FIN435 • Chapter 7 — Bond Valuation

Bond Outlook (2026) — Morningstar “Experts Forecast” (Bonds Only)

Warm-up (before you click): Based on today’s yield environment, what 10-year annual return would you expect for U.S. Aggregate Bonds and High Yield?

Write a number range + one sentence of mechanism. Then reveal the table and compare.

Open Morningstar Article Bonds section only

Click to reveal: Summary + forecast table

Core idea: Across forecasters, bond return expectations tend to cluster in the mid–single digits. A major driver is starting yield (plus spread/credit compensation), which anchors multi-year bond returns more tightly than equities.

Provider	Horizon	Bond segment	Expected return	Notes
Vanguard	10-year	U.S. Aggregate	3.8% – 4.8%	Assumptions as of 10/31/2025.
Vanguard	10-year	U.S. High Yield	4.3% – 5.3%	Credit risk premium.
Vanguard	10-year	Hedged EM sovereign	5.1% – 6.1%	Hedged series.
Vanguard	30-year	U.S. Aggregate	4.1% – 5.1%	Longer horizon.
BlackRock	10-year	U.S. Aggregate	4.1%	Assumptions as of 9/30/2025.
BlackRock	10-year	High Yield	5.7%	Defaults/spreads matter.
BlackRock	10-year	Hedged EM bonds	4.7%	Hedged; still credit exposure.
Fidelity	20-year	U.S. Aggregate	5.1% (nominal)	Longer horizon assumption.
J.P. Morgan	10–15 year	U.S. Aggregate	4.8% (nominal)	Horizon differs.
J.P. Morgan	10–15 year	High Yield	6.1%	Credit premium.
J.P. Morgan	10–15 year	EM sovereign	6.3%	Higher risk.
Schwab	10-year	U.S. Aggregate	4.8% (nominal)	Assumptions as of 10/31/2025.
Research Affiliates	10-year	U.S. Aggregate	4.7% (nominal)	Quoted in Morningstar.
GMO	7-year	U.S. bonds	1.3% (real)	Real return (inflation-adjusted).
GMO	7-year	EM bonds	1.5% (real)	Real return; horizon differs.
Morningstar	10-year	U.S. Aggregate	4.5% (nominal)	As of 12/31/2025.

Mini-discussion prompts

Why do bond forecasts cluster more tightly than stock forecasts? Use “starting yield.”
Why do high-yield forecasts exceed aggregate? What must be true about defaults/spreads?
Why do “real return” and “nominal return” forecasts differ materially?

Bond Types: Characteristics, Suitability, and Risks

Refer to Chapter 6: Every bond yield can be thought of as Real rate + Expected inflation + Maturity premium + Liquidity premium + Default (credit) premium. The “Rate Components” column below indicates which components are typically most relevant for each bond type.

Bond Type	Characteristics	Suitability	Main Risk	Rate Components (Refer to Chapter 6) Real + Infl + Maturity + Liquidity + Default
Short-Term Bonds	Lower price volatility, typically lower yields	Liquidity needs; conservative; near-term spending	Reinvestment risk (rates may fall when you roll over)	Real Infl Mat (low) Liq (low) Def (depends) Short maturity → small maturity premium; returns mostly track short-rate policy + inflation.
Long-Term Bonds	High sensitivity to rate changes; potentially higher yields	Long horizon; higher risk tolerance; liability-matching	Interest-rate risk (duration), inflation risk	Real Infl Mat (high) Liq (varies) Def (depends) Longer maturity → bigger maturity premium and higher duration sensitivity.
Corporate Bonds	Higher yields; issuer fundamentals and ratings matter	Income-seeking with risk capacity; spread pick-up	Default + downgrade risk; liquidity risk; rate risk	Real Infl Mat (varies) Liq (med–high) Def (high) Extra yield is mainly default (credit) premium + often liquidity premium.
Treasuries	Low credit risk; benchmark yield curve for pricing	Stability; recession hedge; collateral/“risk-free” anchor	Interest-rate risk (especially long end); inflation risk	Real Infl Mat (varies) Liq (low) Def (≈0) Minimal default and liquidity premia; yield mostly = real + inflation + maturity.
Municipals	Tax advantages; credit varies by issuer; call features common	Higher tax bracket; tax-efficient income; state-specific strategies	Credit + liquidity risk; call risk; rate risk	Real Infl Mat (varies) Liq (med) Def (varies) Compare after-tax yield. Credit and liquidity premia vary widely across issuers.

Prompt: Which bond type fits a short horizon vs long horizon? Which fits a high-tax investor? Which fits recession-hedging?

Click to reveal: Suggested answers (hidden key)

1) Short horizon vs long horizon

Short horizon: Short-term bonds or short/intermediate Treasuries (lower duration; match near-term cash needs).
Long horizon: Longer-term bonds (often long Treasuries for safety) if liability-matching / locking yields is the goal—accept higher duration risk.

2) High-tax investor

Municipal bonds (especially in higher tax brackets), because interest may be exempt from federal taxes (and sometimes state taxes).
Compare with tax-equivalent yield before choosing.

