FRM Exam Part I · Bond Yields and Return Calculations

Treasury Securities, STRIPS and Day Count Conventions

Updated 11 October 2026 · Fact-checked

U.S. Treasuries are bills (discount, up to one year), notes and bonds (semiannual coupons). STRIPS are zero-coupon securities made from coupons and principal. Price a STRIPS as face ÷ (1 + y/2)^(2T). Day counts set accrued interest: actual/actual for Treasury notes and bonds, 30/360 for corporates, and actual/360 for bills, which are quoted on a discount basis.

Understand Treasury Securities, STRIPS and Day Counts

The U.S. Treasury issues three main types of marketable debt. T-bills mature in one year or less, pay no coupon and are sold at a discount to face value. Notes (2 to 10 years) and bonds (more than 10 years) pay a fixed coupon every six months and repay face value at maturity.

STRIPS (Separate Trading of Registered Interest and Principal of Securities) are zero-coupon securities. Dealers strip a Treasury note or bond into its individual coupon payments and its principal. Each piece trades separately and pays one cash flow at one date. A STRIPS price is simply the discounted value of that single payment. Because there is no coupon, a STRIPS has the highest duration of any bond with the same maturity. Its Macaulay duration equals its maturity. Its modified duration is maturity ÷ (1 + y/2) with semiannual compounding.

T-bills are quoted on a discount yield basis, which uses face value as the base and a 360-day year. This understates the true return. The bond equivalent yield (BEY) uses the price paid as the base and a 365-day year, so it can be compared with coupon bond yields. For the same bill, BEY exceeds the discount yield. The simple BEY formula in this guide applies to bills of 182 days or less.

Day count conventions decide how many days of interest accrue between two dates. Actual/actual (used for Treasury notes and bonds) counts real days in the period over real days in the coupon period. 30/360 (used for most corporate and agency bonds) treats every month as 30 days and the year as 360. Actual/360 (used for T-bills, which are quoted on a discount basis, and for other money market instruments such as SOFR-type rates) counts real days over 360.

Accrued interest matters because a bond buyer pays the dirty price (full price) = clean price (quoted) + accrued interest. Quotes always use the clean price.

Key formulas to remember

STRIPS / zero-coupon price: P = F ÷ (1 + y/2)^(2T); Semiannual compounding is the Treasury convention. T is in years. For annual compounding use (1 + y)^T.
T-bill discount yield: d = (F − P) ÷ F × (360 ÷ t); t is days to maturity. Base is face value, year is 360 days.
T-bill price from discount yield: P = F × (1 − d × t ÷ 360); Rearranged form of the discount yield.
Bond equivalent yield (bill, t ≤ 182 days): BEY = (F − P) ÷ P × (365 ÷ t); Base is price paid, year is 365 days. This simple formula applies only to bills of 182 days or less. Longer bills need a quadratic adjustment, rarely tested.
Accrued interest: AI = Coupon × (days since last coupon ÷ days in coupon period); Coupon is the semiannual payment. Count days by the stated convention.
Dirty price: Dirty = Clean + Accrued interest; The buyer pays the dirty price.
30/360 day count: Days = 360(Y2 − Y1) + 30(M2 − M1) + (D2 − D1); Day 31 is usually treated as 30. Follow the exam's stated rule.

How to solve Treasury Securities, STRIPS and Day Counts questions

Use this order for any question on Treasuries, STRIPS or day counts.

1Identify the instrument: bill, note or bond, or STRIPS. This tells you coupon or no coupon.
2Identify the convention the question names: discount yield, BEY, actual/actual, 30/360 or actual/360.
3Write down the matching formula before using numbers.
4Convert time correctly: days over 360 or 365 for bills, years times 2 for semiannual periods.
5Compute step by step, keeping at least four decimals until the end.
6For bonds, separate clean and dirty price. Add accrued interest only if the question asks what the buyer pays.
7Sense-check: BEY should exceed the discount yield, and a higher yield should mean a lower price.

Quickest way: Shortcut for bill yields and STRIPS prices

When to use it: When the question gives a price or yield and asks you to convert between discount yield, BEY or STRIPS price.

