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In bonds, we assume that coupons are reinvested at the same rate as the current yield rate.

Where do we go and invest the coupons?

Assuming the YTM is 10%, the coupon rate is 10% and the per value is 100 now at first time period: one will receive 10 as the coupon payment.

Where do we go and invest the amount 10 that we received?

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That issue is the definition of "reinvestment risk". When you get the coupon payment you have to decide what to do with that payment. In periods of falling interest rates you'll have to take on more risk to get a similar rate. In periods of rising interest rates you'll have to decide how much duration risk, etc, you'll want to take to get a similar rate.

There is no single right answer as it depends on your situation and priorities.

Reinvestment risk refers to the possibility that an investor will be unable to reinvest cash flows (e.g., coupon payments) at a rate comparable to their current rate of return.

Full description of reinvestment risk

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If the interest rate has not decreased and if the support for the credit-quality-level has not decreased, then it would be possible to re-invest the bond coupons at the same rate by investing in a bond fund. Since it might be possible to re-invest at the same rate then the bond is priced based on the possibility.

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