CFA fixed income tool

Fixed Income Immunization 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

Inputs

Asset A

Asset B

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.
Duration matching balance bar0.02.14.26.38.4Liability 7.00Assets 7.00

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.

Solved asset weightsAsset A weight50.00%Asset B weight50.00%
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.

Asset versus liability convexityAsset portfolio convexity75.00Liability convexity70.00
Hover or focus a bar to inspect the value.

Rate shock values

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

Asset and liability value under rate shocks-200 bps-100 bps0 bps100 bps200 bps-$115,500$231,000$577,500$924,000$1,270,500Rate shockValue
AssetsLiability
Hover or focus a point to inspect the curve.

Stress table

ShockAsset valueLiability valueSurplus
-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

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.