Lesson 3 of 3 11–14% of the exam

By Daniil Tarakanov Updated Oct 21, 20262027 curriculum

Comparing money market instruments: bond equivalent yield

Convert every quote to the same basis: the bond equivalent yield, a 365-day add-on rate. For a discount quote, find the price first, then compute (365/Days) × (FV − PV) ÷ PV, where future value (FV) is the face value and present value (PV) is the price. To compare with semiannual bonds, restate the rate from periodicity 365/Days to 2.

8 min cram, 34 min full read. Based on the 2027 CFA® Program Level I curriculum, Fixed Income, Learning Module 8. Also part of the 2026 curriculum, so it applies to the November 2026 exam too.

Tailor this to you: take the self-assessment

Before this: Yield and Yield Spread Measures for Fixed-Rate Bonds, Bond Valuation: Prices and Yields

On the exam

Calculate and interpret yield measures for money market instruments

Calculate and interpret money market yields on a common basis. Expect to rank three instruments by bond equivalent yield, to compare spreads over a T-bill as a credit signal, and to convert a bond equivalent yield to a semiannual basis.

How deeply to learn each part

Know the idea: Understand it in general. It frames other topics, but you will not calculate with it.
Use it: Understand it well enough to solve a question with it. Recognize when it applies.
Memorize: Learn it by heart. The exam will not give it to you.

You know this one. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still do.

You tested strong here. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still know it.

How do you compare a discount quote with an add-on quote?

Quotes in the money market come in different bases, so the headline rates cannot be compared as they stand. A discount rate divides interest by the face value; an add-on rate divides by the amount invested; and the year can be 360 or 365 days. The common footing is the bond equivalent yield (BEY): a money market rate stated as an add-on rate on a 365-day year. It is also called the investment yield .

Getting to a bond equivalent yield

Start from the quotethen finish on a 365-day add-on basis

Discount rate (any year basis) Memorize find the price first, then compute the add-on rate on 365 days
Add-on rate, 365-day year Memorize already a bond equivalent yield
Add-on rate, 360-day year Use it multiply by 365/360

For a discount-quoted instrument the route has three steps.

Find the price per 100 from the discount rate.
Compute the add-on rate on a 365-day year from that price.
Compare the resulting yields.

Price per 100 from a discount quote Memorize

PV = 100 \times \left(1 - \frac{Days}{Year} \times DR\right)

Bond equivalent yield Memorize

BEY = \frac{365}{Days} \times \frac{FV - PV}{PV}

An add-on quote on a 365-day year is already a bond equivalent yield. An add-on quote on a 360-day year only needs rescaling, because simple interest is proportional to the year length.

Rescaling an add-on rate to a 365-day year Use it

BEY = AOR_{360} \times \frac{365}{360}

Never rescale a discount rate this way. Its denominator is the face value, so the price has to be found first.

InteractiveMoney market quotes compared on one basis

Try this 0 of 3

Raise the CD's rate until it beats the commercial paper
Switch the CD to a 360-day year at the same 4.26%
Stretch the commercial paper to 300 days or more

Days to maturity1 to 365daysQuoted rate%

Price per 10098.6

Bond equivalent yield4.319%

Semiannual basis4.335%

Ranked by bond equivalent yield (365-day add-on rate). CP = commercial paper, CD = certificate of deposit.

Rank	Quote	Price	BEY	Semi.
1. CP120 days	4.20%disc. 360	98.6	4.319%	4.335%
2. CD120 days	4.26%add-on 365	100	4.260%	4.276%

Commercial paper pays the most (BEY 4.319%) even though the certificate of deposit has the highest quoted rate (4.26%).