For bills, find the dollar discount first: F − P, or F × d × t ÷ 360.
Divide that discount by P (not F) and multiply by 365 ÷ t to get BEY.
For a STRIPS, on a calculator set N = 2T, I/Y = y ÷ 2, FV = F, PMT = 0, then compute PV.
Eliminate options: price must be below face value, and BEY must exceed discount yield.

Common mistakes in Treasury Securities, STRIPS and Day Counts

Using 365 days for the discount yield
Students mix the bill discount quote with BEY.
Fix: Discount yield uses 360 and face value. BEY uses 365 and price paid.
Dividing the discount by face value when computing BEY
The discount yield formula is fresh in memory.
Fix: For BEY the base is the price paid P.
Discounting a STRIPS with annual compounding when semiannual is given
Students ignore the Treasury convention.
Fix: Use y/2 and 2T periods unless the question states annual compounding.
Treating the quoted price as the amount paid
Accrued interest is forgotten.
Fix: Quoted price is clean. Add accrued interest for the settlement amount.
Counting actual days under 30/360
Real calendar days feel natural.
Fix: Apply the 30-day month rule and use the 360-day year.
Thinking STRIPS pay coupons or have Macaulay duration below maturity
STRIPS are derived from coupon bonds.
Fix: A STRIPS has one payment, so its Macaulay duration equals its time to maturity. Its modified duration is that figure divided by (1 + y/2).

Worked examples

Example 1

A 180-day T-bill with face value $100 is priced at $97.50. Compute the discount yield and the bond equivalent yield.

Show the solution

Discount = 100 − 97.50 = 2.50.
Discount yield = 2.50 ÷ 100 × 360 ÷ 180 = 0.025 × 2 = 5.000%.
BEY = 2.50 ÷ 97.50 × 365 ÷ 180.
2.50 ÷ 97.50 = 0.025641.
365 ÷ 180 = 2.027778.
BEY = 0.025641 × 2.027778 = 0.05199, about 5.20%.

Answer: Discount yield = 5.00%; BEY ≈ 5.20%.

Example 2

A Treasury STRIPS with face value $1,000 matures in 5 years. The yield is 4% with semiannual compounding. What is its price?

Show the solution

Periods = 2 × 5 = 10.
Periodic yield = 4% ÷ 2 = 2% = 0.02.
Price = 1,000 ÷ (1.02)^10.
(1.02)^10 = 1.218994.
Price = 1,000 ÷ 1.218994 = 820.35.

Answer: Price ≈ $820.35.

Exam tips

Know which convention belongs to which instrument: bills actual/360, Treasury notes and bonds actual/actual, corporates 30/360.
Expect questions that ask which yield is higher. BEY is above the discount yield.
Check whether the question says semiannual or annual compounding before discounting.
Use the calculator's N, I/Y, FV, PMT, PV keys for STRIPS to save time.
If a question asks for the cost to the buyer, add accrued interest to the clean price.

Practice questions from Bond Yields and Return Calculations

Treasury Securities, STRIPS and Day Counts: frequently asked questions

What are Treasury STRIPS?

STRIPS are zero-coupon securities created by separating the coupons and principal of a Treasury note or bond. Each piece pays one cash flow at one date. They sell at a discount to face value.

What is the difference between 30/360 and actual/actual?

30/360 treats each month as 30 days and the year as 360, so accrual is simple and fixed. Actual/actual uses the real number of days in the period and the real number in the coupon period. Treasury notes and bonds use actual/actual; many corporate bonds use 30/360.

Why is the bond equivalent yield higher than the discount yield?

For the same bill, BEY exceeds the discount yield. The discount yield divides the gain by face value, which is larger than the price paid, and uses a 360-day year. BEY divides by the price and uses a 365-day year, so both changes raise the number. The simple BEY formula applies only to bills of 182 days or less; longer bills need an adjusted formula.

How do I price a zero-coupon bond?

Divide face value by (1 + y/2) raised to 2T for semiannual compounding. For annual compounding, divide by (1 + y)^T. Always confirm the compounding stated in the question.