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Separate the coupon from the yield
The coupon rate tells you the promised interest payment relative to face value. The yield is the rate used to relate the cash-flow stream to its current price. A bond can keep the same coupon rate while its market yield moves. Changing the yield therefore does not change the fixed coupon itself.
Trace the discounting effect
For a future positive payment, dividing by a larger discount factor gives a smaller present value. Applying that reasoning to every promised payment explains the inverse price–yield relationship for a bond with fixed cash flows. The relationship curves because payments arrive at different future dates.
| Annual yield | Price for face value 100 |
|---|---|
| 3% | 109.1594 |
| 5% | 100 |
| 7.000000000000001% | 91.7996 |
Explain premium, par and discount prices
Under matching regular-payment conventions, a coupon rate equal to the yield gives a price at face value. A coupon rate above the yield gives a premium; a coupon rate below the yield gives a discount. This comparison is a useful check on a calculation, not a replacement for discounting the actual payments.
Know when fixed cash flows are not enough
A bond with embedded options can have cash flows that depend on future circumstances. A model that holds the payment stream fixed cannot describe every option effect. Start with the fixed-cash-flow case, then study how option-sensitive measures change the analysis.