9.7 Combined Coupon and Term Sensitivities
We now understand a bit about the interaction between coupon and volatility, and maturity and volatility. What about coupon and maturity in combination with respect to volatility? What do we know and what don’t we know?
Observation #1
- As coupon decreases, the average life of a bond’s cash flows (and volatility) increases.
Inference #1
- Therefore, bonds with lower coupons are more sensitive to changes in the discount rate than bonds with higher coupons (from Observation #1 above). AND… Zero-coupon bonds are most sensitive!
Observation #2
- As time (i.e., maturity) increases, price (i.e., present value) volatility of cash flow increases.
Inference #2
- Therefore, long-term bonds are more sensitive to changes in the discount rate than short-term bonds (from Observation #2 above).
Let’s examine the two bonds offered below. Given two bonds, where one has both a short-term maturity and a low coupon versus another bond with a long-term maturity and a high coupon, which will be less sensitive to changes in the discount rate, i.e., less volatile?
Note also that the price effect of interest rates movements and the reinvestment effect are inversely related. That is, as rates go up price goes down, but reinvestment rates go up.
| Short Term | Long Term | |
| High Coupon | Less Volatile | ??? |
| Low Coupon | ??? | More Volatile |
We know that Volatility = ƒ (size of coupon cash flows, time/maturity). We know that a short-term bond with a high coupon is less volatile than a long-term bond with a low coupon, ceteris paribus. However, we have not answered the questions marked in the table above and signified by the question marks. In other words, if you are, say, a conservative investor, which bond would you choose? Would you choose a long-term bond with a high coupon or a short-term bond with a low coupon? We need another tool!
