Forward rate

The forward rate is the future yield on a bond.

It is calculated using the yield curve.

For example, the yield on a three-month Treasury bill six months from now is a forward rate.

[1] To extract the forward rate, we need the zero-coupon yield curve.

We are trying to find the future interest rate

for time period

expressed in years, given the rate

for time period

for time period

To do this, we use the property that the proceeds from investing at rate

for time period

and then reinvesting those proceeds at rate

for time period

is equal to the proceeds from investing at rate

for time period

depends on the rate calculation mode (simple, yearly compounded or continuously compounded), which yields three different results.

Mathematically it reads as follows: Solving for

The discount factor formula for period (0, t)

expressed in years, and rate

for this period being

, the forward rate can be expressed in terms of discount factors:

yields : The discount factor formula for period (0,t)

expressed in years, and rate

for this period being

, the forward rate can be expressed in terms of discount factors:

The discount factor formula for period (0,t)

expressed in years, and rate

, the forward rate can be expressed in terms of discount factors:

is the forward rate between time

is the zero-coupon yield for the time period