V6 Modules 6–9 Errata: Bond Valuation, Yield Measures, and the Term Structure

1. Module 6 — YIELD Treats Rate as Periodic Instead of Annual

Curriculum location: Yield-to-Maturity, p. 135.

The function definition and worked call state:

"rate is the semi-annual (or periodic) coupon"

$$=\mathrm{YIELD}(\mathrm{DATE}(2025,10,15),\mathrm{DATE}(2030,10,15),1.6\%,108.15,100,2,0)$$

For YIELD, the rate argument is the security's annual coupon rate; payment frequency is supplied separately. The BRWA bond pays a 3.2% annual coupon in two semiannual installments. Entering 1.6% as rate therefore describes a different, lower-coupon bond and does not produce the stated annual yield.

Correct reading: Use 3.2% for rate and 2 for frequency: $\mathrm{YIELD}(\dots ,3.2\%,108.15,100,2,0)$. The result is approximately 1.50% per year.

This distinction matters whenever a bond pays coupons more than once per year: do not divide YIELD's rate argument by frequency.

2. Module 6 — Equation 6's Bracketed Present Value Is Attributed to the Excel YIELD Function

Curriculum location: Flat Price, Accrued Interest, and the Full Price, p. 138.

After Equation 6, the curriculum says the bracketed present value is:

"obtained using the Excel YIELD function"

That calculation starts with a known discount rate, number of periods, coupon, and face value, and asks for present value. The next worked example correctly uses PV. YIELD instead starts with a known price and solves for yield.

Correct reading: Obtain the positive bracketed amount with $-\mathrm{PV}(rate,nper,pmt,fv,type)$. Use YIELD only when price is known and the required yield is the unknown.

Choosing the inverse function changes both the required inputs and the output.

3. Module 6 — Matrix Pricing Uses Frequency $2$ for an Annual-Pay Bond

Curriculum location: Matrix Pricing Process, p. 151.

The example describes the liability as:

"four-year, 3% annual coupon payment debt liability"

$$=\mathrm{YIELD}(\mathrm{DATE}(2025,10,1),\mathrm{DATE}(2029,10,1),0.03,102.401,100,2,1)$$

The preceding valuation equation also shows four annual coupons. In YIELD, frequency 1 means annual payments and frequency 2 means semiannual payments. The displayed call therefore encodes a different cash-flow schedule from the bond being valued.

Correct reading: Use frequency 1:

$$\mathrm{YIELD}(\mathrm{DATE}(2025,10,1),\mathrm{DATE}(2029,10,1),0.03,102.401,100,1,1)$$

The corrected result still rounds to approximately 2.36%, but the schedule is now consistent with the stated bond.

At the printed dates and price, frequency 2 gives approximately 2.37%, while frequency 1 gives approximately 2.36%. The numerically close results do not make the original setup valid; frequency can materially affect other bonds.

4. Module 7 — Exhibit 2's Column $6$ Formula Omits the Final $-1$

Curriculum location: Periodicity and Annualized Yields, Exhibit 2, p. 162.

Column 6 is headed:

"Column 6:" $(1+Col.4{)}^{(Col.2)}$

For the annual row, the printed expression produces $1.045640$, but the displayed value is $0.045640$. The heading is therefore giving an accumulation factor rather than the effective rate shown in the table.

Correct reading: Use $(1+\mathrm{periodic}\mathrm{rate}{)}^{\mathrm{periodicity}}-1$ for Column 6.

The final subtraction is what converts the accumulation factor into a rate and reproduces every displayed Column 6 value.

5. Module 7 — The True-Yield "Never Higher" Claim Fails for Negative Yields

Curriculum location: Other Yield Measures and Conventions, pp. 166–167.

The discussion states:

"The true yield is never higher than the street convention yield because weekends and holidays delay the time to payment."

Exhibit 3 repeats:

"True yield is never higher than street convention yield due to the delay in time to payment."

That ordering holds for nonnegative yields, but not universally. For a single cash flow of $100$ priced at $106$, payment at one year gives

$$y(1)=\frac{100}{106}-1\approx -5.6604\%.$$

Delaying the same payment to $1.01$ years gives

$$y(1.01)={\left(\frac{100}{106}\right)}^{1/1.01}-1\approx -5.6059\%,$$

which is higher because it is less negative.

