Price-Yield Summary

Bond prices move inversely to yields, but the relationship is non-linear and complex. This summary distills the chapter into a practitioner's framework: the key metrics to watch, how they interact, and how to translate them into investment decisions.

Key takeaways

• Price-yield relationship is the foundation of all bond investing; understand it before building a portfolio.
• Duration estimates losses and gains in parallel yield shifts; convexity corrects this estimate for large moves.
• Spreads, curve shapes, and yield decomposition reveal whether bonds are attractive and how to position.
• Historical examples (2008, 2020, 2022) show how theory plays out under stress.
• Passive investors benefit from broad bond indices; active investors use these tools to tilt and optimize.

The Essentials

1. Duration is Your Anchor

Duration = weighted average time to receive bond cash flows, expressed in years.

For any bond or bond fund, duration tells you the expected percentage loss if yields rise 1% (and expected percentage gain if yields fall 1%).

Rule of thumb: Memo the formula: Price change ≈ −Duration × Yield change

• A 5-year duration fund loses 5% if yields rise 1%
• A 10-year duration fund loses 10% if yields rise 1%
• A 2-year duration fund loses 2% if yields rise 1%

Duration is observable: Every bond fund reports it (fact sheet, Morningstar, fund website).

Duration varies with:

• Maturity (longer maturity → longer duration)
• Coupon (higher coupon → shorter duration; zero-coupon → duration equals maturity)
• Yield level (higher yield → shorter duration; lower yield → longer duration)

2. Convexity Corrects Large Moves

Duration assumes a linear price-yield relationship. In reality, the curve is convex (bends upward for standard bonds). In large yield moves (2%+), convexity adds back some losses.

Simplified rule: For a 2% yield move, add back approximately 0.5–1% to the duration loss estimate.

Strategic implication: In volatile markets, longer-duration bonds with higher convexity hold up better than the linear duration model suggests. In calm markets, convexity is a non-event.

3. Spreads Are Independent of Rates

A corporate bond price depends on:

• Rate risk: Treasury yield changes (captured by duration)
• Spread risk: Credit premium changes (NOT captured by duration)

Key insight: A Treasury can fall 10% from rising rates. A corporate bond can fall the same 10% from spreading widening, even if Treasury rates are flat. You need to evaluate both risks separately.

Spread widening typically occurs in:

• Recessions (credit stress)
• During Fed tightening (liquidity concerns)
• Sector-specific shocks (e.g., bank crisis, energy crash)

Spreads narrow in:

• Expansions (strong earnings)
• Fed easing (lower rates, improved sentiment)
• Successful crisis management (e.g., Fed backstop)

4. Yield Curve Shapes Matter

Yields at different maturities (2, 5, 10, 30-year) move differently. The shape of the curve—upward-sloping, flat, inverted—indicates market expectations.

Steepening (long rates fall relative to short rates):

• Typically occurs when growth expectations improve but rates stay low, or in recession when the Fed cuts short rates aggressively.
• Helps long-duration bonds, hurts short-duration bonds.

Flattening (long rates rise relative to short rates):

• Typically occurs when short rates rise (Fed hiking) or long-term growth expectations fall (recession fears).
• Helps short-duration bonds, hurts long-duration bonds.

Parallel shift (all rates move by similar amounts):

• Typical in normal economic transitions.
• Duration fully captures the effect.

Key rate analysis:

• 2-year, 5-year, 10-year key rate durations reveal which parts of the curve drive portfolio returns.
• A portfolio with high 10-year key rate duration but low 2-year and 30-year is betting on 10-year yields staying stable.

5. Yield Decomposition Reveals True Value

A Treasury yield consists of three components:

Yield = Real risk-free rate + Inflation expectations + Term premium

Each component has different drivers and cyclicality:

Real rate:

• Driven by Fed policy and growth expectations
• Falls in recessions, rises in strong growth
• Can be inferred from TIPS yields

Inflation expectations:

• Sticky but can shift sharply
• Observable from 10-year breakeven inflation (Treasury yield − TIPS yield)
• Matters for real return calculations

Term premium:

• Compensation for long-term uncertainty
• Driven by Fed QE/QT, economic uncertainty, and supply/demand imbalances
• Can be negative (compression) or positive (expansion)
• Highest in crises, lowest after Fed QE

Strategic use:

• If you expect higher inflation, TIPS offer protection.
• If you expect term premium to expand (recession fears), shorter-duration bonds are safer.
• If you expect Fed to ease, long bonds offer best total returns (falling rates → capital gains + high coupons).

6. Callable Bonds Have Hidden Costs

Callable bonds offer higher yield but with asymmetric risk: capped upside (bond called away if rates fall), full downside (if rates rise, you lose like a straight bond).

Rule: Avoid callable bonds unless:

• You're confident rates will rise (call won't be exercised)
• You're compensated with very high extra yield (wide spread)
• Volatility is low (call option is cheap)

Compare using OAS and effective duration, not simple yield-to-maturity.

The Practitioner's Checklist

When analyzing a bond position or fund:

Step 1: Assess Rate Risk

• Check duration. Is it appropriate for my time horizon and risk tolerance?
• Estimate loss in common scenarios: What if yields rise 1%? 2%?
• Check convexity. In large moves, does convexity help or hurt?

