From the curriculum Page 57: “To achieve immunization, however, it is not *necessary* that the yield curve shifts in a parallel manner. That is, in some cases, the immunization property can prevail even with non-parallel yield curve movements”. How is that possible?

The curriculum uses the following example. The liability is a 6 years zero coupon bond.

The yield curve is steepening shift of 72.19 bps for the 2.5-year bond, 94.96 bps for the 7-year bond, and 120.82 bps for the 10-year bond. The portfolio cash flow yield increases by 100 bps. However, the yield of 6 years zero coupon bond increases by less than 94.96 bps (because yield of 7-year bond increases by 94.96 bps). Therefore, the cash flow yield and zero coupon bond yield increases by different rate, when yield curve is steepening shift. Why does it Achieve Interest Rate Immunization? Exhibit 7. Some Yield Curve Shifts That Achieve Interest Rate Immunization **Change in** **2.5-Year Yield Change in** **7-Year** **Yield** **Change** **in** **10-Year** **Yield** **Change** **in** **Cash Flow** **Yield** +72.19 bps +94.96 bps +120.82 bps +100 bps