## What are Forward Contracts?

A forward contract is a customized contract between two parties to purchase or sell an underlying asset in time and at a price agreed today (known as forward price).

- The buyer of the contract is called the long. The buyer is betting that the price will go up.
- The seller of the contract is called the short. The seller is betting that the price will go down.
- In this, no money changes hands until the settlement date. In fact, the forward price is set so that neither party needs to pay any money at contract initiation.
- They are subject to default risk regardless of their methods of settlement. In both deliverable and cash-settled forward prices, only the party that owns the greater amount can default.

### Value of Forward Contract

At time t = 0, the long and the short agree that the short will deliver the asset to the long at time T for a price of F0 (T).

F0 (T) is the forward price. If at time T, the price of the underlying is ST, the long is obligated to pay F0 (T) to short.

Value of the contract to the Long at expiration = ST – F0 (T).

Value of the contract to the Short at expiration = F0 (T) – ST.

### Settlement of Forward Contract

When a forward contract expires, it can be settled in two ways:

**#1 – Physical Delivery:** In a physical delivery settlement, the long pay the agreed-upon price to the short and receives the underlying asset from the short.

**#2 – Cash Settlement:** In cash settlement, the buyer (seller) receives the difference between the market price and the agreed-upon price if the market price is higher (lower) than the agreed-upon price on the date of settlement.

- Cash-settled contracts are more commonly used when delivery is impractical e.g. in forward contracts on stock index, it would be impractical for the short to deliver to the long a portfolio containing each of the stocks in the stock index proportionate to its weighting in the index.
- The cash-settled forward price is also known as non-deliverable forwards i.e. NDFs.

### How to Calculate Forward Prices in the Contract?

The pricing model used to calculate forward prices makes the following assumptions:

- No transaction costs or short-sale restrictions.
- Same tax rates on all net profits.
- Borrowing and lending at the risk-free rate.
- Arbitrage opportunities are exploited as they arise.

For the development of a forward pricing model, we will use the following notation:

- T = time to maturity (in years) of the forward contract.
- S0 = underlying asset price today (t = 0).
- F0 = forward price today.
- r = continuously compounded risk-free annual rate.

The forward price may be written as:

#### Forward Contract Formula #1

**F0 = S0exp(rT)**

The right-hand side of Equation 1 is the cost of borrowing funds to buy the underlying asset and carrying it forward to time T. Equation 1 states that this cost must equal the forward price. If F0> S0.exp(rT), then arbitrageurs will profit by selling the forward and buying the asset with borrowed funds. If F0< S0.exp(rT), arbitrageurs will profit by selling the asset, lending out the proceeds, and buying the forward. Hence, equality in the formula must hold. Note that this model assumes perfect markets.

**Example:**

Suppose we have an asset currently worth $1,000. The current continuously compounded rate is 4% for all maturities. Calculate the price of a 6-month forward contract on this asset.

F0 = $l,OOO.exp(0.04*0.5) = $1,020.20.

#### Forward Contract Formula #2 (Forward Price with Carrying Costs)

If the underlying pay a known amount of cash over the life of the forward contract, a simple adjustment is made to Equation 1. Since the owner of the contract does not receive any of the cash flows from the underlying asset between contract origination and delivery, the present value of these cash flows must be deducted from the spot price when calculating the forward price. This is most easily seen when the underlying asset makes a periodic payment. We let/represent the present value, of the cash flows over T years. Formula 1 then becomes:

**F0 = (S0 – I) exp(rT)**

#### Forward Contract Formula #3 (Effect of Known Dividend)

When the underlying asset for a forward contract pays a dividend, we assume that the dividend is paid continuously. Letting q represent the continuously compounded dividend yield paid by the underlying asset expressed on a per annum basis, Formula 1 becomes:

**F0 = S0 exp(r-q)T**

### Advantages of Forward Contracts

Some of the advantages are as follows:

- They can be matched with the exposure time period as well as with the exposure cash size.
- It provides a complete hedge.
- Over-the-counter products.
- Using forward products provides price protection.
- They are easy to understand.

### Disadvantages of Forward Contracts

Some of the disadvantages are as follows:

- Capital binding is required. Before settlement, there are no intermediate cash flows.
- It is subject to default risk.
- Contracts can be difficult to cancel.
- Finding a counterparty may be difficult.

### Limitations

- Liquidity risk.
- Counter-party risk.

**Note:**

The parties engaged in forward contracts do not have the option to select the mode of settlement (i.e. delivery or cash-settled) on the settlement date; rather, it is negotiated between the parties at the start.

### Conclusion

- Long gains if asset price higher than forward price.
- Short gains if the asset price is less than the forward price.
- Neither party pays at contract initiation.

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