Show working

Commercial paper (discount 4.20%, 360-day year, 120 days)

1. Price = 100 × (1 − 120/360 × 0.042) = 98.6; interest = 100 − 98.6 = 1.4.

2. BEY = (365/120) × 1.4 ÷ 98.6 = 4.319%.

3. Semiannual basis: m = 365/120 = 3.0417; 2 × [(1 + 0.043188/3.0417)^3.0417/2 − 1] = 4.335%.

Certificate of deposit (add-on 4.26%, 365-day year, 120 days)

1. Already measured against the amount invested: 100 grows to 100 × (1 + 120/365 × 0.0426) = 101.4005.

2. BEY = (365/120) × 1.4005 ÷ 100 = 4.260% (a 365-day add-on rate is already a BEY).

3. Semiannual basis: m = 365/120 = 3.0417; 2 × [(1 + 0.0426/3.0417)^3.0417/2 − 1] = 4.276%.

Commercial paper on your calculator

120÷360×0.042=+|-+1=×100=price 98.6
STO1
100−RCL1=÷RCL1×365÷120=STO3BEY 0.043188
365÷120=STO2periods a year, m = 3.0417
RCL3÷RCL2+1=y^x(RCL2÷2)=−1=×200=4.3347%, semiannual basis

+|- change sign · STO store · RCL recall a stored number · y^x power

1ENTER120ENTER360÷0.042×−100×price 98.6
STO1
100x<>y−RCL1÷365×120÷STO3BEY 0.043188
365ENTER120÷STO2periods a year, m = 3.0417
RCL3RCL2÷1+RCL22÷y^x1−200×4.3347%, semiannual basis

ENTER enter (on the HP, puts the number on the stack) · STO store · x<>y swap the last two numbers · RCL recall a stored number · y^x power

The highest quote is not always the highest return: convert first, then compare.

Worked example Commercial paper against a CD

Two 120-day instruments have equal credit risk. The commercial paper is quoted at a 4.20% discount rate on a 360-day year. The certificate of deposit (CD) is quoted at a 4.26% add-on rate on a 365-day year. Which pays more?

Price of the paper: $100 \times (1 - 120/360 \times 0.042) = 98.60$ .
Its BEY: $365/120 \times (100 - 98.60) \div 98.60 =$ 4.319%.
The CD is already on the right basis: BEY = 4.260%.

The paper pays about 6 bps more despite its lower quote.

On your calculator

120÷360×0.042=+|-+1=×100=STO1 price, 98.6
100−RCL1=÷RCL1×365÷120= 0.043188, against the CD's 0.0426

+|- change sign · STO store · RCL recall a stored number

120ENTER360÷0.042×CHS1+100×STO1 price, 98.6
100RCL1−RCL1÷365×120÷ 0.043188, against the CD's 0.0426

ENTER enter (on the HP, puts the number on the stack) · CHS change sign · STO store · RCL recall a stored number

Rearrange itBond equivalent yield: convert a discount rate, or go back

The question asks for

A 120-day instrument is quoted at a 4.20% discount rate on a 360-day year. Its bond equivalent yield is closest to:

Discount rate, DR%Days to maturityDays in the discount-rate year

P V = 100 (1 - \frac{D a y s}{Y e a r} \times D R), B E Y = \frac{365}{D a y s} \times \frac{100 - P V}{P V}

price 98.6; 365/120 × (100 − 98.6) ÷ 98.6 = 4.319%

Bond equivalent yield, BEY4.32%

On your calculator

120÷360×0.042=+|-+1=×100=STO1price 98.6
100−RCL1=÷RCL1×365÷120=0.043188

+|- change sign · STO store · RCL recall a stored number

120ENTER360÷0.042×CHS1+100×STO1price 98.6
100RCL1−RCL1÷365×120÷0.043188

ENTER enter (on the HP, puts the number on the stack) · CHS change sign · STO store · RCL recall a stored number

Worked example Ranking three 100-day instruments

All three mature in 100 days and have the same credit risk. A certificate of deposit is quoted at a 5.05% add-on rate on a 365-day year. Commercial paper is quoted at a 4.95% discount rate on a 360-day year. A time deposit is quoted at a 4.96% add-on rate on a 360-day year. Which is best?