Correct reading: When yields are nonnegative, delayed payments make true yield no higher than street-convention yield. When yields are negative, true yield can instead be higher.

The missing condition can reverse the sign-sensitive comparison in a module that expressly teaches negative yields.

6. Module 7 — Example 9 Mixes Annual Spot Rates with Half-Year Periods

Curriculum location: Yield Spreads over the Benchmark Yield Curve, Example 9, pp. 178–179.

Status: Officially corrected by CFA Institute.

The example introduces:

"The government spot rates (stated as effective annual rates) are as follows:"

The preceding definition says:

"$Z$ is the Z-spread per period and is the same for all time periods."

Yet the first half-year discount term uses the annual-effective six-month spot rate directly:

$\frac{0.75}{(1+0.00127+Z{)}^1}$

The reported result is:

"The Solver add-in for Microsoft Excel finds $Z=0.00268$, or 27 bps"

The four exponents count half-year periods, so the original calculation combines incompatible rate bases. CFA Institute's official correction relabels the spot rates as annualized by multiplying by two and revises Equation 4 so that each annualized $z_i+Z$ term is divided by two inside the half-year discount factor. Solving that corrected equation gives $Z\approx 0.008997$, or about $90.0$ basis points annualized; the original 27 bps does not follow from the corrected inputs.

Correct reading: Treat the table's spot rates and $Z$ as annualized with periodicity two, divide each $z_i+Z$ term by two in the four half-year discount factors, and solve $Z\approx 0.008997$, or approximately $90.0$ basis points annualized.

Using inconsistent rate bases changes both the method and the worked answer.

7. Module 8 — Question Set Item 4 Uses $0.0025$ for a $250$-bp Quoted Margin

Curriculum location: Question Set item 4 solution, p. 196.

The question states a quoted margin of 250 bps, but the payment substitution displays:

$$\frac{(-0.005+0.0025)\times 100}{4}=\mathrm{0.5.}$$

The displayed inputs do not produce 0.5. A 250 bp quoted margin is 0.0250 in decimal form, not 0.0025.

Correct reading: Use $\frac{(-0.005+0.0250)\times 100}{4}=0.5$. The stated periodic payment of 0.5 and the subsequent discount-margin result then follow from the stated data; the keyed answer does not change.

A candidate following the printed decimal cannot reproduce the periodic payment or the subsequent discount-margin calculation, even though the intended keyed answer remains unchanged.

8. Module 8 — Example 3 Prints $\mathrm{AOR}=0.00122$ and Ranks the CP Above the $0.120\%$ CD

Curriculum location: Commercial-paper comparison example, p. 200.

After computing a price of 99.975 for the commercial paper, the curriculum displays:

$$AOR=\mathrm{0.00122.}$$

It then concludes:

"If the risks are the same, BRWA’s CP offers 0.2 bps more in annual return than CFP Bank’s CD."

Using the curriculum's own formula and price gives $(365/90)\times (100-99.975)/99.975=0.00101414$, or approximately 0.1014%. That is below the CD's 0.120% rate.

Correct reading: The commercial paper's add-on rate (AOR) is approximately 0.1014%. If the risks are the same, CFP Bank's CD offers approximately 1.9 bps more in annual return than BRWA's commercial paper.

Following the printed conclusion can make a candidate choose the lower-return instrument in a like-for-like add-on-rate comparison.

9. Module 8 — Practice Problem 6 States the Rate It Asks You to Find

Curriculum location: Practice Problem 6, p. 207.

The stem says the UK gilt has:

"a discount rate of 0.25%"

and then asks for:

"the discount rate for the UK gilt is closest to:"

Those statements conflict: the face value, price, 91-day term, and 366-day year imply $(366/91)\times (2.0-1.9)/2.0=0.2010989$, not 0.25%.

Correct reading: Delete the stated 0.25% rate from the stem and calculate from the other data. The discount rate is approximately 0.2011, or 20.11%, so choice B remains the intended answer.

As printed, a candidate who treats every stem fact as binding finds no internally consistent choice; deleting the contradictory rate restores choice B without changing the remaining data.

10. Module 9 — The Overview and Exhibit 9 State Par-Below-Spot Without a Sign Condition

Curriculum location: Learning Module Overview, p. 212; Spot, Par, and Forward Yield Curves and Interpreting Their Relationship, Exhibit 9, p. 231.

