Short-Term Yield Conventions and Calculations

Why This Topic Matters
In the AFP Certified Treasury Professional (CTP) body of knowledge, Short-Term Yield Conventions and Calculations sits inside Corporate Liquidity Management because treasury professionals invest excess cash in money market instruments and borrow short term every day. The problem is that different instruments quote their returns in different ways: Treasury bills and commercial paper are quoted on a discount basis, certificates of deposit and repos on an interest-bearing (add-on) basis, money market funds on a 7-day yield, and many bonds on a bond equivalent basis. A 5.00% discount rate is not the same as a 5.00% money market yield, which is not the same as a 5.00% effective annual yield. If a treasurer compares quoted rates without converting them to a common basis, the firm may pick the lower-earning investment or the higher-cost borrowing while believing it did the opposite. The CTP exam tests this heavily because it is one of the few areas where candidates must do actual arithmetic, and because getting it right directly protects shareholder value.

What It Is
Short-term yield conventions are the standardized rules for (1) counting days and (2) expressing a return earned over a period shorter than one year as an annual percentage. The key conventions you must know are:

1. Day-count conventions
- Actual/360 (money market basis): used for U.S. T-bills, commercial paper, bankers acceptances, CDs, repos, Eurodollar deposits and most U.S. money market instruments. Interest accrues on actual days elapsed, but the year is assumed to have 360 days.
- Actual/365: used for the bond equivalent yield and for sterling and some other non-U.S. money markets.
- 30/360: assumes every month has 30 days and the year has 360; used mainly for U.S. corporate and municipal bonds, not for money market instruments.
- Actual/Actual: used for U.S. Treasury notes and bonds.

2. Bank Discount Yield (BDY), also called the discount rate
The quoting convention for T-bills, commercial paper and bankers acceptances. The investor buys at a price below face value and receives face value at maturity. The discount is expressed as a percentage of face value (not the price paid) and annualized on a 360-day year. Because it divides by face value rather than the amount actually invested, BDY understates the true return.

3. Money Market Yield (MMY), also called the CD-equivalent or add-on yield
Expresses the return as a percentage of the price actually paid, annualized on a 360-day year. This is how interest-bearing instruments such as CDs, repos and Eurodollar deposits are quoted. It is always higher than the BDY for the same instrument.

4. Bond Equivalent Yield (BEY), also called the investment yield or coupon-equivalent yield
Return as a percentage of price paid, annualized on a 365-day year. It allows a money market instrument to be compared with a semiannual coupon bond. BEY is always higher than MMY because 365 is larger than 360.

5. Effective Annual Yield (EAY), also called the effective annual rate
The compounded annual return, assuming the holding-period yield can be reinvested at the same rate for the whole year. It is the only measure that reflects compounding and is the most accurate basis for comparing instruments with different maturities.

6. Holding Period Yield (HPY)
The unannualized return actually earned over the holding period: (ending value minus beginning value plus any income) divided by beginning value.

7. Tax-Equivalent Yield
Converts a tax-exempt yield (for example on a municipal security) to the pre-tax yield a taxable instrument would need to offer to be equivalent.

How It Works: The Formulas
Let F = face (par) value, P = purchase price, D = F minus P (the dollar discount), and t = actual days to maturity (or days held).

Bank Discount Yield
BDY = (D / F) x (360 / t)

Price from a quoted discount rate
P = F x [1 minus (BDY x t / 360)]

Money Market Yield
MMY = (D / P) x (360 / t)
Conversion from discount rate: MMY = (360 x BDY) / [360 minus (BDY x t)]

Bond Equivalent Yield
BEY = (D / P) x (365 / t)
Conversion from discount rate: BEY = (365 x BDY) / [360 minus (BDY x t)]
Conversion from MMY: BEY = MMY x (365 / 360)

Holding Period Yield
HPY = D / P = (F minus P) / P

Effective Annual Yield
EAY = (1 + HPY) raised to the power (365 / t), minus 1
Equivalent form using a periodic rate i compounded m times per year: EAY = (1 + i/m) raised to the power m, minus 1

Interest on an add-on instrument (CD, repo, Eurodollar deposit, bank loan)
Interest = Principal x Rate x (t / 360)
Maturity value = Principal + Interest

Tax-Equivalent Yield
TEY = Tax-exempt yield / (1 minus marginal tax rate)

The ordering rule you must memorize
For any discount instrument: BDY is less than MMY, which is less than BEY, which is less than EAY. Why? BDY divides by the larger number (face value) and uses 360 days, so it is the smallest. MMY switches the denominator to the smaller price paid, raising the yield. BEY keeps the price denominator but annualizes over 365 days, raising it further. EAY adds compounding, raising it the most. The gaps widen as the discount rate rises and as maturity lengthens.

