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 , given the rate for time period and rate for time period . To do this, we solve for the interest rate for time period for which 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 . Or, mathematically:
Simple rate
Solving for yields:
Yearly compounded rate
Solving for yields :
Also the discount factor formula for period (0, t), t expressed in years, and rate being:
,
the forward rate can be expressed in terms of discount factors:
Continuously compounded rate
Solving for yields :
is the forward rate between term and term ,
is the time length between time 0 and term (in years),
is the time length between time 0 and term (in years),
is the zero-coupon yield for the time period ,
is the zero-coupon yield for the time period ,
See also
References
- ^ Fabozzi, Vamsi.K (2012), The Handbook of Fixed Income Securities (Seventh ed.), New York: kvrv, p. 148, ISBN 0-07-144099-2.
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