Reinvestment Risk

Am confused why would reinvestment risk increase with higher coupon rrate. Why doesn’t it have inverse relation with regard to interest rate. Lower interest rate would have more reinvestment risk as bond holder will reinvest at lower rrate pls help clear my understanding

Reinvestment risk increases with an increase in the amount of cash you have to reinvest. Higher coupons pay you more cash.

So wouldn’t a bond holder be ok to get higher coupon rate on reinvestment

Not really. If you have a higher coupon, that means a lot of your returns is coming from reinvesting your coupons at the current interest rates. The higher your coupon the more your returns are coming from reinvestment income. That means you are MORE vulnerable to changes in interest rates and your total return could end up being lower if interest rates fall, because you are reinvesting your coupons at a lower interest rate.

If interest rates drop you have more money to invest at lower rates; you’d rather have all your money invested at the YTM of the bond.

Note, too, that risk doesn’t merely mean downside: all variability is considered risky, even if interest rates rise and you earn higher reinvestment income.