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fixed income question

page 339 volume 3 of CFAI text:

“In general, for an upward-sloping yield curve, the immunization target rate of return will be less than the YTM because of the lower reinvestment return.”

Why is this the case? For an upward-sloping yield curve, the future interest rate is going up causing the bond price to go down and therefore the YTM to go up. When the interest rate goes up the reinvestment return should go up, not down as stated in the book.

Anyone got any ideas/comments on this?

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The reinvestment rate will be lower because in an upward-sloping curve, you roll-down (not up) towards maturity; therefore, your reinvestment rate on your 1st coupon cashflows for example is going to be lower than your YTM. Remember your reinvestment rate is applied to cashflows that occur before the bond’s maturity; therefore, in an upward sloping curve environment your reinvestment rate is going to be lower than your YTM.

right….so this means that the immunization rate required is lower than the YTM as we don’t need to secure a rate as high as the YTM due to the lower reinvestment rate.

thanks cfa_gremlin.