# Cash Flow Yield in Immunization

Could someone clarify what the para below means in the immunization context?

“Cash flow yield (IRR) essentially reflects more weight on longer maturity bonds. In an upward-sloping yield curve, the higher yield of longer maturity bonds will pull the portfolio IRR above the more traditional average YTM of the bonds held in the portfolio.”

Isn’t the YTM essentially the IRR for a bond? Why would the two be different whether the yield curve is rising or not?

That’s not what it says.

It says that the IRR of the portfolio won’t be the same as the weighted average of the IRRs of the constitutent bonds.

Put together a 2-bond portfolio in Excel and you’ll see it.

Thanks S2000. So I calculated in Excel and see the portfolio IRR is indeed higher than the weighted avg when the yield curve is upward sloping, but what is the significance of this difference? The CFA text says the goal of immunization is to achieve the return that’s the same as the portfolio IRR and not the weighted avg. Is that all?

Also, I don’t think I understand full why the portfolio IRR is lower than the wtd avg yield when the curve is upward sloping. What is the role of the curve here?

im also confused by this point, if anyone would like to help out

Portfolio IRR comes from the combination of bonds with different maturity. The avg YTM is calculated as weight of allocation for each bond multiplied by each bond’s YTM. Actually this implies IRR > Avg YTM.

When the curve changes, this affects portfolio IRR according to the direction of each bond in the portfolio. But avg YTM again can be computed by the mkt value (allocation weight) times YTM of each bond after the change of yield curve.

Are my assumptions correct for an upward sloping curve?

What I don’t get is how this portfolio IRR will properly discount the liabilities if the portfolio IRR > realized yield? Or is portfolio IRR based on liabilities, and realized yield based on assets?

actually I think this link https://www.analystforum.com/forums/cfa-forums/cfa-level-iii-forum/91350124 (April 30th) confirms that portfolio IRR is based on liabilities, and realized yield is based on assets. Thus, portfolio IRR based on liabilities will be lower than the YTM of the assets (since realized yield < YTM). But if somebody could confirm i would appreciate it.

The immunization target rate of return is the return required to fund the liability?

Yes.

It should be lower than the YTM of assets in an upward sloping yield curve, because the realized return on those assets will be less than the YTM.