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{{distinguish|forward price|forward exchange rate}}
The '''forward rate''' is the future yield on a [[bond (finance)|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''.<ref>{{Citation |last=Fabozzi |first=Vamsi.K|title=The Handbook of Fixed Income Securities |edition=Seventh |location=New York |publisher=kvrv |year=2012 |isbn=0-07-144099-2 |page=148 }}.</ref>
 
==Forward rate calculation==
 
To extract the forward rate, one needs the [[Zero-coupon bond|zero-coupon]] [[yield curve]]. The general formula used to calculate the forward rate is:
 
:<math>r_{t_1,t_2} = \left(\frac{(1+r_2)^{d_2}}{(1+r_1)^{d_1}}\right)^{\frac{1}{d_2-d_1}} - 1 </math>
 
<math>r_{t_1,t_2} </math>  is the forward rate between term <math> t_1 </math> and term <math> t_2 </math>,  
 
<math> d_1 </math> is the time length between time 0 and term <math> t_1 </math> (in years),
 
<math> d_2 </math> is the time length between time 0 and term <math> t_2 </math> (in years),
 
<math> r_1 </math> is the zero-coupon yield for the time period <math> (0, t_1) </math>,
 
<math> r_2 </math> is the zero-coupon yield for the time period <math> (0, t_2) </math>,
 
=== Derivation ===
 
We are trying to find the future interest rate for time period <math>(t_1, t_2)</math>, given the rate <math>r_1</math> for time period <math>(0, t_1)</math> and rate <math>r_2</math> for time period <math>(0, t_2)</math>. To do this, we solve for the interest rate <math>r_{t_1,t_2}</math> for time period <math>(t_1, t_2)</math> for which the proceeds from investing at rate <math>r_1</math> for time period <math>(0, t_1)</math> and then [[reinvestment|reinvesting]] those proceeds at rate <math>r_{t_1,t_2}</math> for time period <math>(t_1, t_2)</math> is equal to the proceeds from investing at rate <math>r_2</math> for time period <math>(0, t_2)</math>. Or, mathematically:
 
:<math>(1+r_1)^{d_1}(1+r_{t_1,t_2})^{d_2-d_1} = (1+r_2)^{d_2}</math>
 
Solving for <math>r_{t_1,t_2}</math> yields the above formula.
 
== Related instruments ==
* [[Forward rate agreement]]
* [[Floating rate note]]
 
A forward discount is when the forward rate of one currency relative to another currency is higher than the spot rate.
 
A forward premium is when the forward rate of one currency relative to another currency is lower than the spot rate.
 
== See also ==
*[[Forward price]]
 
== References ==
{{Reflist}}
{{Portfilo market}}
 
[[Category:Financial economics]]

Revision as of 02:08, 5 January 2014

Template:Distinguish 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, one needs the zero-coupon yield curve. The general formula used to calculate the forward rate is:

rt1,t2=((1+r2)d2(1+r1)d1)1d2d11

rt1,t2 is the forward rate between term t1 and term t2,

d1 is the time length between time 0 and term t1 (in years),

d2 is the time length between time 0 and term t2 (in years),

r1 is the zero-coupon yield for the time period (0,t1),

r2 is the zero-coupon yield for the time period (0,t2),

Derivation

We are trying to find the future interest rate for time period (t1,t2), given the rate r1 for time period (0,t1) and rate r2 for time period (0,t2). To do this, we solve for the interest rate rt1,t2 for time period (t1,t2) for which the proceeds from investing at rate r1 for time period (0,t1) and then reinvesting those proceeds at rate rt1,t2 for time period (t1,t2) is equal to the proceeds from investing at rate r2 for time period (0,t2). Or, mathematically:

(1+r1)d1(1+rt1,t2)d2d1=(1+r2)d2

Solving for rt1,t2 yields the above formula.

Related instruments

A forward discount is when the forward rate of one currency relative to another currency is higher than the spot rate.

A forward premium is when the forward rate of one currency relative to another currency is lower than the spot rate.

See also

References

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