Par Yield

The coupon rate at which a bond would trade at par — derived from the zero curve.

The par yield at tenor T is the coupon rate that makes a bond price exactly at 100 (par), given the current zero curve. Formula: c = freq × (1 − DF(T)) / Σ DF(tᵢ) where DF is the discount factor from the zero curve. Par yields complete the three curves framework (CFA L2): Zero curve (spot rates), Forward curve (implied future rates), and Par curve. The par curve is what you'd see quoted for new bond issues — it's the fair coupon rate at each maturity. If the zero curve is upward sloping, par yields are slightly below zero rates (because interim coupons are discounted at lower short rates).

Formula

c_{\text{par}} = f \times \frac{1 - DF(T)}{\sum_{i=1}^{n} DF(t_i)}