Chapter 4 of 6

Bond yields, duration and the yield curve

Connect fixed cash flows, discount rates, duration and the information—and ambiguity—in a yield curve.

3 min read · Original educational chapter

In this chapter

Yield is inferred from price and cash flows
Duration is a local sensitivity
The curve can reflect several forces
Decision lab: Duration is a local sensitivity
Worked example
Common mistakes
Check your understanding

Yield is inferred from price and cash flows #

For a plain fixed-income claim, valuation discounts expected payments. With fixed contractual cash flows and other assumptions unchanged, a higher required yield produces a lower price. Credit and liquidity changes can move prices independently of the risk-free rate.

Coupon rate describes the contract’s payment rate relative to face value. Yield describes a return relationship implied by price and stated assumptions. A high coupon does not automatically mean a cheap or low-risk bond.

Duration is a local sensitivity #

Modified duration approximates the percentage price change for a small yield move: price change ≈ −duration × yield change in decimal form. Convexity and other effects matter for larger changes. Duration is not simply the bond’s maturity date.

Different cash-flow timing, coupon structure and embedded options can change sensitivity. A floating-rate claim or callable bond should not be modeled using an unqualified fixed-rate example.

The curve can reflect several forces #

A yield curve relates yields to maturity for a comparable class of instruments. Expected future short rates, term premiums, supply–demand conditions and liquidity can all influence its slope. A curve shape is not a guaranteed countdown to a particular event.

Separate government rates from corporate credit spreads and compare consistent conventions. For macro learning, ask which component changed rather than reading every rise in a corporate yield as a pure central-bank effect.

Decision lab: Duration is a local sensitivity #

A hypothetical modified duration of 5 with a yield rise of 0.50 percentage point implies about −2.5% first-order price change, before convexity and other effects. That does not guarantee the bond’s credit spread stays fixed or its liquidation price matches the model.

Stress a parallel yield move and a nonparallel curve move separately. Identify cash-flow dates, yield convention, credit exposure and liquidity. A long-duration asset’s sensitivity is not equivalent to a forecast that rates will move in the direction you prefer.

Hypothetical worked example

One percentage point is 0.01 in the formula

A hypothetical bond has modified duration 5. If its required yield rises by 0.50 percentage points, the local duration estimate is −5 × 0.005 = −2.5%.

A price of 100 would become approximately 97.5 before convexity and other effects. If someone enters 0.50 instead of 0.005, the estimate becomes wildly wrong.

The approximation does not include a credit event or changes in an embedded option. It is a controlled sensitivity exercise, not a promise that an actual bond can be sold at the calculated value.

Common mistakes

Confusing percentage points with percentages in sensitivity formulas.
Treating the yield-curve slope as an infallible forecast.

Check your understanding

With duration 5 and a 0.5 percentage-point yield rise, the approximate price change is what?

Make this chapter useful

Can you defend the reasoning?

Before moving on, answer the self-check in your own words and write why each alternative fails. Use the worked example to test that explanation. Then apply it in the module research task; keep the assumptions and the evidence that could change your answer.

Sources and further reading

Further-reading references from the curriculum source list. Contract sizes, expiry calendars, settlement references, margin parameters and tax treatment can change; verify the current operative documents for the actual product. Worked figures are illustrative, not current quotes.

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General financial education. No securities recommendation, assured outcome or personal advice. Read the risk disclosures.