Forward_rate

Forward rate

Forward rate

Future yield on a bond


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]

Forward rate calculation

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

We are trying to find the future interest rate for time period , and expressed in years, given the rate for time period and rate 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:

Simple rate

Solving for yields:

Thus

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:

Yearly compounded rate

Solving for 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:

Continuously compounded rate


Solving for yields:


STEP 1→
STEP 2→
STEP 3→
STEP 4→
STEP 5→

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:

is the forward rate between time and time ,

is the zero-coupon yield for the time period , (k = 1,2).

See also


References

  1. Fabozzi, Vamsi.K (2012), The Handbook of Fixed Income Securities (Seventh ed.), New York: kvrv, p. 148, ISBN 978-0-07-144099-8.

Share this article:

This article uses material from the Wikipedia article Forward_rate, and is written by contributors. Text is available under a CC BY-SA 4.0 International License; additional terms may apply. Images, videos and audio are available under their respective licenses.