	Quote	Price per 100	BEY
Certificate of deposit	5.05% add-on, 365	not needed	5.050%
Commercial paper	4.95% discount, 360	98.625	5.089%
Time deposit	4.96% add-on, 360	not needed	5.029%

Certificate of deposit: already a 365-day add-on rate, so BEY $= 5.050\%$ .
Commercial paper: price $100 \times (1 - 100/360 \times 0.0495) = 98.625$ ; BEY $= 365/100 \times 1.375 \div 98.625 = 5.089\%$ .
Time deposit: $4.96\% \times 365/360 = 5.029\%$ .

The ranking is the commercial paper, then the CD, then the time deposit. The CD has the highest quote, 5.05%, yet the paper with the lowest quote wins once everything is converted.

On your calculator

100÷360×0.0495=+|-+1=×100=STO1 paper price, 98.625
100−RCL1=÷RCL1×365÷100= paper, 0.050887
0.0496×365÷360= time deposit, 0.050289

+|- change sign · STO store · RCL recall a stored number

100ENTER360÷0.0495×CHS1+100×STO1 paper price, 98.625
100RCL1−RCL1÷365×100÷ paper, 0.050887
0.0496ENTER365×360÷ time deposit, 0.050289

ENTER enter (on the HP, puts the number on the stack) · CHS change sign · STO store · RCL recall a stored number

Exam tip The highest quote is not always the highest return. Convert first, then compare.

How does the bond equivalent yield show credit risk?

Once instruments share a basis, their yields can be set against a risk-free reference such as a T-bill of the same maturity. The spread is compensation for credit risk, so a larger spread points to a riskier issuer.

Worked example Corporate paper against a bank CD

A 60-day corporate paper issue is quoted at a 4.80% discount rate on a 360-day year. A 60-day bank CD is quoted at a 4.85% add-on rate on a 365-day year. The 60-day T-bill has a BEY of 4.10%. Which has the higher credit risk?

Paper: price $100 \times (1 - 60/360 \times 0.048) = 99.20$ ; BEY $= 365/60 \times 0.80 \div 99.20 = 4.906\%$ .
CD: already a 365-day add-on rate, so BEY = 4.85%.
Spreads over the bill: paper 4.906% − 4.10% = 81 bps; CD 4.85% − 4.10% = 75 bps.

The paper carries the larger spread, so it points to higher credit risk. Comparing the raw quotes, 4.80% against 4.85%, would have given the opposite answer.

On your calculator

60÷360×0.048=+|-+1=×100=STO1 price, 99.2
100−RCL1=÷RCL1×365÷60= 0.049059
−0.041= 0.008059, so 81 bps

+|- change sign · STO store · RCL recall a stored number

60ENTER360÷0.048×CHS1+100×STO1 price, 99.2
100RCL1−RCL1÷365×60÷ 0.049059
0.041− 0.008059, so 81 bps

ENTER enter (on the HP, puts the number on the stack) · CHS change sign · STO store · RCL recall a stored number

How do you match the periodicity of a bond?

A bond yield has one periodicity, usually 2. The periodicity of a money market rate is $365 \div Days$ , because the rate is simple interest, so it differs for every maturity. A 120-day rate assumes the investment repeats about 3 times a year.

Periodicity of a money market rate Memorize

m = \frac{365}{Days}

To compare with a bond that pays semiannual coupons, put the rate on a semiannual bond basis . Use the periodicity formula from the fixed-rate yields lesson, taking $m = 365/Days$ and $n = 2$ .

Restating on a semiannual bond basis Use it

APR_2 = 2\left[\left(1 + \frac{BEY}{m}\right)^{m/2} - 1\right], \quad m = \frac{365}{Days}

Worked example A 120-day CD on a semiannual basis

The CD above has a BEY of 4.26% over 120 days. Restate it on a semiannual bond basis.

Periodicity: $m = 365/120 = 3.0417$ .
Periodic rate: $0.0426 \div 3.0417 = 1.4005\%$ .
Grow it for $m/2 = 1.5208$ periods: $1.014005^{1.5208} = 1.021378$ .
$APR_2 = 2 \times 0.021378 =$ 4.276%.