Step 2: Assess Spread Risk

• For corporate bonds: Is spread wide or tight historically? Is credit cycle favorable?
• Check sector composition: Are we concentrated in cyclical (banks, industrials) or defensive (utilities, consumer staples) sectors?
• Check ratings: What % is investment-grade vs high-yield? What's the default probability?

Step 3: Assess Curve Risk

• Check average duration and key rate durations. Are we overweight short, intermediate, or long?
• Assess curve environment: Is the curve steep (favor long), flat (favor short), or in transition?
• Check maturity ladder. Are we barbell, bullet, or ladder? This reveals positioning.

Step 4: Assess Yield Attractiveness

• Decompose yields. What real returns am I getting after inflation? Am I compensated for duration risk?
• Compare spreads to history. Are spreads rich or cheap relative to long-term averages?
• Assess forward returns. If yields don't change, coupon income is your return (typically 2–5% depending on credit quality and duration).

Step 5: Decide and Monitor

• Match duration to time horizon. If you need money in 5 years, hold 5-year duration bonds (or shorter).
• Stay diversified. Don't concentrate in one maturity, one sector, or one credit.
• Rebalance when duration drifts. As time passes, duration shortens; as yields change, duration changes; periodically rebalance to target.

Quick Reference: Bond Fund Profiles

Safety (SHV, VGSH): 1–2 year duration

• Loss if rates rise 1%: −1% to −2%
• Return driver: coupon income
• Best for: near-term liabilities, capital preservation
• Trade-off: low yield, miss any rally if rates fall

Core (BND, AGG, VBTLX): 5–6 year duration

• Loss if rates rise 1%: −5% to −6%
• Return driver: coupon + capital appreciation/depreciation
• Best for: diversified portfolios, long-term buy-and-hold
• Trade-off: moderate volatility, neutral positioning (no big bets)

Extended (IEF, VGIT): 7–10 year duration

• Loss if rates rise 1%: −7% to −10%
• Return driver: capital appreciation if rates fall, coupon income
• Best for: investors expecting rate cuts, longer time horizons
• Trade-off: significant volatility, underperforms in rising-rate environments

Long (TLT, VGLT): 15–20 year duration

• Loss if rates rise 1%: −15% to −20%
• Return driver: capital appreciation from falling rates
• Best for: investors with very long horizons, strong conviction on rate cuts
• Trade-off: extreme volatility (2022 was −30%), major losses if rates rise

Corporate (LQD, VWOB): 5–6 year duration + 80–100 bps credit spread

• Loss if rates rise 1%: −5% to −6%
• Loss if spreads widen 1%: −5% to −6%
• Return driver: coupon + rate + spread movements
• Best for: investors seeking higher income, taking credit risk
• Trade-off: losses in recessions (spreads widen), correlation with stocks

High-Yield (HYG, VWEH): 3–5 year duration + 400–500 bps credit spread

• Loss if rates rise 1%: −3% to −5%
• Loss if spreads widen 1%: −3% to −5%
• Return driver: coupon (8–10%+) + spread compression in recoveries
• Best for: investors seeking maximum income, comfortable with equity-like volatility
• Trade-off: losses worse than stocks in recessions, requires conviction and patience

Historical Scenarios

Scenario: Recession expected, rates to fall

• Allocate to: Long duration (TLT), high-quality corporates (LQD), avoid high-yield
• Rationale: Rate decline drives capital gains; quality spreads compress; HY spreads widen

Scenario: Expansion expected, rates to rise

• Allocate to: Short duration (SHV, IEF), high-yield (HYG for income)
• Rationale: Duration losses are small; high yield compensates for rate rise; economy strong

Scenario: Inflation surprise expected

• Allocate to: TIPS, short-duration nominal (SHV), avoid long Treasuries
• Rationale: TIPS pay real + actual inflation; short bonds suffer less; long bonds lose to inflation

Scenario: Credit stress expected, growth stable

• Allocate to: Treasuries (TLT, IEF), avoid corporates
• Rationale: Flight-to-quality; spreads widen; Treasury yields may fall to offset

The Mathematics in One Table

Scenario	Yield Change	Duration 5yr Loss	Duration 10yr Loss	Convexity Help	Typical Real Loss
+1% parallel	+1.00%	−5%	−10%	+0.2%	−4.8% / −9.8%
+2% parallel	+2.00%	−10%	−20%	+0.8%	−9.2% / −19.2%
Steepening (+1% short, flat long)	+1% short	−2.5%	0%	—	−2.5% to 0%
Flattening (flat short, +1% long)	+1% long	−5%	−10%	—	−5% to −10%
+1% rise, +100 bps spread widen (corp)	+2.0% equivalent	−10% to −15%	—	+0.8%	−9.2% to −14.2%

Forward-Looking Framework

The Bottom Line

Bond price-yield relationships are governed by three factors: duration (rate sensitivity), spreads (credit risk), and curve shape. Understanding these three—and how they interact—is sufficient for competent bond investing. Passive investors benefit from broad diversified bond funds (BND, AGG) that implicitly diversify across maturities, sectors, and credit quality. Active investors use these tools to tilt portfolios toward better expected returns.

The worst mistake is taking on bond duration risk without understanding it. The best approach is matching bond duration to your time horizon, holding broad diversified indices to avoid hidden bets, and rebalancing periodically to maintain your target duration as yields change.

Related concepts

• The Inverse Price-Yield Relationship
• Yield Changes of 1 Percent
• Bond Fund Component