Worked Example 1: Treasury bill
A 91-day T-bill with $1,000,000 face value is purchased for $990,000. D = $10,000.
- BDY = (10,000 / 1,000,000) x (360 / 91) = 0.0100 x 3.956 = 3.96%
- MMY = (10,000 / 990,000) x (360 / 91) = 0.010101 x 3.956 = 4.00%
- BEY = (10,000 / 990,000) x (365 / 91) = 0.010101 x 4.011 = 4.05%
- HPY = 10,000 / 990,000 = 1.0101%
- EAY = (1.010101) raised to (365/91 = 4.011), minus 1 = 4.11%
Notice the ordering: 3.96% < 4.00% < 4.05% < 4.11%.

Worked Example 2: Pricing commercial paper from a quoted discount rate
A company issues $10,000,000 of 30-day commercial paper at a 5.00% discount rate.
- P = 10,000,000 x [1 minus (0.05 x 30 / 360)] = 10,000,000 x (1 minus 0.004167) = $9,958,333
- Dollar discount = $41,667
- MMY = (41,667 / 9,958,333) x (360 / 30) = 0.004184 x 12 = 5.02%
- Check with the conversion formula: MMY = (360 x 0.05) / [360 minus (0.05 x 30)] = 18 / 358.5 = 5.02%. Same answer.
The issuer's true all-in cost on the cash actually received is 5.02%, not 5.00%.

Worked Example 3: Interest-bearing CD
A $5,000,000 CD pays 4.80% for 182 days (Actual/360).
- Interest = 5,000,000 x 0.048 x (182 / 360) = $121,333
- Maturity value = $5,121,333
- HPY = 121,333 / 5,000,000 = 2.4267%
- EAY = (1.024267) raised to (365/182 = 2.0055), minus 1 = 4.92%

Worked Example 4: Comparing a muni to a taxable instrument
A tax-exempt security yields 3.00%. The company's marginal tax rate is 25%.
- TEY = 0.03 / (1 minus 0.25) = 0.03 / 0.75 = 4.00%
A taxable instrument must yield more than 4.00% to beat the muni.

Worked Example 5: Choosing between two quoted rates
Instrument A: 90-day T-bill quoted at a 4.90% discount rate. Instrument B: 90-day CD quoted at a 4.95% add-on (MMY) rate. Which earns more?
- Convert A to MMY: (360 x 0.049) / [360 minus (0.049 x 90)] = 17.64 / 355.59 = 4.96%
- A at 4.96% MMY slightly beats B at 4.95% MMY, even though its quoted rate looked lower. This is exactly the trap the exam sets.

Instrument-by-Instrument Quoting Summary
- U.S. Treasury bills: discount basis, Actual/360; often also shown as BEY (investment yield) in Treasury auction results.
- Commercial paper: discount basis, Actual/360 (some is issued interest-bearing).
- Bankers acceptances: discount basis, Actual/360.
- Negotiable CDs: add-on (interest-bearing), Actual/360.
- Repurchase agreements: add-on, Actual/360; the repo rate is the implied interest rate between the sale and repurchase prices.
- Eurodollar time deposits: add-on, Actual/360.
- Money market mutual funds: 7-day yield (simple and compounded/effective versions); SEC-mandated disclosure.
- Sterling instruments: typically Actual/365.

