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.
Load an immunization case
Inputs
Asset A
Asset B
$500,000
$500,000
Target equals liability duration
Assets should meet or exceed liability convexity
- 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.
PV match gauge
Scaled asset portfolio covers the liability present value.
Asset mix
Weights are solved from duration, then scaled to the liability present value.
Convexity cushion
A higher asset convexity helps preserve surplus when rates move away from the initial yield level.
Rate shock values
Negative shocks should raise both values; positive shocks should lower both values.
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 |
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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.