The forward rate is the future yield on a
bond. It is calculated using the
yield curve
In finance, the yield curve is a graph which depicts how the yields on debt instruments - such as bonds - vary as a function of their years remaining to maturity. Typically, the graph's horizontal or x-axis is a time line of months or ye ...
. For example, the yield on a three-month
Treasury bill six months from now is a ''forward rate''.
[.]
Forward rate calculation
To extract the forward rate, we need the
zero-coupon yield curve
In finance, the yield curve is a graph which depicts how the yields on debt instruments - such as bonds - vary as a function of their years remaining to maturity. Typically, the graph's horizontal or x-axis is a time line of months or ye ...
.
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).
Related instruments
*
Forward rate agreement In finance, a forward rate agreement (FRA) is an interest rate derivative (IRD). In particular it is a linear IRD with strong associations with interest rate swaps (IRSs).
General description
A forward rate agreement's (FRA's) effective descript ...
*
Floating rate note
See also
*
Forward price The forward price (or sometimes forward rate) is the agreed upon price of an asset in a forward contract. Using the rational pricing assumption, for a forward contract on an underlying asset that is tradeable, the forward price can be expressed in ...
*
Spot rate
In finance, a spot contract, spot transaction, or simply spot, is a contract of buying or selling a commodity, security or currency for immediate settlement (payment and delivery) on the spot date, which is normally two business days after the ...
References
{{Reflist
Financial economics
Swaps (finance)
Fixed income analysis
Interest rates