Forwards

A forward contract is a contractual agreement between two parties to buy or sell an asset at a price agreed upon today for delivery at a specified future date. It is different from a spot contract, which is a contract to buy or sell an asset on the spot that is today itself. A forward contract is a non-standardized contract normally used by traders to hedge their existing long or short positions in the market. The party that agrees to buy the asset in future is taking a long position while the counterparty that sells is taking a short position. The price agreed upon by the parties is called the delivery price or the forward price.

Typically, a forward contract implies that the delivery of the asset takes place at the specified future date while the price is paid today. It one of the several forms of trades where the value date when the asset or securities change hands is different from the date that the trade is entered into.

Except in rare cases, the forward price is almost always different from the spot price even if the difference is insignificant. The spot price is the price current market price, the price at which the asset is available for delivery today. The difference between the forward and spot price is the forward premium or discount.

Forward contracts, just like any other derivative product, is a speculative product used by traders to hedge risk in the stock, currency and commodity markets or in any other financial securities market where such a product is available. It also provides an opportunity to speculators to take advantage of price movements in time sensitive assets.

Forward contracts are almost similar to futures contracts except for the fact that forwards are not tradable in exchanges, nor standardized contracts. They are also different from futures as they typically do not have any mechanism for interim partial settlements as it is the case in leveling up of margin requirement in a futures contract. In a forward contract the parties do not exchange property to secure the party at gain; the unrealized gain (or loss) keeps building up as long as the contract is open. However, since it is traded over-the-counter (OTC), the specification of a forward contract can be customized and the arrangement may require the party at loss to pledge collateral for securing the party in profit.

Forward Payoffs

The maturity value of a forward contract depends upon the deliver or forward price (K) and the price of the asset (S_T) at that time of maturity.

• For the party who bought the asset, the payoff is: ¦_T = S_T  – K
• For the party who sold the asset, the payoff is: ¦_T =K – S_T

How it works

Let us suppose that John wants to buy a house owned by Paul and both agree that the price today is $ 100,000. Since John wants some time, both agree to complete the transaction one year from now and agree on a sale price of $ 104,000 a year from now. This is what a forward contract is. Since John is buying the underlying asset, he is said to have created a long position. In contrast, Paul has gone short.

After one year, when the ownership of the house is to change hands, suppose the current market price of Paul’s house is $ 109,000. Paul is obliges to sell the house at $ 104,000 to John, who makes a profit of $ 5,000. This is easily understood by realizing that John can buy the house from Paul at $ 104,000 and immediately sell it to someone else at $ 109,000. Paul, on the other hand, has suffered a notional loss of $ 5000 and made an actual profit of $ 4,000.

A similar situation occurs in foreign exchange or forex forward contracts where one trader creates a long or short position in a currency pair ( for example, a contract to buy Euros) to expire at a specified future date with the motive of protecting them from the risk of fluctuation in the exchange rate over a period of time. As the exchange rate between the US dollar and the euro fluctuates between the dates on which the contract is entered into and the expiry date, one party gains while the counterparty loses as one currency strengthens against the other.

A forward position may be opened for different reasons. In this case, the party that buys Euros may be doing so because it needs the currency for payment of a debt at a future date and feels that the exchange rate will move favorably. Or, the party may buying Euros may be hedging a risk or simply speculating on the euro hoping to make a profit on closing the contract.

An exchange rate forward contract has a specified notional amount so currencies, for example, a contract to buy $ 100 million Euros for 121.4 million USD at the prevailing price. Both the amounts are notional amounts. The notional amount is apparently a large number but the cost (margin) of opening a trade of this magnitude is considerably less due to the leverage created. Leverage is typical in all derivative contracts.

How Forward Price Is Agreed Upon

Let us carry the example of Paul’s house a bit further. Paul knows that he can sell his house for $100,000 on the spot and put the money in his bank. Since he is agreeing to wait for one year, he wants to be paid for waiting. If at that point in time, the risk-free rate of return on a 365-day bank deposit is 4%, then the money would grow to $ 104,000 in one year’s time. This means that to cover the opportunity cost, Paul would want at least $ 104,000 for the house for the deal to be worthwhile for him.

