# Fixed Income Immunization Tool

Free CFA fixed income immunization calculator for two-asset duration matching, PV match, convexity cushion, asset weights, and rate shock stress tests.

Canonical URL: https://exclam.ai/cfa/fixed-income-immunization-calculator/

CFA fixed income tool

Solve a two-asset duration match, scale the portfolio to the liability present value, and stress whether convexity protects the surplus under rate shocks.

Examples

## Load an immunization case

Baseline

Clean duration match

Load

Positive weights, PV match, and asset convexity above liability convexity.

A good first case for understanding the mechanics.

Constraint

Target duration outside asset range

Load

Liability duration exceeds both assets, forcing leverage and a short position.

Use this to see why duration targets need feasible assets.

Convexity

Duration match with weak convexity

Load

Duration matches, but the asset mix has less convexity than the liability.

Duration alone is not a complete immunization test.

Impossible

Equal asset durations

Load

Both assets have the same duration, so no two-asset duration equation can be solved.

The warning explains why the hedge cannot be built from these assets.

## Inputs

Liability PVLiability durationLiability convexity

### Asset A

ValueDurationConvexityYield

%

### Asset B

ValueDurationConvexityYield

%

Weight A

50.00%

$500,000

Weight B

50.00%

$500,000

Portfolio duration

7.00

Target equals liability duration

Expected yield

4.50%

Portfolio convexity

75.00

Liability convexity

70.00

Convexity cushion

Pass

Assets should meet or exceed liability convexity

Live interpretation

- Solved weights are 50.00% in Asset A and 50.00% in Asset B, scaled to the liability PV.
- Portfolio duration is 7.00 versus liability duration 7.00.
- Asset convexity 75.00 is at least the liability convexity 70.00.
- Worst displayed surplus under the rate shocks is $63.

Figure: Duration matching balance bar

### PV match gauge

Assets $1,000,000Liability $1,000,000

Scaled asset portfolio covers the liability present value.

## Asset mix

Weights are solved from duration, then scaled to the liability present value.

Figure: Solved asset weights

Hover or focus a bar to inspect the value.

## Convexity cushion

A higher asset convexity helps preserve surplus when rates move away from the initial yield level.

Figure: Asset versus liability convexity

Hover or focus a bar to inspect the value.

## Rate shock values

Negative shocks should raise both values; positive shocks should lower both values.

Figure: Asset and liability value under rate shocks

AssetsLiability

Hover or focus a point to inspect the curve.

## Stress table

| Shock | Asset value | Liability value | Surplus |
| --- | --- | --- | --- |
| -200 bps | $1,155,000 | $1,154,000 | $1,000 |
| -100 bps | $1,073,750 | $1,073,500 | $250 |
| -50 bps | $1,035,938 | $1,035,875 | $63 |
| +50 bps | $965,938 | $965,875 | $63 |
| +100 bps | $933,750 | $933,500 | $250 |
| +200 bps | $875,000 | $874,000 | $1,000 |

Related calculators

## CFA finance tools

[CFA hub](https://exclam.ai/cfa/index.md)

[BA II Plus-style calculator TVM, cash-flow, amortization, NPV, and IRR practice with algebraic entry. All levels Calculator keystrokes](https://exclam.ai/cfa/ba-ii-plus-calculator/index.md)

[HP 12C-style calculator RPN arithmetic and core financial calculator workflows in the browser. All levels RPN practice](https://exclam.ai/cfa/hp12c-calculator/index.md)

[Binomial option pricing visualizer Stock tree, option tree, risk-neutral probability, delta, and American exercise nodes. Level II Option trees](https://exclam.ai/cfa/binomial-option-pricing-calculator/index.md)

[Bond price, yield, and duration calculator Bond pricing, YTM, Macaulay duration, modified duration, convexity, and DV01. Levels I-II Bond math](https://exclam.ai/cfa/bond-price-yield-duration-calculator/index.md)

[Black-Scholes and Greeks visualizer Call and put pricing with delta, gamma, vega, theta, rho, and sensitivity curves. Level II Greeks](https://exclam.ai/cfa/black-scholes-greeks-calculator/index.md)

[Brinson attribution calculator Allocation, selection, interaction, waterfall, and active return reconciliation. Level III Performance attribution](https://exclam.ai/cfa/brinson-attribution-calculator/index.md)

## FAQ

What does the immunization calculator solve?

It solves the two-asset weights that match the liability duration, scales the portfolio value to the liability present value, and checks convexity cushion.

What approximation is used for rate shocks?

Rate shocks use the standard duration-convexity approximation: percentage value change is about negative duration times yield change plus one half convexity times yield change squared.

Does this replace full asset-liability modeling?

No. It is a CFA-style teaching tool for duration matching and convexity intuition, not a production ALM model with key-rate durations or stochastic cash flows.