Why higher coupon rate has higher reinvestment risk?
Because you are more dependent on a higher rate of interest to maintain yield. Remember, yield assumes you can reinvest coupons at the coupon rate. It would be easier to find a security to obtain an equal coupon rate of 1% than it would be to find one at 6%.
Think of it this way:
- If you have $60 to invest every 6 months (a 6% coupon on a $1,000 par bond), the difference between a reinvestment rate of 0% and a reinvestment rate of 10% is $6 per year
- If you have $20 to invest every 6 months (a 2% coupon on a $1,000 par bond), the difference between a reinvestment rate of 0% and a reinvestment rate of 10% is $2 per year
Clearly, a 6% coupon has a higher reinvestment risk (measured as the variance or standard deviation of the reinvestment income (interest) earned) than a 2% coupon.
All else equal, reinvestment risk is higher when cash flows come earlier. Here’s why:
- The higher the coupon, the sooner on average the bond’s cash flows are received (NOTE: that’s essentially what Macauley Duration measures)
- so the longer on average they must be reinvested.
- therefore, the higher the coupon rate, the more reinvestment rate risk it is exposed to
A bit off topic, but if it helps to remember: You can also think of it as the contra risk to the price fluctuations due to interest rate of the bond. For example, all else equal, buying a premium bond will shorten your duration giving you lower volatility with interest rate fluctuations. However, you’ll have higher reinvestment risk since you are getting that cash flow earlier. You have a greater risk throughout the life of the bond of not being able to reinvest at the original rate.