The semiannual figure is higher than 4.26% because there are fewer compounding periods in it. At low rates the gap shrinks.

On your calculator

365÷120=STO1 m
0.0426÷RCL1+1=y^x(RCL1÷2)=−1=×2= 0.042755

STO store · RCL recall a stored number · y^x power

365ENTER120÷STO1 m
0.0426RCL1÷1+RCL1ENTER2÷y^x1−2× 0.042755

ENTER enter (on the HP, puts the number on the stack) · STO store · RCL recall a stored number · y^x power

Rearrange itMoney market yield on a semiannual bond basis: convert either way

The question asks for

A 120-day instrument has a bond equivalent yield of 4.26%. Restated on a semiannual bond basis, the yield is closest to:

Money market yield, 365-day add-on basis%Days to maturity

A P R_{2} = 2 [(1 + \frac{B E Y}{m})^{m /2} - 1], m = \frac{365}{D a y s}

m = 365/120 = 3.0417; 2 × [(1 + 0.0426 ÷ 3.0417)^(3.0417/2) − 1] = 4.276%

Yield on a semiannual bond basis4.28%

On your calculator

365÷120=STO1m
0.0426÷RCL1+1=y^x(RCL1÷2)=−1=×2=0.042755

STO store · RCL recall a stored number · y^x power

365ENTER120÷STO1m
0.0426RCL1÷1+RCL1ENTER2÷y^x1−2×0.042755

ENTER enter (on the HP, puts the number on the stack) · STO store · RCL recall a stored number · y^x power

Go deeper Why the periodicity conversion moves the rate the way it does

Below 183 days, $m$ is more than 2. Moving from more periods a year to fewer raises the stated rate, the same direction rule as in the bond periodicity lesson. For an instrument longer than about 183 days, $m$ is below 2 and the semiannual figure comes out lower.

Rates in this lesson are low and maturities short, so the conversions change the rate by only a few basis points. They matter most when rates are high.

Memorize this

MemorizeThree steps to a bond equivalent yield

Step	Discount quote	Add-on quote
1. Price per 100	$100 \times (1 - \frac{Days}{Year} DR)$	not needed
2. 365-day add-on rate	$\frac{365}{Days} \times \frac{100 - PV}{PV}$	365-day year: as quoted. 360-day year: $\times \frac{365}{360}$
3. Compare	rank by BEY	rank by BEY

Memory hook Price, add-on, compare. A discount rate can never be compared as it stands: it must go through the price.

Know it cold Never scale a discount rate by 365/360. Scaling is for add-on rates only.

MemorizePeriodicity and semiannual conversion

Memory hook A 120-day rate is earned about 3 times a year; a bond coupon, twice. Fewer periods, higher stated rate (below 183 days).

Know it cold $m = 365/Days$ . Use $(1 + APR_m/m)^m = (1 + APR_2/2)^2$ . The gap grows with the rate level.

Getting to a bond equivalent yield

Start from the quotethen finish on a 365-day add-on basis

Discount rate (any year basis) Memorize find the price first, then compute the add-on rate on 365 days
Add-on rate, 365-day year Memorize already a bond equivalent yield
Add-on rate, 360-day year Use it multiply by 365/360

What the bond equivalent yield is for

Bond equivalent yielda 365-day add-on rate, also called the investment yield

Rank money market instruments Memorize the highest quote is not always the highest return
Measure spread over a T-bill Use it a bigger spread signals more credit risk
Compare with bond yields Use it restate from periodicity 365/Days to 2

Price per 100 from a discount quote

PV = 100 \times \left(1 - \dfrac{Days}{Year} \times DR\right)

Quick example

A 91-day bill at a 3.70% discount rate (360-day year): 100 × (1 − 91/360 × 0.037) = 99.06.

