What Duration and Convexity Immunization Guarantees for Mortgage Funding

Summary

The document poses a fixed-income immunization question involving a mortgage asset with fixed payments, prepayment and option-adjusted spread models, and calculated price, duration, and convexity. The asset and a blend of liabilities are assumed to trade at par initially. The liabilities are selected to match the asset’s duration and convexity while minimizing their time-weighted initial cost, and the investor plans to hold the mortgage until it prepays or matures.

It asks what this hedge means for income: whether matching duration and convexity locks in the initial yield spread between the asset and funding liabilities against parallel yield-curve moves. No answer, derivation, or empirical evidence is included, so the document does not establish that such a spread is guaranteed. Its setup highlights the need to consider model assumptions, prepayment behavior, and the shape of yield changes when assessing immunization. It is a research question rather than a complete method or conclusion.

Key ideas

• The setup pairs a mortgage asset with a liability blend matched on duration and convexity.
• The liability blend is chosen to minimize time-weighted initial cost, with all positions initially at par.
• The question is whether this immunization protects the asset-to-funding yield spread from parallel curve shifts.
• The document provides no derivation or conclusion about the income guarantee.

Tags

# Portfolio Immunization from Yield Perspective


# Portfolio Immunization from Yield Perspective












Let's say we have the following situation: an asset (mortgage) with fixed payments, a prepayment & oas models to run through, and calculations for duration, convexity, and price, based on them. The asset is priced at par. We never sell the asset, i.e., hold it until it prepays completely or matures.

We are funding the asset with a blend of liabilities that have the same duration and convexity as the asset, and a minimized time-weighted initial cost. All liabilities also trade at par initially.

The question is: what exactly does this immunization guarantee from income point of view? Are we locking in the initial delta in asset ytm - liabilities blend ytm and immunizing that spread vs parallel changes in the yield curve?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.