Measure a bond's price sensitivity to parallel yield curve shifts with the effective duration formula, then estimate DV01, scenario price moves.
Last updated
Measure bond price sensitivity from up/down yield shocks Enter the base price plus modelled prices after equal down and up yield shocks. The calculator returns
effective duration, DV01-style price risk, scenario price moves, and a convexity/asymmetry signal.
Display currency
Currency affects only optional position-value and money-at-risk outputs; bond prices can still be entered as price per 100 or price per bond.
Common yield-shock presets
Example scenario presets
Scenario move to estimate
Input order and assumptions
The repricing shock should match the way P− and P+ were generated. Use parallel yield-curve shocks for
ordinary effective duration; key-rate, spread, or non-parallel shocks need separate risk measures.
Result
4
A 4 effective duration implies about a 4% price move for a 1 percentage-point parallel yield shift.
Price change per 1% yield shift
≈ 4%
Shock used
50 bps
Scenario price move
≈ 4%
DV01 per price point
0.04
Estimated price if yields rise
96
Estimated price if yields fall
104
Formula trace
(102 - 98) / (2 x 100 x 0.005) = 4
Price asymmetry
0 (flat convexity signal)
Dollar duration per price point
4 for a 100 bp move per 100 price base
Scenario market-value move
≈ $40,000.00 for the entered position value
How to read this result
An effective duration of 4 means the bond price is expected to
change by approximately 4% for every 1 percentage point parallel
shift in the yield curve. Higher duration indicates greater interest-rate risk, while convexity determines
how quickly that linear estimate breaks down for larger shocks.
Effective duration explained: measuring bond price sensitivity to yield changes
Effective duration estimates how much a bond's price will change when the benchmark yield curve shifts by a given amount. Unlike Macaulay or modified duration, effective duration works for bonds with embedded options — callables, putables, and mortgage-backed securities — because it uses observed or modelled price changes rather than closed-form assumptions.
What effective duration measures
Effective duration captures the first-order sensitivity of a bond's price to a parallel shift in the yield curve. A bond with an effective duration of 5 is expected to lose approximately 5% of its market value for every 1 percentage point increase in yields, and gain approximately 5% for every 1 percentage point decrease.
The metric is essential for portfolio managers, risk analysts, and fixed-income traders who need to quantify interest rate risk across instruments that may not follow simple present-value discounting — particularly callable bonds whose cash flows change when issuers exercise early redemption options.
Effective duration formula
The calculation requires three price observations: the bond's current price (P₀), the price when yields decrease by a small amount (P−), and the price when yields increase by the same amount (P+). The yield shift (Δy) must be expressed as a decimal.
By averaging the upward and downward price responses and normalising by the initial price and the size of the yield shock, effective duration provides a symmetric, unitless sensitivity measure.
Effective Duration = (P− − P+) / (2 × P₀ × Δy)
Where P− is the price when yield falls by Δy, P+ is the price when yield rises by Δy, P₀ is the current price, and Δy is the yield change as a decimal (e.g. 0.005 for 50 basis points).
Effective duration vs modified duration
Modified duration assumes that cash flows do not change when yields shift. This is valid for plain-vanilla fixed-rate bonds but breaks down for callable bonds, where the issuer may redeem the bond early if rates fall, truncating future coupon payments and capping price appreciation.
Effective duration accounts for these cash-flow changes because it is computed from repriced models or observed market prices under different yield scenarios, not from a closed-form derivative of the price–yield function. For option-free bonds, effective duration and modified duration converge to the same value.
Worked example
A callable corporate bond is currently priced at 100. An analyst shifts the benchmark yield curve down by 50 basis points and reprices the bond at 102.10 using an option-adjusted spread model. Shifting yields up by 50 basis points gives a repriced value of 97.80.
Effective Duration = (102.10 − 97.80) / (2 × 100 × 0.005) = 4.30 / 1.00 = 4.30. The bond has an effective duration of 4.30, meaning its price is expected to change by approximately 4.30% for every 1% parallel shift in the yield curve.
Choosing a yield shock in basis points
Most effective duration calculations use a small, symmetric yield shock such as 10, 25, 50, or 100 basis points. The shock should be large enough that the pricing model produces stable P− and P+ values, but small enough that the duration estimate still behaves like a first-order price sensitivity measure.
Enter the repricing shock as a percent value in the calculator. For example, a 50 basis point shock is entered as 0.50%, which the formula converts to Δy = 0.005. If a competitor, spreadsheet, or risk system asks for Δy in decimal form, divide the percent value by 100 before using the formula.