On your calculator

91÷360×0.037=+|-+1=×100= 99.0647

+|- change sign

91ENTER360÷0.037×CHS1+100× 99.0647

ENTER enter (on the HP, puts the number on the stack) · CHS change sign

Bond equivalent yield

BEY = \dfrac{365}{Days} \times \dfrac{FV - PV}{PV}

Quick example

A 150-day bill priced at 98.00 per 100: 365/150 × 2 ÷ 98 = 4.966%.

On your calculator

100−98=÷98×365÷150= 0.049660

100ENTER98−98÷365×150÷ 0.049660

ENTER enter (on the HP, puts the number on the stack)

Rescaling an add-on rate to a 365-day year

BEY = AOR_{360} \times \dfrac{365}{360}

Quick example

A CD at a 3.90% add-on rate on a 360-day year: 3.90% × 365/360 = 3.954%.

On your calculator

0.039×365÷360= 0.039542

0.039ENTER365×360÷ 0.039542

ENTER enter (on the HP, puts the number on the stack)

Periodicity of a money market rate

m = \dfrac{365}{Days}

Quick example

A 75-day instrument has periodicity 365 ÷ 75 = 4.87.

On your calculator

365÷75= 4.8667

365ENTER75÷ 4.8667

ENTER enter (on the HP, puts the number on the stack)

Restating on a semiannual bond basis

APR_2 = 2\left[\left(1 + \dfrac{BEY}{m}\right)^{m/2} - 1\right], \quad m = \dfrac{365}{Days}

Quick example

A 60-day BEY of 5.27%: m = 365/60 = 6.0833, so 2 × [(1 + 0.0527 ÷ 6.0833)^(6.0833/2) − 1] = 5.317%.

On your calculator

365÷60=STO1 m
0.0527÷RCL1+1=y^x(RCL1÷2)=−1=×2= 0.053167

STO store · RCL recall a stored number · y^x power

365ENTER60÷STO1 m
0.0527RCL1÷1+RCL1ENTER2÷y^x1−2× 0.053167

ENTER enter (on the HP, puts the number on the stack) · STO store · RCL recall a stored number · y^x power

How it is asked

Bond equivalent yield of a discount quote

90-day CP at a 4.60% discount rate, 360-day year.

Price 98.85; BEY = 365/90 × 1.15 ÷ 98.85 = 4.718%. Trap: 4.60% (no conversion), 4.66% (rescale only).
Which instrument pays more?

CP at 4.60% discount (360) against a CD at 4.66% add-on (365), both 90 days.

CP BEY 4.718% beats the CD at 4.66%: the CP. Trap: picking the higher quote.
Restate on a semiannual bond basis

73-day bill, BEY 3.60%.

m = 365/73 = 5; 2 × [(1 + 0.036/5)^(5/2) − 1] = 3.619%. Trap: 3.58% (wrong direction).
Credit risk from spreads

Two 60-day instruments with BEYs of 4.91% and 4.85% against a 4.10% bill.

Spreads 81 and 75 bps: the first carries more credit risk.

Exam traps

Comparing a discount rate directly with an add-on rate. Convert the discount rate to a bond equivalent yield first.
Rescaling a discount rate by 365/360 without converting it to an add-on rate first. That treats it as an add-on quote.
Using a 360-day year in the bond equivalent yield. The BEY always uses 365.
Converting the periodicity the wrong way. Going from 365/Days (more than 2 for a short bill) to 2 raises the stated rate.

Checkpoint

5 exam-style questions. About 90 seconds each.

1A 150-day commercial paper issue is quoted at a 4.40% discount rate (360-day year). Its bond equivalent yield is closest to:
2Two 150-day instruments have the same credit risk: commercial paper at a 4.40% discount rate (360-day year) and a CD at a 4.50% add-on rate (365-day year). Which offers the higher return?
3A 61-day bill has a bond equivalent yield of 4.00%. Restated on a semiannual bond basis it is closest to:
4A 60-day certificate of deposit is quoted at a 5.00% add-on rate on a 360-day year. Its bond equivalent yield is closest to:
5The periodicity of a money market rate on a 45-day instrument, using a 365-day year, is closest to:

Key takeaways

Bond equivalent yield = a 365-day add-on rate. Convert discount quotes through the price first.
Rank money market instruments only after converting them to the same basis.
Money market periodicity = 365 ÷ Days. Convert to 2 to compare with semiannual bonds.
Spreads over a T-bill, measured in bond equivalent yield, signal relative credit risk.