Spot-Forward Parity

It is however not always so simple to agree upon a forward price. For example, in liquid assets the link between spot and forward price is provided by spot–forward parity. Known as cost of carry, it is basically a combination of several components. The cost of carry is determined by whether the underlying asset:

• is an income yielding asset and if yes, whether it is discrete or continuous
• is associated with storage cost
• is an investment asset such as gold or financial instruments
• is a consumable asset held primarily for consumption such as oil, iron ore etc

Determining Forward Price of Investment Assets

Relationship between spot (S₀) and current forward price (F₀) of Investments assets with no known income is

F₀ = S_0eT^T

In the formula, refers to risk-free rate of return and T is time to maturity. The basis of this result is that in a perfect capital market there should be no difference between buying the underlying asset today and holding and buying a forward contract and taking delivery to own the asset at time T. – in present value terms, both approaches should cost the same.

The relationship between spot and forward price of an asset that provides a known income is

• for discrete income yielding assets: F₀ = (S₀ – I)_eT^T
• for continuous income yielding assets: F₀ = S₀e^(r-q)T

Here, I = the current value of the discrete income at time t₀ < T and q% p.a.is the continuously compounded dividend yield over the life of the contract. In this case, the basis is that in case of income yielding assets, there is an advantage in holding an asset instead of buying a forward contract because you get to receive the income. Hence, for reflecting this benefit, the income (I or q) must be subtracted. An asset that yields discrete income may be a stock and assets that yield continuous income may be a foreign currency or a stock index.

Investment assets, commodities such as gold and silver attract storage cost, which must be considered as ‘negative income.’ Just as income may be discrete or continuous, ‘negative income’ too can be discrete or continuous. The relationship between spot and forward price of assets with storage cost is:

• for discrete: F₀ = (S₀ + U)_eT^T
• for continuous: F₀ = S_0e(r+u)^T

Here, U = current storage cost at time t₀ < T and u% p.a. is the continuously compounded storage cost, proportional to the price of the commodity, hence a negative yield. The basis of this result is that since storage cost makes the final price higher, it should be added to the spot price.

Determining Forward Price of Consumption Assets

Consumption assets are in the nature of raw materials that are used in production processes or energy sources. Examples of consumption assets are iron ore and crude oil. There is a distinct advantage in holding these assets in inventory over buying forward contracts. These advantages include the opportunity to profit from shortages and/or keeping the production process running. These advantages are referred to as convenience yield. The relationship between spot and forward price of consumption assets is:

• for those with discrete storage costs: F₀ = (S₀ + U) e ^(r-y)T
• for those with continuous storage costs: F₀ = S₀e ^(r+u-y)T

where y % p.a. is the convenience yield over the life of the contract. Convenience yield is beneficial to the holder of the asset but not to the forward contract owner. As such, it can be treated as a dividend yield. However, it must be noted that convenience yield is an intangible asset and is reflective of the market’s expectation of the availability of the commodity in future. There are greater chances of shortage if users have low inventories, which imply a higher convenience yield. In contrast, the convenience yield is low when inventories are high.

Cost of Carry or Net Cost of Holding

The net cost of holding (or carrying) an asset relative to the cost of holding the forward contract of that asset is reflected in the relationship between the spot and forward price. This indirectly means that all costs and advantages or benefits can be summarized as the cost of carry – indicated by the symbol C.

• for discrete: F₀  = (S₀ + U – I)e ^(r-y)T
• for continuous: F₀ = S₀ e^ct where c = r-q+u-y

Forward Price and Expected Future Spot Price

Expected future spot price of an asset is basically what the market expects the spot price to be in future. The primary question here for traders is whether the spot price in future is predicted by the current forward price or not.  A number of different hypotheses try to explain the relationship between the current forward price F₀ and the expected future spot price E (S_T).

