Forwards & Par Yields

Forward Rates

Forward rates are implied by adjacent discount factors.

highlighted = computed this step

Forward from adjacent discounts

A one-period forward rate compares adjacent discount factors. Use the previous discount factor divided by the current one, then subtract one.

ft=dt−1dt−1f_t=\frac{d_{t-1}}{d_t}-1

Implied one-period forwards

The implied forwards are exact 1/24, 1/15, and 1/14, shown rounded as 4.17%, 6.67%, and 7.14%.

(f1,f2,f3)=(1/24,1/15,1/14)(f_1,f_2,f_3)=(1/24,1/15,1/14)
Forward, spot, and par summaryForwards and par yield are recomputed from discount factors.Forward, spot, and par summaryYearDiscount factorForward rateSpot annualized3y par yield124/251/24 (4.17%)1/24 (4.17%)29/101/15 (6.67%)5.41% rounded321/251/14 (7.14%)5.98% rounded8/135 (5.93%)

Implied, not forecast

A forward rate is implied by this curve. It is a pricing relation under the stated discount factors, not a forecast of future rates.

forward rates are implied prices\text{forward rates are implied prices}