The Immunization Target Return

Hi

For an upward sloping yield curve,The Immunization target return will be less than YTM due to lower reinvestment return.

How is this?

when we have upward sloping yield curve meaning interest rates are expected to increase which means higher reinvestment return?!

Thanks

This has been discussed many times here.

Your suggestion that interest rates are expected to increase is the pure expectations theory of the yield curve; that’s not the only theory out there.

Nevertheless, if the yield curve slopes upward, the rate at which you can reinvest the coupons is less than the YTM: you’re reinvesting the coupons for a shorter period than the original time to maturity. Lower reinvestment means that the realized yield will be less than the YTM.

I’m a bit confused.

Am I getting lower reinvestment because the rate at which I can reinvest the coupons is less than the YTM (why) or because of shorter period (also why)?

Thanks Bill!

Both.

Because the yield curve is upward sloping, that means the shorter time periods have a smaller yield, so the more time passes by, the less yield you get with each reciept re-invested at the time remaining to maturity.

If the yield curve was downward sloping, you would re-invest all your reciepts at the shortest tenor, because it gives the highest possible yield, and the effect would be reversed.

For a flat yield curve, reinvestment yield = YTM.

Thanks Mr Smart

Just to clear my confusion.

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.

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Because the yield curve is upward sloping, that means the shorter time periods have a smaller yield, so the more time passes by, the less yield you get with each reciept re-invested at the time remaining to maturity.

If the yield curve was downward sloping, you would re-invest all your reciepts at the shortest tenor, because it gives the highest possible yield, and the effect would be reversed.

For a flat yield curve, reinvestment yield = YTM.

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With a downward sloping yield curve, we are still reinvesting for a shorter period of time. So why is the reinvestment yield > YTM?

you are earning a higher interest for that time period - so you reinvestment return is higher than the flat YTM over the entire life of the investment.