How to Answer Exam Questions on This Topic
Step 1: Identify what the question gives you (face, price, discount rate, days) and what it asks for (price, BDY, MMY, BEY, EAY, interest, TEY).
Step 2: Identify the instrument and therefore the convention. Discount instrument or add-on instrument? 360 or 365 days?
Step 3: Write the formula before plugging in numbers. Most errors come from using face value where price belongs, or 360 where 365 belongs.
Step 4: Compute the dollar discount or dollar interest first. Everything else flows from it.
Step 5: Annualize using the correct day count.
Step 6: Sanity check the answer against the ordering rule (BDY < MMY < BEY < EAY). If your MMY is lower than your BDY, you made an error.
Step 7: If the question compares two instruments, convert both to the same basis (usually MMY, BEY or EAY) before deciding.

Exam Tips: Answering Questions on Short-Term Yield Conventions and Calculations

Tip 1: Face value versus price is the number one trap. The bank discount yield is the only measure that uses face value in the denominator. Every other yield measure (MMY, BEY, HPY, EAY) uses the price actually paid. Distractor answers are frequently built by swapping these two.

Tip 2: 360 versus 365 is the number two trap. BDY and MMY use 360. BEY and EAY use 365. If a question says bond equivalent or investment yield, think 365. If it says money market, discount, CD-equivalent or add-on, think 360.

Tip 3: Memorize the ordering rule and use it to eliminate answers. For a discount instrument, BDY < MMY < BEY < EAY. If the question asks for BEY and offers four choices, the correct answer must be higher than any MMY figure you compute and lower than the EAY. This alone often eliminates two choices.

Tip 4: Know when to compound and when not to. BDY, MMY and BEY are simple annualizations (multiply by 360/t or 365/t). Only EAY compounds (raise to the power 365/t). Questions that say effective, compounded or annual equivalent are asking for EAY.

Tip 5: When pricing from a quoted discount rate, subtract from 1. Price = Face x [1 minus (d x t/360)]. Candidates sometimes add instead of subtract or forget to multiply by face value.

Tip 6: Interest-bearing instruments earn interest on principal, not face. For CDs, repos and loans: Interest = Principal x Rate x t/360. The maturity value is principal plus interest. Do not apply discount formulas to add-on instruments.

Tip 7: Comparison questions require a common basis. If one instrument is quoted on a discount basis and another on an add-on basis, the exam wants you to convert before comparing. The instrument with the lower quoted discount rate frequently turns out to be the higher-yielding choice after conversion.

Tip 8: Tax-equivalent yield divides, it does not multiply. TEY = tax-exempt yield / (1 minus tax rate). A distractor will show tax-exempt yield x (1 minus tax rate), which is how you would convert a taxable yield to an after-tax yield, the reverse operation.

Tip 9: Watch the units and rounding. Rates may be given as percentages or decimals; days may be given directly or as a date range you must count. Carry at least four decimal places through intermediate steps and round only at the end. Answer choices are often separated by only a few basis points.

Tip 10: Remember the conceptual questions too. Not every question is numerical. Be ready to state that BDY understates the true yield because it uses face value and a 360-day year, that EAY is the most accurate comparison measure because it reflects compounding, that T-bills and commercial paper are discount instruments while CDs and repos are interest-bearing, and that money market funds disclose a 7-day yield.

Tip 11: Think like a treasurer, not just a calculator. The exam may frame a question as a borrowing decision (what is the true cost of issuing commercial paper at a given discount rate) or an investing decision (which instrument maximizes return for a given maturity). The math is identical; what changes is whether a higher number is good (investing) or bad (borrowing).

Tip 12: Practice until the conversions are automatic. Work the formulas forward (from price to yield) and backward (from yield to price) using different maturities (30, 90, 182, 270 days) until the ordering and magnitudes feel intuitive. Under exam time pressure, familiarity is what prevents the small errors that cost points.

One-Paragraph Summary
Short-term yield conventions exist because money market instruments quote returns in incompatible ways. Bank discount yield measures the discount against face value on a 360-day year and understates return; money market yield measures it against price paid on a 360-day year; bond equivalent yield uses price paid and a 365-day year; effective annual yield compounds the holding-period yield over a 365-day year and is the truest comparison measure. Interest-bearing instruments accrue interest on principal at Actual/360. To succeed on the CTP exam, identify the instrument and its convention, write the formula, use price (not face) except for BDY, use 365 only for BEY and EAY, compound only for EAY, convert everything to a common basis before comparing, and always check your answer against the ordering BDY < MMY < BEY < EAY.