Definition, Formula for Calculation, and Example

What is a Forward Value

Forward price is the predetermined provide price for an underlying commodity, foreign exchange, or financial asset as determined throughout the buyer and the seller of the forward contract, to be paid at a predetermined date in the future. At the inception of a forward contract, the forward price makes the cost of the contract 0, alternatively changes in the price of the underlying will reason the forward to take on a excellent or destructive value.

The forward price is made up our minds thru the following manner:


$\begin{array}{cc}& F_0=S_0\times e^{rT}\end{array}$

get started{aligned} &F_0 = S_0 cases e^{rT} end{aligned} ​F0​=S0​×erT​

Basics of Forward Value

Forward price is in keeping with the prevailing spot price of the underlying asset, plus any wearing costs akin to interest, storage costs, foregone interest or other costs or selection costs.

Even though the contract has no intrinsic value at the inception, over time, a contract would perhaps gain or lose value. Offsetting positions in a forward contract are very similar to a zero-sum game. For example, if one investor takes a chronic position in a red meat abdomen forward agreement and every other investor takes the temporary position, any certain sides inside the long position equals the losses that the second investor incurs from the short position. Thru to begin with setting the cost of the contract to 0, every occasions are on an identical ground at the inception of the contract.

Forward Value Calculation Example

When the underlying asset inside the forward contract does not pay any dividends, the forward price will also be calculated the use of the following manner:


$\begin{array}{cc}& F=S\times e^{(r\times t)}\\ & \text{where:}\\ & F=\text{the contract’s forward price}\\ & S=\text{the underlying asset’s provide spot price}\\ & e=\text{the mathematical irrational constant approximated}\\ & \text{thru 2.7183}\\ & r=\text{the risk-free rate that applies to the existence of the}\\ & \text{forward contract}\\ & t=\text{the provide date in years}\end{array}$

get started{aligned} &F = S cases e ^ { (r cases t) } &textbf{where:} &F = text{the contract’s forward price} &S = text{the underlying asset’s provide spot price} &e = text{the mathematical irrational constant approximated} &text{thru 2.7183} &r = text{the risk-free rate that applies to the life of the} &text{forward contract} &t = text{the availability date in years} end{aligned} ​F=S×e(r×t)where:F=the contract’s forward priceS=the underlying asset’s provide spot pricee=the mathematical irrational constant approximatedthru 2.7183r=the risk-free rate that applies to the existence of theforward contractt=the provide date in years​

For example, assume a security is at the moment purchasing and promoting at $100 in keeping with unit. An investor needs to enter proper right into a forward contract that expires in 365 days. The existing annual risk-free interest rate is 6%. The usage of the above manner, the forward price is calculated as:


$\begin{array}{cc}& F=\$100\times e^{(0.06\times 1)}=\$106.18\end{array}$

get started{aligned} &F = $100 cases e ^ { (0.06 cases 1) } = $106.18 end{aligned} ​F=$100×e(0.06×1)=$106.18​

If the there are wearing costs, that is added into the process:


$\begin{array}{cc}& F=S\times e^{(r+q)\times t}\end{array}$

get started{aligned} &F = S cases e ^ { (r + q) cases t } end{aligned} ​F=S×e(r+q)×t​

Proper right here, q is the wearing costs.

If the underlying asset pays dividends over the life of the contract, the process for the forward price is:


$\begin{array}{cc}& F=(S-D)\times e^{(r\times t)}\end{array}$

get started{aligned} &F = ( S – D ) cases e ^ { ( r cases t ) } end{aligned} ​F=(S−D)×e(r×t)​

Proper right here, D equals the sum of each and every dividend’s supply value, given as:


$\begin{array}{cc}D=& \text{PV}\left(d\right(1\left)\right)+\text{PV}\left(d\right(2\left)\right)+\cdots +\text{PV}\left(d\right(x\left)\right)\\ =& d\left(1\right)\times e^{-(r\times t(1\left)\right)}+d\left(2\right)\times e^{-(r\times t(2\left)\right)}+\cdots +\\ \phantom{=}& d\left(x\right)\times e^{-(r\times t(x\left)\right)}\end{array}$

get started{aligned} D =& text{PV}(d(1)) + text{PV}(d(2)) + cdots + text{PV}(d(x)) =& d(1) cases e ^ {- ( r cases t(1) ) } + d(2) cases e ^ { – ( r cases t(2) ) } + cdots + phantom{=}& d(x) cases e ^ { – ( r cases t(x) ) } end{aligned} D===​ PV(d(1))+PV(d(2))+⋯+PV(d(x)) d(1)×e−(r×t(1))+d(2)×e−(r×t(2))+⋯+ d(x)×e−(r×t(x))​

The usage of the example above, assume that the safety pays a 50-cent dividend every 3 months. First, the present value of each and every dividend is calculated as:


$\begin{array}{cc}& \text{PV}\left(d\right(1\left)\right)=\$0.5\times e^{-(0.06\times \frac{3}{12})}=\$0.493\end{array}$

get started{aligned} &text{PV}(d(1)) = $0.5 cases e ^ { – ( 0.06 cases frac { 3 }{ 12 } ) } = $0.493 end{aligned} ​PV(d(1))=$0.5×e−(0.06×123​)=$0.493​


$\begin{array}{cc}& \text{PV}\left(d\right(2\left)\right)=\$0.5\times e^{-(0.06\times \frac{6}{12})}=\$0.485\end{array}$

get started{aligned} &text{PV}(d(2)) = $0.5 cases e ^ { – ( 0.06 cases frac { 6 }{ 12 } ) } = $0.485 end{aligned} ​PV(d(2))=$0.5×e−(0.06×126​)=$0.485​


$\begin{array}{cc}& \text{PV}\left(d\right(3\left)\right)=\$0.5\times e^{-(0.06\times \frac{9}{12})}=\$0.478\end{array}$

get started{aligned} &text{PV}(d(3)) = $0.5 cases e ^ { – ( 0.06 cases frac { 9 }{ 12 } ) } = $0.478 end{aligned} ​PV(d(3))=$0.5×e−(0.06×129​)=$0.478​


$\begin{array}{cc}& \text{PV}\left(d\right(4\left)\right)=\$0.5\times e^{-(0.06\times \frac{12}{12})}=\$0.471\end{array}$

get started{aligned} &text{PV}(d(4)) = $0.5 cases e ^ { – ( 0.06 cases frac { 12 }{ 12 } ) } = $0.471 end{aligned} ​PV(d(4))=$0.5×e−(0.06×1212​)=$0.471​

The sum of the ones is $1.927. This amount is then plugged into the dividend-adjusted forward price manner:


$\begin{array}{cc}& F=(\$100-\$1.927)\times e^{(0.06\times 1)}=\$104.14\end{array}$

get started{aligned} &F = ( $100 – $1.927 ) cases e ^ { ( 0.06 cases 1 ) } = $104.14 end{aligned} ​F=($100−$1.927)×e(0.06×1)=$104.14​