"In upward-sloping term structures, par rates will be lower than their corresponding spot rates"

"Below spot curve"

The overview and Exhibit 9 present the familiar positive-rate ordering as a general rule: an upward-sloping spot curve has the par curve below it. Yet the module's own later solution states that the upward-sloping German and Swiss negative-rate curves have par rates above spot rates. The Swiss one- through five-year data confirm the reversal: the five-year par rate is approximately -0.4741%, slightly above the five-year spot rate of -0.4757%.

Correct reading: Qualify the overview and Exhibit 9 par-versus-spot ordering as applying to non-negative spot rates. With negative rates, the ordering can reverse; for the module's upward-sloping Swiss curve, the five-year par rate is approximately -0.4741%, slightly above the five-year spot rate of -0.4757%.

Candidates should derive or check curve ordering from discount factors when rates are negative rather than applying an unqualified slope mnemonic.

11. Module 9 — Question Set Item 1 Marks True That Coupon-Bond Yields and Interpolation Create the Spot Curve

Curriculum location: Maturity Structure of Interest Rates and Spot Rates, Question Set item 1 solution, p. 219.

"the spot curve is created using yields on recently issued coupon-paying government bonds and linear interpolation."

The solution marks the statement True. On p. 214, the module defines spot rates as yields on default-risk-free zero-coupon bonds. On p. 219, the same Question Set notes that the coupon bond's yield is slightly below its five-year spot rate. A coupon bond has several dated cash flows, while its yield-to-maturity is one internal rate that reproduces the bond's total price. Recently issued government coupon bonds can provide market observations for curve estimation, but interpolating their quoted yields does not convert them into maturity-specific zero-coupon rates. The US Treasury's methodology likewise distinguishes observable coupon-security inputs from the curve-fitting process used to derive its published curve.

Correct reading: The answer should be False. Coupon-bond observations can be inputs, but a spot curve must be estimated as a zero-coupon curve, for example by stripping or bootstrapping from market prices and cash flows.

Confusing the two curves can lead a candidate to discount every cash flow at a coupon-bond yield rather than at its maturity-matched spot rate.

12. Module 9 — Question Set Item 3 Prints $\mathrm{PV}=101.34$ for a $101.314$ Spot-Rate Valuation

Curriculum location: Maturity Structure of Interest Rates and Spot Rates, Question Set item 3 solution, p. 220.

$PV=101.34$

Substituting the stated cash flows and spot rates gives 101.313873. The source first displays that result correctly as 101.314, but the following valuation and YTM equations change it to 101.34. The printed decimal rate $r=0.022195$ is the six-decimal rounding of the YTM from the unrounded 101.313873 valuation; 101.34 implies a different yield.

Correct reading: The spot-rate valuation is 101.313873, displayed as 101.314. Solving from the unrounded valuation gives $r\approx 0.022194727$, which rounds to the printed decimal 0.022195 and percentage 2.22%.

A candidate who uses 101.34 in the YTM equation cannot reproduce the printed $r=0.022195$; the unrounded 101.313873 price must carry into the yield calculation.

13. Module 9 — Question Set Item 4 Enters $0.9500\%$ as $0.095$ Instead of $0.0095$

Curriculum location: Maturity Structure of Interest Rates and Spot Rates, Question Set item 4 solution, p. 220.

$(1+0.095{)}^2$

The two-year input is 0.9500%, and the solution uses it as $Z_2$, but the denominator converts it to 0.095, which is 9.5%. Following the printed equation does not reproduce the stated price. The printed answer 99.126 is nevertheless correct because it was calculated with 0.0095.

Correct reading: Convert 0.9500% to 0.0095, so the two-year discount factor is $(1+0.0095{)}^2$. The printed bond price 99.126 remains correct.

This is a reusable percentage-to-decimal check: a tenfold rate-entry error can materially change a discounted cash flow.

14. Module 9 — Example 3 Substitutes the $1.88\%$ and $2.77\%$ Forward Rates and Solves for the Two-Year Spot Rate

Curriculum location: Par and Forward Rates, Example 3 solution, p. 224; correct Canadian inputs, p. 222.

$(1+0.0188)\times (1+0.0277)=(1+Z_2{)}^2$.

The example asks for a one-year forward rate beginning two years from now. The exact Canadian two- and three-year spot rates are 0.5680% and 0.7977%, but the displayed substitution instead uses 1.88% and 2.77% from the next forward-rate sequence and solves for a two-year spot rate. It cannot derive the requested forward rate, although the printed 1.26% answer is correct.

