Question on Reinvestment risk

Hi guys,

I am struggling with a BASIC question from Kaplan regarding reinvestment risk. Maybe someone can help?

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All else being equal, which of the following bond characteristics will lead to lower levels of coupon reinvestment risk for bonds that are held to maturity?
(a.) longer maturities and higher coupon levels
(b.) shorter maturities and lower coupon levels
(c.) shorter maturities and higher coupon levels.
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The answer is supposed to be (b) with the following reasoning: Other things being equal, the amount of reinvestment risk embedded in a bond will decrease with lower coupons because there will be a lesser dollar amount to reinvest and with shorter maturities because the reinvestment period is shorter.

What I do not get here is that according to the coupon effect, a lower cpn bond has a greater % price change than a higher cpn bond when the market discount rate change by the same amount. This is why I thought answer c should be the correct option.

Can someone please explain what I am missing here?

Thanks in advance!

The focus of this question is on reinvestment risk: The risk of reinvesting at a rate other than the YTM. If you have higher coupons and you are not able to reinvest at the YTM, your dollar risk is much higher than for lower coupons.

What you are describing is the change in price of the bond given a change in its yield. The question is asking for reinvestment risk, a related but different concept.

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Ah okay - I understand! Now that I think of it the answer provided also makes a lot of sense. Tbh I still can’t remember where this was written in the materials (and also did not find it) but I guess in the end it is just important to remember the differences in the concepts.