Question

1. In class, we saw that immunization reduces a firm or investor's exposure to interest rate risk by matching the durations of assets and liabilities. We also know that duration breaks down as a good approximation to interest rate sensitivity for large(r) changes in rates. Could immunization be implemented with a convexity adjustment? Why or why not?

Answer 1

The biggest disadvantage of classical immunization is that it only hedges against parallel shifts in yield curves, which is an unrealistic occurrance. This is because classical immunization is implemented by matching durations, and duration as a measure of interest rate risk is only limited to parallel shifts in interest rates.

Another disadvantage is that classical immunization applies to small changes in interest rates, not large ones. This disadvantage can be reduced by properly aligning convexities between assets and liabilities.

If liabilities and assets are duration matched but not convexity matched, any economic surplus will be exposed to variation in value resulting from the convexity mismatch. Thus in a scenario with upward sloping interest rates and a large parallel shift in interest rates the convexity effect will cause the portfolio to outperform relative to the liability. This is because the initial decline in the portfolio’s value is overestimated vs. using duration alone.

For an immunization strategy, one way of mitigating the model risk as well as interest rate risk arising from not-so-well-behaved yield curves (i.e., nonparallel shifts, especially bear steepeners) is to build the portfolio to resemble that which works best – a zero-coupon bond maturing at or close to the horizon.

Matching market value, duration, and convexity is the same as matching market value, dollar duration, and dollar convexity.

Asset market value = Liability market value

Asset dollar duration = Liability dollar duration

Asset dollar convexity = Liability dollar convexity

STEPS:

• Set the initial PV of Assets to be greater than or equal to the initial PV of Liabilities
• Match the Durations of assets to liabilities
• Minimize portfolio convexity (i.e. minimize the dispersion of cash flows around the liability)
• Regularly rebalance the portfolio as duration or yields change. In this process you must consider the risk of NOT rebalancing against the costs of doing so