3) Recession-hedging goal

Treasuries (often intermediate-to-long) are the classic hedge: minimal credit risk and potential price gains if rates fall.
High yield is typically not a hedge in recessions (spreads widen, defaults rise).

Relationship Between Bond Prices and Interest Rates

Key rules

When market rates rise, fixed-rate bond prices fall.
Lower coupon bonds have more interest-rate risk than higher coupon bonds.
Longer maturities have more interest-rate risk than shorter maturities.

SEC reading: Interest Rate Risk

Core approximation

If yields change a little:

ΔP/P ≈ −(Modified Duration) × Δy

Example: Modified Duration = 7.8 ⇒ if yields rise by 1.00%, price falls by about 7.8%.

Images

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image149.jpg image004.jpg Untitled-modified (1).jpg

Duration: Meaning + Mini-Check (Interactive)

Meaning

Duration measures a bond’s interest-rate sensitivity.
High duration = price moves a lot when yields move (more volatile).
Low duration = price moves less when yields move (more stable).

Rule of thumb: longer maturity + lower coupon → higher duration.

Dropping-rate environment

If rates are expected to drop, high-duration bonds tend to gain more (bigger price increase).
Tradeoff: if yields later rise, high duration means larger price losses.
After rates drop, new reinvestment yields are lower (reinvestment risk increases).

Quick idea

Approximation: ΔP/P ≈ −(ModDur) × Δy

Use the mini-check below to sanity-check your intuition.

Duration Mini-Check

Enter a Modified Duration and a yield change (Δy). The tool computes the approximate price impact. Use +1 for +1.00% and -1 for -1.00%.

Modified Duration (e.g., 7.8)

Higher = more rate sensitivity.

Yield change Δy (in %) (e.g., +1 or -0.50)

+ means yields rise; − means yields fall.

Optional: Bond price (for $ impact)

Use 1000 for a par bond example.

Approx % price change

—

Uses: −ModDur × (Δy/100).

Approx $ change (using your price)

—

Approx $ impact = Price × (% change).

Interpretation

—

Rates up → price down; rates down → price up.

Click to reveal: Instructor note (how to talk through this)

Students should say: “High duration is a lever. If you expect yields to fall, you want more duration; if you fear yields rising, you want less.”
Remind: This is a first-order approximation; convexity matters for bigger moves and for callable bonds.

Bond Pricing and Duration in Excel

Price (annual coupon)

Price = ABS( PV( ytm, years, coupon*1000, 1000 ) )

Example: =ABS(PV(8.2%, 8, 65, 1000))

Yield to Maturity (annual)

YTM = RATE( years, coupon*1000, -price, 1000 )

Example: =RATE(15, 85, -1120, 1000)

Semiannual coupon

Price = ABS( PV( ytm/2, years*2, coupon*1000/2, 1000 ) )

YTM = RATE( years*2, coupon*1000/2, -price, 1000 ) * 2

Click to reveal: Duration functions (Excel) + interpretation

Macaulay Duration

=DURATION(settlement, maturity, coupon, yld, frequency, basis)

Example: =DURATION(DATE(2026,1,27),DATE(2036,1,27),0.05,0.045,2,0)

Interprets as a cash-flow “center of gravity” (years).

Modified Duration (use for sensitivity)

=MDURATION(settlement, maturity, coupon, yld, frequency, basis)

Example: =MDURATION(DATE(2026,1,27),DATE(2036,1,27),0.05,0.045,2,0)

If ModDur = 8, then +1% yield move ≈ −8% price move.

Convexity (optional extension)

=CONVEXITY(settlement, maturity, coupon, yld, frequency, basis)

Convexity improves accuracy for larger yield moves (and highlights why callable bonds behave differently).

Basis is the day-count convention (0 = US 30/360 is common in textbook problems).

Tip: be consistent with sign conventions in Excel (price is negative inside RATE()).

In-Class Practice Problems (Exam Prep)

Problems + Excel answers

#	Problem (given)	Answer (Excel)
1	8-year bond, coupon $65, YTM 8.2%. Price?	$903.04 ABS(PV(8.2%,8,65,1000))
2	Price $1,120, 15 years, coupon $85. YTM?	7.17% RATE(15,85,-1120,1000)
3	Price $1,180, coupon $105, 15 years, callable in 5 years at $1,100. YTC and YTM.	YTC 7.74% RATE(5,105,-1180,1100) YTM 8.35% RATE(15,105,-1180,1000)
4	Price $1,050, coupon $75. Current yield?	7.14% =75/1050
5	20-year, 9.5% coupon, semiannual, require 8.4% nominal YTM. Max price?	$1,105.69 ABS(PV(8.4%/2,40,47.5,1000))
6	20-year 7.5% coupon issued at par one year ago. Market rate now 5.5%. Price with 19 years left?	$1,232.15 ABS(PV(5.5%,19,75,1000))
7	Price $1,250, coupon $90, 25-year, callable in 5 years at $1,050. Difference YTM − YTC?	2.62% RATE(25,90,-1250,1000) − RATE(5,90,-1250,1050)
8	Price $1,150, coupon 6.35% ($63.50), 20-year, callable in 5 years at $1,067.50. Expected return?	4.20% RATE(5,63.5,-1150,1067.5)
9	25-year 8.5% coupon bond sells for $925. If YTM stays constant, what is price 5 years from now?	$930.11 ABS(PV(RATE(25,85,-925,1000),20,85,1000))

Practice #1 “Next Step”: Solve YTM in Excel (Annual & Semiannual)

Annual coupon (freq = 1)

YTM (annual):

=RATE(Years, Coupon, -Price, FaceValue)

Example: =RATE(8,65,-903.04,1000)

Sanity check: if Price < 1000, then YTM > coupon rate.

