Subject 2. Forward and futures prices

In assigning a forward price, we set the price such that the value of the contract is zero at the start. During the life of the forward contract, the value will fluctuate as market conditions change. The original contract price, however, remains the same.

Unlike forward contract prices, however, futures prices fluctuate in an open and competitive market. The marking-to-market process results in each futures contract being terminated every day and reinitiated.

If we ignore the credit risk issue (futures contracts are essentially free of default risk as they are settled daily but forward contracts are subject to default risk), we should conclude that:

  • The price of a futures contract will equal the price of an otherwise equivalent forward contract one day prior to expiration. At this time point both the futures and forward contracts have one day to go. At expiration they will both settle. Therefore these contracts are the same. At any other time prior to expiration, futures and forward prices can be the same or different.

  • The price of a futures contract will equal the price of an otherwise equivalent forward contract if interest rates are known or constant. Under this condition, any effect of the addition or subtraction of funds from the marking-to-market process can be shown to be neutral.

  • The price of a futures contract will equal the price of an otherwise equivalent forward contract if interest rates are uncorrelated with future prices.

    • If interest rates are positively correlated with future prices, futures will carry higher prices than forwards.

      • Traders with long positions will prefer futures over forwards, because futures will generate gains when interest rates are going up (and thus future prices are going up as they are positively correlated), and traders can invest these gains for higher returns.
      • Traders will incur losses when interest rates are going down and can borrow to cover those losses at lower rates.
      • Gold futures are good examples in this case, as gold futures prices and interest rates would tend to be positively correlated.

    • If futures prices are negatively correlated with interest rates, traders will prefer not to mark to market, so forward contracts will carry higher prices. Interest rate futures are good examples in this case: interest rate and fixed-income security price move in opposite directions.

If we simplify our assumptions to ignore the effects of marketing a futures contract to market, we can conclude that the value of a futures contract at expiration, before marking to market, is

vT(T) = fT(T) - f0(T) = ST - f0(T)

Practice Question 1

The price of a futures contract will equal the price of an otherwise equivalent forward contract if:

A. interest rates are uncorrelated with future prices.
B. interest rates are positively correlated with future prices.
C. interest rates are negatively correlated with future prices.
Correct Answer: A

Practice Question 2

The price of a futures contract will equal the price of an otherwise equivalent forward contract if it is one day prior to expiration. What about the contract creation day and the contract expiration day?
Correct Answer: Their prices should equal as well.

Practice Question 3

If futures prices are positively correlated with interest rates, which derivatives will be more desirable to holders of long positions?

A. forward contracts.
B. futures contracts.
C. none.
Correct Answer: B

Rising prices lead to futures profits, which can be reinvested in periods of rising interest rates. Losses occur in periods of falling interest rates.

Practice Question 4

Other things equal, futures will carry lower prices than forwards when

A. interest rates are uncorrelated with future prices.
B. interest rates are positively correlated with future prices.
C. interest rates are negatively correlated with future prices.
Correct Answer: C

If interest rates are positively correlated with future prices, futures will carry higher prices than forwards. For example, futures will generate gains when interest rates are going up (and thus future prices are going up as they are positively correlated), and traders with long positions can invest these gains for higher returns.

Practice Question 5

If interest rates are known to be going up by 0.25% each month for the next 10 months, the price of a 6-month futures contract will be ______ the price of an otherwise equivalent forward contract.

A. lower than.
B. equal to.
C. higher than.
Correct Answer: B

The price of a futures contract will equal the price of an otherwise equivalent forward contract if interest rates are known or constant. Under this condition, any effect of the addition or subtraction of funds from the marking-to-market process can be shown to be neutral. In this case we know the interest rates, although they are not constant.

Practice Question 6

The price of a futures contract will equal the price of an otherwise equivalent forward contract if:

I. It is one day prior to expiration.
II. It is the expiration day.
III. It is the contract creation day.

A. I and II
B. I, II and III
C. I and III
Correct Answer: B

The price of a futures contract will equal the price of an otherwise equivalent forward contract one day prior to expiration. At this time point both the futures and forward contracts have one day to go. At expiration they will both settle. Therefore these contracts are the same. At the contract initiation date the value of a futures and forward contracts are both 0, and their prices should equal to each other.