Enter Values

Liability
$
Future payment obligation
years
Years until liability is due
Bond
%
Current market yield
%
Annual coupon rate of the bond
years
Years to bond maturity
$
Par value of the bond
Coupon payment frequency

Quick Reference

Bond Price
P = Σ C/(1+y)t + F/(1+y)n
Macaulay Duration
D = [Σ t×C/(1+y)t + n×F/(1+y)n] / P / freq
Immunization Condition
Macaulay Duration = Investment Horizon
Ryan O'Connell, CFA
Calculator by Ryan O'Connell, CFA

Immunization Status

--
Bond Price --
Macaulay Duration --
PV of Liability --
Bonds Required --
Target Accumulated Value --
Duration - Horizon --

Formula Breakdown

Immunization: Macaulay Duration = Liability Horizon
Step-by-step computation of bond metrics

Yield Shift Scenarios

Yield Shift New Yield Accumulated Value Surplus / Deficit

Immunization Effectiveness

Model Assumptions
  • Yield curve is flat (single yield for all maturities)
  • Only parallel yield curve shifts are modeled (not twists or butterfly shifts)
  • Coupons are reinvested at the new yield after the shift
  • No credit risk or default modeled
  • Single-liability immunization only (for multiple liabilities, see textbook Section 4.1.2)

For educational purposes. Not financial advice. Market conventions simplified.

Immunization Interpretation

Status Condition Meaning
Immunized |Duration - Horizon| ≤ 0.1 years Duration closely matches horizon; portfolio is immunized against parallel shifts
Close |Duration - Horizon| ≤ 0.5 years Duration is near horizon; partial protection exists but rebalancing is recommended
Not Immunized |Duration - Horizon| > 0.5 years Significant duration mismatch; portfolio is exposed to interest rate risk

Understanding Bond Immunization

What is Bond Immunization?

Bond immunization is a fixed-income strategy that matches a bond portfolio's Macaulay duration to the investment horizon so that the portfolio's accumulated value at the horizon date is protected against parallel interest rate changes. When rates rise, reinvestment income increases but the bond's market price falls; when rates fall, the opposite occurs. Duration matching ensures these effects offset each other.

Immunization Conditions
1. Macaulay Duration = Investment Horizon
2. PV(Portfolio) ≥ PV(Liability)
3. Minimize portfolio dispersion (convexity)
Classical single-liability immunization (MTMP Ch. 6)

Price Risk vs. Reinvestment Risk

Rates Rise

Bond price falls (price risk), but coupon reinvestment earns more (reinvestment gain). If duration = horizon, the two effects cancel.

Rates Fall

Bond price rises (price gain), but coupon reinvestment earns less (reinvestment risk). Duration matching offsets these effects.

When to Use This Calculator vs. Bond Duration Calculator

The Bond Duration Calculator computes Macaulay and Modified duration for a single bond as standalone metrics. This calculator uses duration as one input to a larger immunization analysis — checking whether a bond's duration matches a liability horizon, computing how many bonds are needed, and stress-testing the surplus/deficit under yield curve shifts.

Key Insight: Immunization is not a set-and-forget strategy. As time passes and yields change, the bond's duration shifts, requiring periodic rebalancing to maintain the duration match.

Frequently Asked Questions

Bond immunization is a strategy that matches a bond portfolio's Macaulay duration to the investment horizon so that the portfolio value at the horizon date is protected against parallel interest rate changes. When rates rise, reinvestment income increases but bond prices fall; when rates fall, the opposite occurs. Duration matching ensures these effects offset each other, locking in the target return regardless of rate movements.

Classical single-liability immunization requires three conditions: (1) the portfolio's Macaulay duration equals the liability horizon, (2) the present value of the portfolio equals or exceeds the present value of the liability, and (3) portfolio dispersion (convexity) is minimized to reduce structural risk from non-parallel yield curve shifts. This calculator checks the first two conditions and stress-tests the portfolio under parallel shifts.

Duration matching works because it balances two opposing effects of interest rate changes: price risk and reinvestment risk. When a bond's Macaulay duration equals the investment horizon, the gain (or loss) from reinvesting coupons at the new rate exactly offsets the loss (or gain) in the bond's market price at the horizon date. This is why Macaulay duration, not Modified duration, is the relevant measure for immunization.

Contingent immunization is a hybrid strategy that allows active management as long as the portfolio value stays above a safety net (the immunized floor). The manager actively trades bonds to try to outperform, but if active management erodes the surplus to zero, the manager switches to a fully immunized strategy to lock in the minimum acceptable return. It combines the upside potential of active management with the downside protection of immunization.

Key limitations include: immunization only protects against parallel yield curve shifts, not twists or butterfly shifts; it requires periodic rebalancing as duration changes over time; it assumes coupons can be reinvested at the prevailing yield; and it does not account for credit risk or default. Additionally, for large yield changes, the linear duration approximation becomes less accurate, and convexity effects become significant.

Cash flow matching (dedication) buys bonds whose coupon and principal payments exactly match each liability payment date, eliminating both price and reinvestment risk entirely. Immunization uses duration matching to protect against rate changes but does not require exact cash flow alignment. Cash flow matching is more conservative and eliminates reinvestment risk entirely, but it is typically more expensive and less flexible than immunization.
Disclaimer

This calculator is for educational purposes only. It assumes a flat yield curve with parallel shifts and does not model credit risk, liquidity risk, or non-parallel curve movements. Real-world immunization requires periodic rebalancing and consideration of multiple risk factors. This tool should not be used for investment decisions.

Related Calculators

Professional finance illustration representing Bond Pricing Calculator: Clean Price, Dirty Price, and Accrued Interest

Bond Pricing Calculator: Clean Price, Dirty Price, and Accrued Interest

Calculate clean price, dirty price, and accrued interest for fixed-rate bonds. Supports annual and semi-annual...

Try Calculator →
Professional finance illustration representing Yield to Maturity (YTM) Calculator

Yield to Maturity (YTM) Calculator

Calculate yield to maturity for coupon and zero-coupon bonds using iterative bisection. Analyze bond returns...

Try Calculator →
Professional finance illustration representing Bond Convexity Calculator

Bond Convexity Calculator

Calculate bond convexity, modified duration, and estimate price changes for interest rate shifts. Analyze the...

Try Calculator →

Course by Ryan O'Connell, CFA, FRM

Fixed Income Investing: Bond Fundamentals to Portfolio Management

Master fixed income from bond pricing fundamentals to portfolio immunization strategies. Covers yield curves, duration, convexity, credit analysis, and liability-driven investing.

  • Bond pricing, duration, and convexity deep dives
  • Immunization and cash flow matching strategies
  • Credit risk analysis and spread decomposition
  • Hands-on exercises with real bond market data
View Course