Price per 100 from a discount quote

PV = 100 \times \left(1 - \dfrac{Days}{Year} \times DR\right)

Quick example

A 91-day bill at a 3.70% discount rate (360-day year): 100 × (1 − 91/360 × 0.037) = 99.06.

On your calculator

91÷360×0.037=+|-+1=×100= 99.0647

+|- change sign

91ENTER360÷0.037×CHS1+100× 99.0647

ENTER enter (on the HP, puts the number on the stack) · CHS change sign

Bond equivalent yield

BEY = \dfrac{365}{Days} \times \dfrac{FV - PV}{PV}

Quick example

A 150-day bill priced at 98.00 per 100: 365/150 × 2 ÷ 98 = 4.966%.

On your calculator

100−98=÷98×365÷150= 0.049660

100ENTER98−98÷365×150÷ 0.049660

ENTER enter (on the HP, puts the number on the stack)

Rescaling an add-on rate to a 365-day year

BEY = AOR_{360} \times \dfrac{365}{360}

Quick example

A CD at a 3.90% add-on rate on a 360-day year: 3.90% × 365/360 = 3.954%.

On your calculator

0.039×365÷360= 0.039542

0.039ENTER365×360÷ 0.039542

ENTER enter (on the HP, puts the number on the stack)

Periodicity of a money market rate

m = \dfrac{365}{Days}

Quick example

A 75-day instrument has periodicity 365 ÷ 75 = 4.87.

On your calculator

365÷75= 4.8667

365ENTER75÷ 4.8667

ENTER enter (on the HP, puts the number on the stack)

Restating on a semiannual bond basis

APR_2 = 2\left[\left(1 + \dfrac{BEY}{m}\right)^{m/2} - 1\right], \quad m = \dfrac{365}{Days}

Quick example

A 60-day BEY of 5.27%: m = 365/60 = 6.0833, so 2 × [(1 + 0.0527 ÷ 6.0833)^(6.0833/2) − 1] = 5.317%.

On your calculator

365÷60=STO1 m
0.0527÷RCL1+1=y^x(RCL1÷2)=−1=×2= 0.053167

STO store · RCL recall a stored number · y^x power

365ENTER60÷STO1 m
0.0527RCL1÷1+RCL1ENTER2÷y^x1−2× 0.053167

ENTER enter (on the HP, puts the number on the stack) · STO store · RCL recall a stored number · y^x power

All Fixed Income formulas, every lesson

Practice exam-style questions on Yield and Yield Spread Measures for Floating-Rate Instruments

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Yield and Yield Spread Measures for Floating-Rate Instruments on 3 pages

What to memorize, the concept maps, every formula with a worked example and keystrokes for the TI BA II Plus and HP 12C, how each idea is asked, and the traps. Print it, or keep it on your phone.

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Term Structure: Spot, Par and Forward Curves Fixed Income
Pricing and Valuing Forward Contracts and FRAs Derivatives
Monetary Policy Economics

Questions candidates ask

What is the bond equivalent yield of a money market instrument?

Its return expressed as a simple add-on rate on a 365-day year, measured against the price paid. It is also called the investment yield.

How do you convert a discount rate to a bond equivalent yield?

Price the instrument from the discount rate, then compute 365 over days times the interest earned divided by the price. Scaling the discount rate alone gives the wrong answer.

Why convert money market yields to a semiannual basis?

To compare them with yields on bonds that pay coupons twice a year. The conversion uses the money market periodicity, 365 over days, and a bond periodicity of 2.

How does a bond equivalent yield show credit risk?

Compare each instrument's bond equivalent yield with a T-bill of the same maturity. A larger spread over the bill points to more credit risk.

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