Forwards & Par Yields

Par Yield Reconciliation

The par yield prices a coupon bond exactly to face value.

highlighted = computed this step

Par yield formula

A par yield is the coupon rate that makes a coupon bond price to face. With discount factors summing to 27/10 and final discount factor 21/25, the three-year par yield is 8/135, shown rounded as 5.93%.

cpar=1−dn∑t=1ndtc_{\text{par}}=\frac{1-d_n}{\sum_{t=1}^{n}d_t}

Prices to par

The exact coupon amount is 16000/27 cents. Discounting that coupon stream plus face with the curve gives exactly $100.00, so the bond prices to par.

P=cpar∑t=1ndt+face⋅dn=$100.00P=c_{\text{par}}\sum_{t=1}^{n}d_t+\text{face}\cdot d_n=\$100.00
Par yield reconciliationThe par yield prices the bond to par from the discount factors.Par-yield reconciliationItemExact valueDisplayΣ discount factors27/1027/101 - d_n4/254/25Par yield8/1358/135 (5.93%)Coupon each year16000/2716000/27 centsPar bond price10000$100.00

Model reconciliation

This is the same DCF idea as a flat-rate valuation, but the discount factors can differ by maturity. The result is descriptive under the stated curve, frictionless assumptions, and no credit or liquidity spread; it is not investment advice.

par yield reconciles coupon cash flows to face value\text{par yield reconciles coupon cash flows to face value}