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Read the role of the percentage
A three-year par coupon is selected so that its complete coupon-plus-redemption schedule prices at face. The calculation uses earlier-date factors as well as the terminal factor. A label that mentions three years does not make it a three-year zero rate.
Inspect a nonflat curve
For annual spots 4%, 5%, 6%, the three-year par coupon is 5.922069%. Discounting a three-year zero at that coupon produces a different value from 100/1.06³. The coupon-weighted par equation and the single-payment equation ask different questions.
| Rate | Schedule it describes |
|---|---|
| Three-year spot | One payment at year three |
| Three-year par coupon | Equal annual coupons plus redemption at year three |
Locate the incorrect substitution
Look for a formula that uses the par coupon in every denominator. That assumes a flat discount curve at that percentage. If the original factors are nonflat, the substitution silently changes the curve even if one particular par instrument still looks familiar.
Return to dated factors
Price each payment with its actual dated factor. If the task is to calculate the par coupon, solve the par equation from those factors. Retain a flat-curve exception as a special case rather than treating it as the general method.