What is Forward Price?

Forward price can be defined as a forecasted delivery price of an underlying financial asset, or in other words, it is a price at which an underlying financial asset or commodity is delivered by a supplier to the customer of a forward contract and it is entirely based upon the spot price of an underlying financial asset that includes carrying costs like foregone costs, interest, etc.

Explanation

This is used in a forward contract for enabling the physical delivery of an underlying asset or a commodity. The price is paid by the seller to the customer of the forward contract at a pre-decided period against the delivery of an underlying asset or an item. It can be calculated by adding up the spot price with carrying costs like rate of interests, expenses about the storage of goods, etc.

Forward Price Formula

The formulas used for the calculation of the forward price of financial security depends on the fact whether it has no income, known cash income, or known dividend yield. The formulas used for the determination of financial security in each case are:

With no income is, it is –

F = S₀e^rT

With known cash income, the formula is-

F = (S₀– I) e^rT

With known dividend yield is, the formula is-

F = S₀e^(r-q)T

Where,

F is the forward price of the contract
S₀ is the financial security’s latest spot price
e is the irrational arithmetical costs
I am the P.V. (present value) of the cash income
q is the rate of dividend yield
r is the risk-free rate of interest that is applicable for the entire term of the forward contract
T is the delivery date expressed in years

Assumptions

Forward rates are calculated on a “no arbitrage” assumption. Arbitrage is a mechanism that enables trading profits to be entirely from risks. So, calculating forward rates on a no-arbitrage assumption will mean that the profits earned by the traders will not be free from any risk.
This assumption is mere because the financial securities are simultaneously traded, i.e., purchased and sold. Another reason for calculating forward rates based on a “no arbitrage” assumption can be the fact that the occurrence of arbitrage is just rare in a developed security exchange market.
However, whenever the arbitrage opportunities arise in a financial security exchange market, the investors can readily identify and eliminate the same to derive maximum advantages arising out of such a scenario. In a no-arbitrage condition, only two portfolios that result in duplicate payments can be equally priced. The equal pricing of these two portfolios or financial securities can be used to evaluate the rate.

How to Calculate?

It can be calculated for each scenario using the following steps-

Steps #1 – Steps to follow when there is no income –

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In the first step, the users will need to identify the financial security’s ongoing spot price (S₀)
In the next step, the users will need to identify the irrational arithmetical costs (e)
Next, the users will need to identify the risk-free rate of interest (r) and the delivery date expressed in years (t)
The users will need to take all the values and place them in the formula (F = S₀e^rT) to find the forward rate of financial security with no income.

Steps #2 – Steps to following when there is known income –

In the first step, the users will need to identify the financial security’s ongoing spot price (S₀)
In the next step, the users will need to identify the P.V. of the cash income (I)
Next, the users will need to identify the irrational arithmetical costs (e)
Next, the users will need to identify the risk-free rate of interest (r) and the delivery date expressed in years (t)
The users will need to take all the values and place them in the formula (F = (S₀– I) e^rT) to find the forward rate of the financial security with known income.

Steps #3 – Steps to follow when there is dividend yield –

In the first step, the users will need to identify the financial security’s ongoing spot price (S₀)
In the next step, the users will need to identify the rate of dividend yield (q)
Next, the users will need to identify the irrational arithmetical costs (e)
Next, the users will need to identify the risk-free rate of interest (r) and the delivery date expressed in years (t)
The users will need to take all the values and place them in the formula (F = S₀e^(r-q)T) to find the forward rate of the financial security with known dividend yield.

Examples

A Limited and B Limited entered into a 5-month forward contract to trade a bond at $60. The five-month risk-free rate of interest upon this bond is 6 percent per annum.

Solution:

S₀or Spot Rate = $60
R or risk-free rate of interest = 6 % p.a.
T or the maturity term = 5 months or 0.417.

F = S₀e^rT

= 60 * e ^{(0.06 * 0.417)}
= 60 * 1.025336
= $61.52

Therefore, the FP is $61.52

Forward Price vs. Future Price

The forward price must not be confused with future prices. The forward price is concerned with the physical delivery of an underlying financial asset, commodity, security or a currency whereas future prices can be defined as a price of a commodity or stock in a futures contract. Forward price represents the supply and demand for a particular type of commodity whereas future price represents the international supply and demand.

Conclusion

This is usually evaluated on the recent spot price of an underlying financial asset, commodity, security or a currency inclusive of carrying costs that may include costs pertaining to storage, foregone interest, rate of interest, opportunity costs, etc.

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Forward Price