It was argued by economists John Maynard Keynes and John Hicks that the natural hedgers are those who wish to sell a commodity sometime in the future. Going by their argument, hedgers will collectively hold short positions in the forward market. The counterparties in the contracts who hold long positions will be speculators. The only motive of hedgers is to reduce risk and will thus accept losing money on forward contracts. Speculators, on the other hand, are in it for the profit and will enter in a forward contract only if they expect to make a profit. This indirectly means that if speculators are holding long positions, the expected future spot price is greater than the forward price.

For the speculator, the expected payoff at maturity is:

E(S_T – K) = E(S_T) – K, where K is the delivery price at maturity

As a logical conclusion, if the speculators expect to profit,

E(S_T) – K > 0

E(S_T) > K

E(S_T) > F₀, as K = F₀ when they enter the contract

E(S_T) > F₀ in a market situation that is referred to as normal backwardation. Since forward/futures prices tend to meet with the spot price at maturity, the implication of normal backwardation is that futures prices for a specific maturity are increasing with time. In contrast, where E(S_T) < F0, the situation is referred to as contango, which implies that future prices for a specific maturity are falling with time.

Rational Pricing

If S_t is the spot price of an asset at time t, and r is the continuously compounded rate, then the forward price at a future time T must satisfy F_t,T = S_t e^r(T-t)

For proving this, let us suppose it is not the case: we then have two possible scenarios.

Scene 1: Cash and Carry Arbitrage

Supposing F_t,T > S_te^r(T-t) then the following trades can be executed at time t:

1. a loan can be raised by the trader from the bank to the amount S at the continuously compounded rate r
2. the trader buys one unit of stock for S_t
3. at the same time, the trader creates one position short forward contract costing – a short forward contract implies that the trader owes the stock at time T to the other party to the contract

The cost of the trades at the time totals zero.

On maturity of the forward contract that is time T  the trader can reverse the trades that were initiated at time . Mirroring the initial trades (1, 2 and 3 above):

1. the loan is paid back to the bank – the inflow to the trader is – S_te^r(T-t)
2. the short forward contract is settled by the trader by selling the stock for F_t,T the cash inflow to the trader is now F_t,T because the buyer receives S_T from the trader

Inflow from 1 and 2 is equal to F_t,T – S_te^r(T-t), which is by hypothesis, positive. This is the profit made from the arbitrage opportunity. Arbitrage is a kind of hedged investment with the intention of making a profit from slight differences in prices in two different markets, in this case, the spot and forward. In case the non-arbitrage condition remains, we have a contradiction. In market terminology this is known as cash and carry arbitrage because you “carry” (hold) the stock until the maturity of the forward contract.

Scene 2: Reverse Cash and Carry Arbitrage

In this case, let us suppose that Ft,T < S_te^r(T-t) then the trader can takes positions contrary to what has been done in scene 1. However, if by looking at the convenience yield, the trader sees that there is finite investor, then the reverse ‘cash and carry’ arbitrage may not be always available. For forward contracts such as this, everything depends upon the elasticity of demand for the underlying asset.

More on the Forward Pricing Formula

Assume that FV_T (X) is the time value of cash flows X at the maturity of the contract time T. The forward price is then arrived at by using the formula:

F_t,T = S_te^r(T-t) – FV_T (all cash flows over the life of the contract)

The cash flows, as discussed above, may either be by way of dividends or any other income received from holding the asset or a negative value such as costs of maintaining the asset.

An arbitrage opportunity for riskless profit exists if these price relationships do not hold.

It is deduced from this that the fact that a forward market is there, the expectations of the future price will be reflected in the spot prices today. A natural conclusion from this is that the forward price of non-perishable commodities, currency or securities is as much a forecaster of the future price as the spot price is. Whereas the relationship between forward and spot prices is determined by the interest rate, arbitrage does not work for perishable commodities.

The above forward pricing formula can also be expressed as:

F_t,T = (S_t – I_t)e^r(T-t)

Where I is the time t value of all cash flows over the duration of the contract

Why a Forward Contract Exists – Theories

Allaz and Vila (1993) suggest that in an imperfect competitive market, there is also a strategic reason for the existence of forward trading. Forward trading can be used even in an environment without uncertainty. This is because firms have Stackelberg incentives (in which the leader firm moves first and the following firms move in consecutively) to anticipate their production through forward contracts.