Semiannual coupon (freq = 2)

Periodic yield (per 6 months):

=RATE(Years*2, Coupon/2, -Price, FaceValue)

Nominal annual YTM (APR):

=RATE(Years*2, Coupon/2, -Price, FaceValue) * 2

Example: =RATE(16,32.5,-903.04,1000)*2

Optional: Effective annual rate (EAR)

If your periodic rate is r/2:

EAR = (1 + r/2)^2 − 1

Most textbook “YTM” quotes are nominal APR for semiannual coupons.

Cash-Flow Timeline (Practice #1 — Given YTM, find Price)

Change the inputs and click Update to see how cash flows move on the timeline. (Price today is a negative cash flow at t=0.)

Years to maturity

Coupon ($ per year)

Face value (FV)

Price today (t=0)

Payments per year

If semiannual: coupon per period = coupon/2.

Price (t=0) Coupons / FV

Standard: show inputs clearly (Rate, Nper, Pmt, PV, FV).

Where to Invest in 2026 (Key Takeaways) — “Duration matters” (JPMorgan / Priya Misra)

Video: Bond market outlook (Priya Misra, JPMorgan)

Key message: bonds can look attractive, but duration drives how much your price moves when yields move.

Open on YouTube If embed is blocked, use “Open on YouTube”.

Core themes (talking points)

Cash yields can reset downward quickly.
If rates fall, longer-duration bonds may benefit from price gains.
Credit spreads can be tight; risk is not always well-compensated.
EM yields can be higher but add FX + political risk.

Quick definitions (for students)

Duration: sensitivity of price to yield changes.
Rule of thumb: ΔP/P ≈ −(ModDur) × Δy.
Tradeoff: higher duration helps more if rates fall, hurts more if rates rise.

Discussion prompt

If the market expects rate cuts, do you move to longer-term bonds now? What tradeoffs matter most: duration, reinvestment risk, or credit risk?

Write: (1) your choice (short/intermediate/long), (2) one sentence on “why duration,” (3) one risk you’re accepting.

Suggested structure (hidden key)

View: “I expect yields to (fall / stay / rise) over the next (X) months.”
Duration choice: “Therefore I want (more / less) duration.”
Risk tradeoff: “The key risk is (price volatility / reinvestment / credit spread widening).”

Market Data & Reference Tools

FINRA Fixed Income

FINRA Fixed Income data

Use for yields, spreads, and corporate bond references.

FRED: 10Y–2Y spread

T10Y2Y (10-year minus 2-year)

Curve shape is informative; interpret with caution.

Checklist

YTM, duration, convexity, rating/spread, call features, liquidity, tax status.

Chapter 7 Quiz

Take the Chapter 7 quiz here (True/False with instant feedback).

Open Chapter 7 Quiz Bookmark

Chapter 7 Assignments (Due with Midterm 1)

1) Chapter 7 Case Study

Submit with the first midterm exam.

Case Study Questions (XLSX) Case Study Video — Part 1 (MP4) Part 2 (MP4)

Download/open chapter_7_case_questions_spring_2025.xlsx and complete the questions in Excel.

2) Critical Thinking Challenge (choose ONE)

Option A — 10Y vs 2Y spread interpretation (Yield Curve Signal)

Using the current 10Y–2Y spread, what do you conclude about the coming year? Would you recommend short-duration, intermediate, or long-duration bonds today? Defend using recession risk, rate expectations, and Fed policy.

Data: FRED T10Y2Y

Include the latest value (and the date) you used from FRED.
State your duration choice clearly (short / intermediate / long) and why.
One risk you are watching (inflation surprise, growth shock, credit spreads, etc.).

Option B — Duration Stress Test (numbers required)

Pick one bond type you would hold today (Treasury, investment-grade corporate, high yield, or municipal). Use a modified duration (from Excel MDURATION, a fund fact sheet, or another credible source) and estimate the price impact if yields move:

Shock	Compute
+1.00% yield change	ΔP/P ≈ −(ModDur) × (0.01)
−1.00% yield change	ΔP/P ≈ −(ModDur) × (−0.01)

Show your ModDur value and where it came from.
Report both % price changes (two numbers).
Explain (5–7 sentences) why that duration risk fits your horizon and risk tolerance.
Note one caveat: convexity, callable bonds, spread changes, or reinvestment risk.

Standard: concise, structured response with at least one data reference (FRED, fund fact sheet, or Excel output) and a clear recommendation.

Core Materials

Quick Video (YouTube Shorts)

Quick Question (Class)