# What are the limits of bond portfolio immunization against interest rate changes?

I'm currently reading through an article on bond portfolio immunization against changes in the interest rate.

I learned that the immunization can be done against instant changes in interest rate etc., but the investor can also bet on small or big changes occurring in the interest rate, i.e. he profits if the interest rate changes by at most $\pm0.5\%$, and loses if it changes by more than $\pm0.5\%$, so in this example no risk-free profit would be possible.

Could one set up a portfolio that will profit if the interest rate changes by $\pm4\%$, and lose otherwise? I believe no interest rate will change by more than 4%. What is the limitation here?

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Hi Marie, welcome to quant.SE. Can you post a reference or link to the article in question? It is difficult to understand precisely what "bet" you are referring to. –  Tal Fishman Dec 22 '11 at 12:43
Hello, the article is called "Duration, Convexity, and Time Value" by christensen and Sorensen, taken from The Journal of Portfolio Management, page 58. –  Marie. P. Dec 22 '11 at 14:09
@Marie.P.: you should really be more specific. Give the details in your question (the article is not available for free). Right now, this question is unclear and should/will be closed. –  SRKX Dec 25 '11 at 18:34
Can someone please explain me how to mitigate basis risk in a bond portfolio with swaps against parallel shift and non-parallel shift of yield curve. –  user2629 Jul 2 '12 at 12:13
@Elango You need to ask a new question. Don't just post on someone else's question. –  chrisaycock Jul 2 '12 at 16:01

you can set up sucha portfolio using options. However I doubt you can make any money unless you are going for some very volatile IR.

Using Options you can both buy a call and sell a put at 4% difference to the current IR. You will loose the premiums you paid on the oprions, if IR stay within the 4% premium.

Using bonds, it is easy. if IR rise, you will loose, no matter what bond you have.

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I believe you can pay for a hedge (for example duration hedging) which allows you to reduce the losses if rates increase. I do not think she was referring to options. But we need more info. –  SRKX Dec 25 '11 at 22:12

The purpose of bond portfolio immunization is to protect against large interest rate movements. Hence what you describe is really not immunization (a form of hedging), but rather speculation. Of course, the speculative bet you've laid out can be done with options, and the only limit is in the lower liquidity in deep out of the money options, such as would likely be the case for the 4% move you use as an example.

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There are a couple limitations to bond portfolio immunization.

Let's start by analyzing cash-flow matching which is a dedication strategy that is the alternative to immunization. Cash-flow matching can completely eliminate interest rate risk. The cash-flow match is setup such that the liabilities (outflows) are precisely offset by portfolio inflows on the same dates.

The challenge is that it is not easy to find bonds with the precise cash-flow payoff patterns. Moreover, bonds are subject to credit risk and potentially contingent claims risk (i.e. callable bonds) so the immunization is not risk-free presenting some limitations. Cash-flow matching will protect against any change in the shape of the yield curve including large interest rate changes (since the key rate durations of the liabilities precisely match the key rate durations of the assets).

Also, cashflow matching is more expensive than alternatives such as contingent immunization or optimizing a portfolio that minimizes a measure such as IRS (interest rate sensitivitiy). For example, if I have a view that rates are rising I would not want to use a zero-coupon bond to cash-flow match a single liability -- I'd rather receive some coupons that I can re-invest at a higher rate.

Contingent immunization can provide some scope for active management which can potentially lower the cost of immunizing a portfolio.

There are multiple immunization strategies -- single period immunization, multiple liability immunization, and immunization for general cash flows.

The necessary conditions for a successful immunization are that i) the PV of the Assets = the PV of the Liabilities, ii) the portfolio duration = duration of the Liabilities, and iii) the distribution of the durations of the assets must have higher variance than the distribution of liabilities.

As a result, some of the limitations of immunization are that: - works for parallel shifts only (so you are exposed to yield curve risk. (Use of optimization with the Interest Rate Sensitivity measure can address this) - Needs continuous monitoring and re-balancing of portfolio duration levels - This re-balancing creates transaction costs - If any bond defaults a major rebalancing or cash infusion is required

One can use derivatives (such as binary options or credit spread options) to construct portfolios that payoff if the interest rate changes by +/- 4%.

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