2 improved clarity
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  1. Per USD invested, the lower coupon bond is risker.
  2. Per USD face value, the higher coupon bond is riskier.

2.) is trivial because itsthe higher coupon bond consistsconstitutes of the one in 1.)original bond plus a series of positive coupons with. The two has the same sign of their its risk, i.e. they lose present value with higher yield. So the higher coupon bond is riskier, it has the risk of the lower coupon bond plus the risk of the extra coupons.

Looking at 1.) and partitioning it into the repayment and the coupons; consider that that the repayment is riskier per amount invested as it is longer than the coupons. Then a reallocation towards the repayment through decreasing the coupons is a reallocation towards the riskier constituent, hence lower coupons increse the relative risk.

  1. Per USD invested, the lower coupon bond is risker.
  2. Per USD face value, the higher coupon bond is riskier.

2.) is trivial because its bond consists of the one in 1.) plus a series of positive coupons with the same sign of its risk.

Looking at 1.) and partitioning it into the repayment and the coupons; consider that that the repayment is riskier per amount invested as it is longer than the coupons. Then a reallocation towards the repayment through decreasing the coupons is a reallocation towards the riskier constituent, hence lower coupons increse the relative risk.

  1. Per USD invested, the lower coupon bond is risker.
  2. Per USD face value, the higher coupon bond is riskier.

2.) is trivial because the higher coupon bond constitutes of the original bond plus a series of positive coupons. The two has the same sign of their its risk, i.e. they lose present value with higher yield. So the higher coupon bond is riskier, it has the risk of the lower coupon bond plus the risk of the extra coupons.

Looking at 1.) and partitioning it into the repayment and the coupons; consider that that the repayment is riskier per amount invested as it is longer than the coupons. Then a reallocation towards the repayment through decreasing the coupons is a reallocation towards the riskier constituent, hence lower coupons increse the relative risk.

1
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  1. Per USD invested, the lower coupon bond is risker.
  2. Per USD face value, the higher coupon bond is riskier.

2.) is trivial because its bond consists of the one in 1.) plus a series of positive coupons with the same sign of its risk.

Looking at 1.) and partitioning it into the repayment and the coupons; consider that that the repayment is riskier per amount invested as it is longer than the coupons. Then a reallocation towards the repayment through decreasing the coupons is a reallocation towards the riskier constituent, hence lower coupons increse the relative risk.