount of 1.2%. Calculate its market price and its annualized add-on yield based on a 365-day year.

A $1 million negotiable CD with 120 days to maturity is quoted with an add-on yield of 1.4% based on a 365-day year. Calculate the payment at maturity for this CD and its bond equivalent yield.

A bank deposit for 100 days is quoted with an add-on yield of 1.5% based on a 360-day year. Calculate the bond equivalent yield and the yield on a semiannual bond basis.

Answer:

The discount from face value is 1.2% × 90 / 360 × 1,000 = $3 so the current price is 1,000 – 3 = $997.

The equivalent add-on yield for 90 days is 3 / 997 = 0.3009%. The annualized add-on yield based on a 365-day year is 365 / 90 × 0.3009 = 1.2203%. This add-on yield based on a 365-day year is referred to as the bond equivalent yield for a money market security.

The add-on interest for the 120-day period is 120 / 365 × 1.4% = 0.4603%.

At maturity, the CD will pay $1 million × (1 + 0.004603) = $1,004,603.

The quoted yield on the CD is the bond equivalent yield because it is an add-on yield annualized based on a 365-day year.

Because the yield of 1.5% is an annualized yield calculated based on a 360-day year, the bond equivalent yield, which is based on a 365-day year, is:

365 / 360 × 1.5% = 1.5208%

We may want to compare the yield on a money market security to the YTM of a semiannual-pay bond. The method is to convert the money market security’s holding period return to an effective semiannual yield, and then double it.

Because the yield of 1.5% is calculated as the add-on yield for 100 days times 100 / 360, the 100-day holding period return is 1.5% × 100 / 360 = 0.4167%. The effective annual yield is 1.004167365/100 − 1 = 1.5294%, the equivalent semiannual yield is 1.015294½ − 1 = 0.7618%, and the annual yield on a semiannual bond basis is 2 × 0.7618% = 1.5236%.

Because the periodicity of the money market security, 365 / 100, is greater than the periodicity of 2 for a semiannual-pay bond, the simple annual rate for the money market security, 1.5%, is less than the yield on a semiannual bond basis, which has a periodicity of 2.