Correct reading: Use $(1+0.005680{)}^2(1+{\mathrm{IFR}}_{2,1})=(1+0.007977{)}^3$. Solving gives ${\mathrm{IFR}}_{2,1}$ of approximately 1.26%, so the printed answer remains unchanged.

The correction restores both the maturity indexing and the spot-to-forward method candidates need for exam calculations.

15. Module 9 — The Direct Forward-Curve Line Prints $Z_3=0.27278$ Instead of $0.027278$

Curriculum location: Par and Forward Rates, direct three-year spot-rate calculation, p. 225.

$Z_3=0.27278$

The stated one-year gross rates imply $Z_3=0.027278$. The preceding derivation and the displayed 2.73% percentage also confirm that value. The direct-calculation line moves the decimal point one place to the right.

Correct reading: The three-year spot rate is $Z_3=0.027278$, or approximately 2.73%.

Checking consistency between decimal and percentage forms prevents a tenfold rate error from being carried into valuation.

16. Module 9 — Example 4 Uses $1.0012587$ Instead of the $1.012587$ Gross Factor

Curriculum location: Par and Forward Rates, Example 4 bond valuation, p. 226.

$1.0012587$

The forward-rate table gives 1.2587%, whose decimal form is 0.012587 and whose one-period gross factor is 1.012587. The printed 1.0012587 factor corresponds to only 0.12587%. Following it does not reproduce the stated bond price, although the printed 99.126 answer is correct.

Correct reading: Use 1.012587 as the gross accumulation factor for the 1.2587% forward rate. The printed three-year bond price 99.126 remains unchanged.

A candidate who uses 1.0012587 understates the forward-rate component by a factor of ten and cannot reproduce the printed 99.126 price.

17. Module 9 — The Par-Rate Equation Counts the Final Coupon Twice

Curriculum location: Par and Forward Rates, Question Set item 2 solution, p. 226.

$\frac{PMT}{(1+0.026{)}^3}+\frac{PMT+100}{(1+0.026{)}^3}$

For a three-year annual-pay bond, the maturity-date cash flow is the final coupon plus principal. The expanded equation adds a standalone third-year coupon and then adds that same coupon again inside the final coupon-plus-principal term. The next factored line correctly includes only three coupon discount factors, which is why the printed 2.607% answer remains correct.

Correct reading: Discount coupons at years one and two, then discount the combined coupon and principal once at year three. The printed par coupon rate 2.607% remains unchanged because the following factored line uses the correct cash flows.

A candidate who counts the maturity coupon twice solves for approximately 1.966% rather than the printed 2.607% par coupon.

Complete Valuation, Yields, and Term Structure Errata Index

Scope: Modules 6–9, pp. 127–238 (printed page numbers).

Reviewed modules. Module 6, pp. 127–156; Module 7, pp. 157–186; Module 8, pp. 187–210; and Module 9, pp. 211–238.

What this review covers. Errors in the printed curriculum that would change a candidate's answer or understanding: wrong numbers, wrong formulas, reversed logic, and statements that contradict the volume's own data. It does not list spelling mistakes, equation-numbering slips, or wording that is loose but defensible.

The table lists every high-value, objectively confirmed curriculum error admitted for these modules. Repeated instances of the same defect are consolidated into one row. Extraction or import-fidelity problems, disputed readings, and low-value editorial issues are outside the public errata scope.

References

• Microsoft Support — YIELD function
• Google Docs Editors Help — YIELD
• Microsoft Support — PV function
• CFA Institute — The Term Structure of Interest Rates: Spot, Par, and Forward Curves
• Bank of England — Yield curves: terminology and concepts
• Microsoft Support — RATE function
• U.S. TreasuryDirect — Understanding Pricing and Interest Rates
• US Treasury Yield Curve Methodology
• Bank of England: Yield Curve Terminology and Concepts
• CFA Institute — 2027 CFA Program Level I Errata Notice

This article is an independent candidate-focused analysis of substantive errors identified in our review of the CFA Level I 2027 Curriculum, Volume 6 Fixed Income, Modules 6–9. It is not an official CFA Institute errata notice, and inclusion here must not be read as CFA Institute confirmation, endorsement, or approval.