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At any given time during the life of a forward or futures contract, there is likely to be a difference between the quoted futures price

At any given time during the life of a forward or futures contract, there is likely to be a difference between the quoted futures price and the spot price of the underlying asset. For example:

In the lecture example, the spot price of gold was USD 1550 per ounce, but the forward price for Jun-2020 delivery was USD 1600.

In Question 4, the spot exchange rate was AUD 1.00 = CHF 0.74, but the forward rate for delivery in 6 months was AUD 1.00 = CHF 0.7450.

However, as a forward/futures contract approaches the delivery date, the quoted delivery price for the contract converges to the spot price of the underlying asset.

For example, consider a forward contract to deliver 100 ounces of gold on 30 June. The quoted delivery price is $1600/ounce. The current (spot) price of gold is probably something different to $1600. As time passes between now and June, the quoted forward price for the delivery of gold at the end of June will change.1 However, by the expiry day, the quoted forward price for October delivery of gold must equal the spot price of the underlying gold.

Why does this happen? To answer the question, consider the following scenario. Assume that just one hour before the expiry of the June forward contract, the spot price of gold is $1580/ounce. However, assume that the quoted delivery price on the forward contract is $1600. What would an arbitrageur do in these circumstances?

What would the arbitrageur do if the June-delivery gold forward contract was quoted at $1560 just hours before expiry?

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