FINM7405 Chap.4 Interest Rate and Fixed-Income Risk
Interest Rate and Fixed-Income Risk
Fixed bond cash flows change in value when the rates used to discount them change. This chapter develops the inverse price-yield relationship and the sensitivity measures used to control it. Macaulay duration describes weighted cash-flow timing, modified duration estimates first-order price response, and DV01 translates a one-basis-point move into currency.
Convexity captures the curvature missed by the duration tangent. Portfolio and key-rate duration, spread duration, fixed-income VaR and immunisation then separate parallel rate exposure from curve shape, credit spread and funding risks.
The core geometry is local. A positive yield shock produces a negative first-order price change for a conventional long bond.
The convexity term is positive for either shock direction because the yield change is squared. It therefore reduces the duration-only loss for a rate rise and increases the estimated gain for a rate fall. Exact discounted-cash-flow repricing remains the benchmark when all cash flows are available.
A portfolio can have the right total duration and the wrong maturity distribution.
Key-rate duration reveals sensitivity to separate curve points, while spread duration isolates credit repricing from government or swap rates. Immunisation matches asset and liability values and durations, adds a convexity condition for larger moves, and requires rebalancing as time and yields change. None of these controls removes liquidity or optionality.
What this chapter covers
- 01
Bond pricing and the price-yield curve
- 02
Macaulay and modified duration
- 03
DV01 and portfolio duration
- 04
Convexity and key-rate duration
- 05
Spread risk and immunisation
Worked example · free
Duration plus convexity
This mark allocation supports the duration walkthrough and is not an official university assessment scheme.
- +1Convert 40 basis points to 0.0040.
- +1Duration effect is -6.4 x 0.0040 = -2.56%.
- +1Convexity effect is 0.5 x 52 x 0.0040^2 = +0.0416%.
- +1Combined percentage change is -2.5184%.
- +1Dollar change is approximately -$629,600.
Key terms
- Macaulay Duration
- The present-value-weighted average time until a bond's cash flows are received.
- Modified Duration
- The first-order percentage sensitivity of bond price to a small yield movement.
- DV01
- The approximate currency change in value for a one-basis-point yield movement.
- Spread Duration
- The sensitivity of a credit instrument's price to a change in its credit spread.
Interest Rate and Fixed-Income Risk FAQ
Why do bond prices fall when yields rise?
The contractual cash flows are discounted at the higher required yield, reducing their present value. The inverse relationship is strongest for long-duration cash flows because more of their value arrives farther in the future.
What does convexity add to duration?
Duration follows the local tangent to the price-yield curve. Convexity adds a second-order curvature correction, improving the approximation as the yield movement grows. Positive convexity reduces a duration-only loss estimate for a conventional bond.
Does duration matching remove all fixed-income risk?
No. It protects locally against a selected rate movement and drifts through time. Non-parallel curve changes, credit spread movements, optional cash flows, liquidity and funding can still cause asset and liability values to diverge.
Exam move
Write the yield movement in decimal form and state the price direction before calculating. Practise duration-only, convexity-adjusted and DV01 answers from the same portfolio so percentage, currency and one-basis-point units stay distinct. Compare the approximation with exact repricing whenever cash flows are supplied, and explain why the error grows with shock size.
Rebuild target dollar duration after a futures, swap or immunisation calculation to catch sign errors independently. Draw a simple curve with short, medium and long key-rate buckets and test whether a parallel-duration hedge survives a steepening. Then add a credit spread shock to show why Treasury-rate duration is not enough for a corporate bond.
For immunisation, list the value, duration and convexity conditions and explain why they drift. End each response by separating risk-free rate, curve-shape, spread, optionality, liquidity and funding risks rather than treating total yield as one factor. Keep a cash-flow timeline beside every duration answer. It anchors the maturity, coupon frequency and discount basis before an aggregate sensitivity hides those details.
For a supplied bond, calculate the exact price at the original yield and at the shocked yield, then compare the true percentage change with duration-only and duration-plus-convexity estimates. Record the approximation error so you can explain why curvature matters.
Convert every portfolio sensitivity into both percentage and currency form: modified duration for a proportional response, dollar duration for scale and DV01 for a one-basis-point move. In immunisation problems, match asset and liability measures at the same valuation date and yield convention, then advance time to show why rebalancing is necessary.
Construct one steepener and one flattener scenario using key-rate buckets; a zero aggregate duration should not be mistaken for zero bucket risk. For credit portfolios, decompose a total-yield shock into risk-free curve and spread components, then consider whether their correlation worsens in stress. Before choosing futures or swaps, compare deliverable, maturity, collateral cash flows and counterparty structure.
Close with an exact statement of which sensitivity was neutralised and over what local shock range.
Working through Interest Rate and Fixed-Income Risk in FINM7405? Sia is AskSia’s AI Finance tutor — ask any FINM7405 Interest Rate and Fixed-Income Risk question and get a clear, step-by-step explanation grounded in how FINM7405 is taught and assessed. Read this chapter free, then take your hardest questions to Sia.