# Forward Price Definition

## What is a forward price

The forward price is the predetermined delivery price for an underlying commodity, currency or financial asset, as decided by the buyer and seller of the futures contract, to be paid on a predetermined date in the future. At the start of a futures contract, the futures price makes the value of the contract zero, but changes in the price of the underlying will cause the futures contract to take on a positive or negative value.

The forward price is determined by the following formula:

The

begin {aligned} & F_0 = S_0 times e ^ {rT} \ end {aligned}

TheF0The=S0The×erTTheThe

## Basics of the forward price

The forward price is based on the current spot price of the underlying asset, plus any finance charges such as interest, storage charges, lost interest or other charges or opportunity costs.

Although the contract has no intrinsic value at first, over time, a contract can gain or lose value. Clearing positions in a futures contract are equivalent to a zero sum game. For example, if an investor takes a long position in a pork belly futures contract and another investor takes the short position, any gain in the long position equals the losses the second investor takes from the short position. By initially setting the value of the contract to zero, the two parties are on an equal footing at the start of the contract.

### Key points to remember

• The futures price is the price at which a seller delivers an underlying asset, financial derivative or currency to the buyer of a futures contract on a predetermined date.
• It is roughly equal to the cash price plus associated shipping costs such as storage costs, interest rates, etc.

## Example of calculating forward prices

When the underlying asset of the futures contract does not pay any dividends, the futures price can be calculated using the following formula:

The

begin {aligned} & F = S times e ^ {(r times t)} \ & textbf {where:} \ & F = text {the contract forward price} \ & S = text {the underlying current asset price}} \ & e = text {the approximate irrational mathematical constant} \ & text {par 2,7183} \ & r = text {the risk-free rate that applies to the life of the} \ & text {forward contract} \ & t = text {the delivery date in years} \ end {aligned}

TheF=S×e(r×t)or:F=the forward price of the contractS=the current spot price of the underlying assete=the approximate irrational mathematical constantby 2.7183r=the risk-free rate that applies to the lifetime of theforward contractt=delivery date in yearsTheThe

For example, suppose a security is currently trading at 100 per unit. An investor wishes to conclude a futures contract which expires in a year. The current annual risk-free interest rate is 6%. Using the above formula, the forward price is calculated as follows: The begin {aligned} & F = 100 times e ^ {(0,06 times 1)} = 106,18 \ end {aligned} TheF=100×e(0.06×1)=106.18TheThe If there are shipping costs, this is added to the formula: The begin {aligned} & F = S times e ^ {(r + q) times t} \ end {aligned} TheF=S×e(r+q)×tTheThe Here, q is the cost of ownership. If the underlying asset pays dividends during the term of the contract, the formula for the forward price is as follows: The begin {aligned} & F = (S – D) times e ^ {(r times t)} \ end {aligned} TheF=(Sre)×e(r×t)TheThe Here, D is equal to the sum of the present value of each dividend, given by: The begin {aligned} D = & text {PV} (d (1)) + text {PV} (d (2)) + cdots + text {PV} (d (x)) \ = & d (1) times e ^ {- (r times t (1))} + d (2) times e ^ {- (r times t (2))} + cdots + \ ghost {=} & d (x) times e ^ {- (r times t (x))} \ end {aligned} re===The PV(re(1))+PV(re(2))++PV(re(X)) re(1)×e(r×t(1))+re(2)×e(r×t(2))++ re(X)×e(r×t(X))TheThe Using the example above, assume that the security pays a dividend of 50 cents every three months. First, the present value of each dividend is calculated as follows: The begin {aligned} & text {PV} (d (1)) = 0.5 times e ^ {- (0.06 times frac {3} {12})} = 0.493 end {aligned} ThePV(re(1))=0.5×e(0.06×123The)=0.493TheThe The begin {aligned} & text {PV} (d (2)) = 0.5 times e ^ {- (0.06 times frac {6} {12})} = 0.485 end {aligned} ThePV(re(2))=0.5×e(0.06×126The)=0.485TheThe The begin {aligned} & text {PV} (d (3)) = 0.5 times e ^ {- (0.06 times frac {9} {12})} = 0.478 end {aligned} ThePV(re(3))=0.5×e(0.06×129The)=0.4seven8TheThe The begin {aligned} & text {PV} (d (4)) = 0.5 times e ^ {- (0.06 times frac {12} {12})} = 0.471 end {aligned} ThePV(re(4))=0.5×e(0.06×1212The)=$0.4seven1TheThe The sum of these amounts is$ 1,927. This amount is then inserted into the dividend-adjusted forward price formula:

The

begin {aligned} & F = ( 100 – 1.927) times e ^ {(0.06 times 1)} = 104.14 \ end {aligned}

TheF=($100$1.92seven)×e(0.06×1)=\$104.14TheThe

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