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Structural risk to an immunizing strategy

In order for a bond portfolio structured to immunize a single liability, why do we have to minimize the portfolio convexity statistic.

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If the durations are matched and the convexities are matched (so net convexity is zero), then the price change of the asset and the price change of the liability will be the same even for large changes in interest rates.

If the durations are matched but the convexities are not (so net convexity is not zero), then the price change of the asset and the price change of the liabiity will not be the same, even for small changes in interest rates.

Simplify the complicated side; don't complify the simplicated side.

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Thank you!

But I still do not understand this sentence from book: “The structural risk to the immunization strategy is the potential for non-parallel shifts and twists to the yield curve, which lead to changes in the cash flow yield that do not track the change in the yield on the zero-coupon bond. This risk is minimized by selecting the portfolio with the lower convexity.”

I think this sentence means: Selecting the portfolio with the lower convexity can lead to changes in the cash flow yield to closely track the change in the yield on the zero-coupon bond no matter how the yield curve shifts.

Why is that?

remember the equation

Price Change = -Duration * Rate Change + Convexity * Rate Change ^2

Even for a smaller rate change - the potential of Convexity impacting the Price more is bigger. (And it does not matter what the rate change direction is. Whether positive or negative - there is always a Price Change impact due to convexity. When rates fall - Duration term causes Price increases due to Rate Change being negative, and when Rates rise - price change is negative due to duration. but Convexity impact is always positive.

So keeping the lower convexity portfolio - makes sure the impact is not as much. (and the portfolio will track closer to the Zero Coupon Bond.

(S2000 - please feel free to educate me is anything of what I state above is incorrect).

CP

Thank you all!

Lizihengtotti getting on that Level 3 vibe already, damn son. Nice.

.....woof

cpk123 wrote:

remember the equation

Price Change = -Duration * Rate Change + Convexity * Rate Change ^2

Even for a smaller rate change - the potential of Convexity impacting the Price more is bigger. (And it does not matter what the rate change direction is. Whether positive or negative - there is always a Price Change impact due to convexity. When rates fall - Duration term causes Price increases due to Rate Change being negative, and when Rates rise - price change is negative due to duration. but Convexity impact is always positive.

So keeping the lower convexity portfolio - makes sure the impact is not as much. (and the portfolio will track closer to the Zero Coupon Bond.

(S2000 - please feel free to educate me is anything of what I state above is incorrect).

Actually I’m not sure I understand this. Whatever calculation I made with the above equation (actually in the book it says 1/2 convexity - but I remember there was a debate on this back at level 1) it always turned out that the effect of convexity is almost negligable, because you thake the square of the yield change in decimals, the second part of the equation will be way less than the effect of the duration.

Why is this?