Using DV01 and position value for practical risk checks
A bare duration number is useful, but portfolio risk decisions usually need a money translation. DV01, also called price value of a basis point, estimates how much price changes for a 1 basis point move in yields. The calculator reports DV01 from the effective duration result so a bond duration calculation can be tied to hedging, position sizing, and interest-rate risk limits.
If you add a position market value, the calculator also estimates the money-at-risk for a chosen scenario move. This makes it easier to compare a callable bond, mortgage-backed security, or bond fund exposure with other fixed-income positions that may have different prices, coupons, and maturities.
Input checklist for callable bonds and MBS
For option-sensitive bonds, P− and P+ should come from a consistent valuation model, not from a simple fixed-cash-flow discounting shortcut. Use the same option-adjusted spread convention, prepayment assumption, call model, benchmark curve, and settlement date for both shifted prices.
Check whether the down-rate price gain is smaller than the up-rate price loss. That pattern is a negative convexity signal and often appears when a callable bond approaches its call boundary or when mortgage prepayment assumptions accelerate as rates fall.
Convexity and second-order effects
Duration is a linear approximation. For large yield changes, the actual price change diverges from the duration estimate because of convexity — the curvature of the price–yield relationship. Positive convexity (typical of non-callable bonds) means the bond gains more when rates fall than it loses when rates rise. Negative convexity (typical of callable bonds when rates are near the call strike) flattens the upside.
For more precise risk management, analysts combine effective duration with effective convexity to build a second-order Taylor approximation of price change: ΔP/P ≈ −Duration × Δy + 0.5 × Convexity × (Δy)².
Limitations of this calculator
This tool requires the user to supply pre-computed prices under shifted yield scenarios. It does not perform bond valuation, option-adjusted pricing, or yield-curve construction. The accuracy of the result depends entirely on the quality of the input prices. For bonds with embedded options, those prices should come from an appropriate valuation model (binomial tree, Monte Carlo, OAS model) rather than simple present-value discounting.
Frequently asked questions
When should I use effective duration instead of modified duration?
Use effective duration whenever a bond's cash flows depend on the level of interest rates — callable bonds, putable bonds, mortgage-backed securities, and any instrument with embedded optionality. For plain-vanilla fixed-rate bonds with no embedded options, modified duration and effective duration produce the same result.
What yield change should I use for the calculation?
A 25 to 50 basis point parallel shift is standard practice. Smaller shocks (e.g. 10 bps) can be more accurate for highly non-linear instruments but may amplify rounding errors. Larger shocks (100 bps) capture more convexity but may overweight second-order effects in the duration estimate. The CFA Institute curriculum typically uses 50 bps.
What is the difference between percent, percentage points, and basis points in this effective duration calculator?
The input is a percentage-point yield shift. Enter 0.50 for a 50 basis point shift, not 50 and not 0.005. Internally, the formula converts 0.50% to the decimal Δy value of 0.005.
How is DV01 related to effective duration?
DV01 translates effective duration into price movement for a 1 basis point yield change. For a price base P₀, approximate DV01 equals Effective Duration × P₀ × 0.0001. It is useful when you need price or money-at-risk rather than only a percentage duration measure.
Why do my effective duration results differ from a modified duration calculator?
Modified duration assumes fixed cash flows and usually starts from coupon, maturity, yield, and payment frequency. Effective duration uses shifted scenario prices, so it captures embedded-option effects, prepayment assumptions, and other modelled cash-flow changes. For option-free bonds with small shocks, the two measures should be close.
Can I use this calculator as a bond price sensitivity calculator for a portfolio?
Yes, if each position already has consistent shifted prices. Calculate effective duration and DV01 position by position, then aggregate the money-at-risk or DV01 figures. For non-parallel curve moves, use key-rate duration instead of a single effective duration number.
Can effective duration be negative?
Negative effective duration is rare but possible for certain exotic instruments such as interest-only mortgage strips, inverse floaters, or deeply out-of-the-money callable bonds. A negative duration means the instrument's price rises when yields rise — the opposite of the standard bond relationship.
How does effective duration relate to portfolio immunisation?
Portfolio managers use duration matching to immunise portfolios against interest rate movements. By matching the effective duration of assets and liabilities, small parallel yield shifts produce offsetting price changes, stabilising surplus or funded status. Effective duration is preferred for this purpose when the portfolio contains bonds with embedded options.
