Strategic Financial Management · Interest Rate Derivatives

Interest Rate Risk and How to Measure It

Updated 11 October 2026 · Fact-checked

Interest rate risk is the chance that a change in market interest rates hurts the value of a bond or the cost of a loan. You measure it with duration, modified duration and basis point value (PV01). Estimate the price change as −modified duration × yield change × price.

Understand Interest Rate Risk and Its Measurement

Interest rate risk arises because rates move and cash flows do not. If you hold a fixed-rate bond and market yields rise, the bond's price falls, because its fixed coupons are now less attractive. If yields fall, the price rises.

The risk works differently for borrowers. A company with a floating-rate loan pays more interest when the benchmark rate rises. A company with a fixed-rate loan is safe from this but loses out if rates fall and it cannot benefit.

There are two main types:

Price risk: the market value of a fixed-income asset changes when yields change.
Reinvestment risk: coupons and maturity proceeds get reinvested at a different rate than expected. Price risk and reinvestment risk pull in opposite directions.

For borrowers, a third form is cash-flow (repricing) risk: floating interest payments change at each reset date.

To measure exposure, you need a number. Macaulay duration is the weighted average time to receive a bond's cash flows, where each time is weighted by the present value of that cash flow. Modified duration converts this into a price sensitivity: it tells you the approximate percentage price change for a 1% (100 basis point) change in yield. Basis point value (PV01) gives the same idea in rupees: the change in price for a 1 basis point (0.01%) change in yield.

Duration is a linear approximation. For large yield moves, the real price curve bends (convexity), so duration alone is less accurate. Longer maturity and lower coupon generally mean higher duration and more risk.

Key rules to remember

Macaulay duration: D = Σ [t × PV(CFt)] ÷ Σ PV(CFt); Denominator equals the bond's current price. t is in years. For a zero-coupon bond, D equals its maturity.
Modified duration: MD = D ÷ (1 + y); y is the yield per period. For annual coupons, use the annual yield. For semi-annual coupons, divide D (in years) by (1 + y/2) and keep MD in years.
Approximate price change: ΔP ≈ −MD × Δy × P; Δy in decimal form (1% = 0.01). The negative sign shows price and yield move opposite ways. Valid for small yield changes.
Basis point value (PV01): BPV = MD × 0.0001 × P; The rupee change in price for a 1 basis point change in yield. For a portfolio, add the BPVs of the positions.
Basis point: 1 basis point = 0.01% = 0.0001; 100 basis points = 1%.

How to solve Interest Rate Risk and Its Measurement questions

Use this order for any question on interest rate risk, duration or BPV.

1Identify who bears the risk: a bondholder (price falls when yields rise) or a borrower with a floating loan (interest cost rises when rates rise).
2List the cash flows with their time in years, and note the yield and the coupon frequency.
3Find the present value of each cash flow at the given yield. Their sum is the bond's price.
4Compute Macaulay duration as Σ(t × PV) ÷ price, unless the question already gives it.
5Convert to modified duration: divide by (1 + y), using the yield per period.
6Apply ΔP ≈ −MD × Δy × P, or BPV = MD × 0.0001 × P, as the question asks.
7State the answer with direction (rise or fall), the rupee amount and a one-line interpretation, such as which bond is riskier.

Quickest way: Shortcut for duration questions

When to use it: Use when the question gives duration or modified duration, or involves a zero-coupon bond, and asks only for price change or BPV.

If the bond is zero-coupon, Macaulay duration equals its maturity. No table needed.
If modified duration is given, skip the table and go straight to ΔP ≈ −MD × Δy × P.
For BPV, multiply price by MD by 0.0001.
For a portfolio, add the BPVs of each holding. Do not average durations unless you weight them by value.
Check the sign: yield up means price down.

Common mistakes in Interest Rate Risk and Its Measurement

Forgetting the negative sign and saying price rises when yield rises.
Students focus on the formula and not on the direction of the relationship.
Fix: Before writing the answer, ask: yield up, price down. Write the direction in words.
Using Macaulay duration directly as the price sensitivity.
The two terms look similar and both are called duration.
Fix: Divide by (1 + y) first to get modified duration. Use MD, not D, in ΔP and BPV.
Entering 1% as 1 instead of 0.01 in the formula.
Rushing with percentages and basis points.
Fix: Convert to decimals first: 1% = 0.01, 1 bp = 0.0001.
Taking duration as exact for large yield changes.
The formula looks precise, but it is a linear approximation.
Fix: State that the result is approximate. Mention convexity when the yield move is large.
Using weights of time instead of PV-weighted time in Macaulay duration.
Students average the cash-flow dates or use nominal cash flows.
Fix: Discount every cash flow first, then compute t × PV and divide by the total PV.
Ignoring who gains. A borrower with a floating loan is hurt when rates rise, while a fixed-rate borrower is not hurt in cash terms.
Students apply the bond-price logic to every case.
Fix: First classify the position as an asset or a liability and as fixed or floating.

Worked examples

Example 1

A 2-year bond has a face value of ₹1,000, pays an annual coupon of 10% and has a yield of 10%. Find (a) its price, (b) Macaulay duration, (c) modified duration, and (d) the approximate price change if the yield rises by 50 basis points.

Show the solution

Cash flows: ₹100 at year 1 and ₹1,100 at year 2. Yield is 10%.
PV at year 1 = 100 ÷ 1.10 = ₹90.91. PV at year 2 = 1,100 ÷ 1.21 = ₹909.09. Price = ₹1,000.
Σ(t × PV) = 1 × 90.91 + 2 × 909.09 = 90.91 + 1,818.18 = 1,909.09.
Macaulay duration = 1,909.09 ÷ 1,000 = 1.909 years.
Modified duration = 1.909 ÷ 1.10 = 1.736.
Yield change = +0.50% = 0.005. ΔP ≈ −1.736 × 0.005 × 1,000 = −₹8.68.

Answer: Price ₹1,000; Macaulay duration about 1.91 years; modified duration about 1.74; the price falls by about ₹8.68 to roughly ₹991.32.

Example 2

A bank holds a bond portfolio worth ₹50,00,00,000 with modified duration of 4.5. Find the basis point value and the approximate loss if yields rise by 25 basis points.

Show the solution

BPV = MD × 0.0001 × P = 4.5 × 0.0001 × 50,00,00,000.
4.5 × 0.0001 = 0.00045. 0.00045 × 50,00,00,000 = ₹2,25,000.
Loss for 25 bp = 25 × 2,25,000 = ₹56,25,000.
Check using the main formula: 4.5 × 0.0025 × 50,00,00,000 = ₹5,62,50,000 × 0.1 = ₹56,25,000. Recompute: 4.5 × 0.0025 = 0.01125; 0.01125 × 50,00,00,000 = ₹56,25,000. This matches.

Answer: BPV is ₹2,25,000 per basis point. A 25 bp rise in yield reduces the portfolio value by about ₹56,25,000.

Exam tips

Section A questions often give modified duration and ask for the price change or BPV. Learn the formulas so you can answer in under a minute.
In written answers, show the table of t, cash flow, PV and t × PV. Marks are given for method even if the final figure slips.
Always state the direction of change and the rupee amount, then add one line on what it means for the bank or company.
Keep decimals to at least three places in duration until the final step to avoid rounding drift.
Link the measure to a hedge: a high BPV points to the need for swaps, futures or FRAs.

Practice questions from Interest Rate Derivatives

Interest Rate Risk and Its Measurement in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Interest Rate Risk and Its Measurement: frequently asked questions

What are the main types of interest rate risk?

The main types are price risk, where bond values change with yields, and reinvestment risk, where cash flows are reinvested at different rates. Borrowers also face repricing risk on floating-rate loans. Price and reinvestment risk offset each other to some extent.

What is the difference between duration and modified duration?

Macaulay duration is the PV-weighted average time to receive cash flows, measured in years. Modified duration equals Macaulay duration divided by (1 + yield per period). Modified duration is the one you use to estimate the percentage price change.

What is basis point value or PV01?

It is the rupee change in a bond's or portfolio's value for a 1 basis point change in yield. You compute it as modified duration × 0.0001 × price. Banks use it to set limits and size hedges.

Why is duration only an approximation?

The price-yield relationship is curved, not a straight line. Duration captures the slope at the current yield, so it works for small changes. For larger changes you need to add a convexity adjustment.