Forex spot futures arbitrage

A futures contract is a contract to arbitrage and sell a futures asset at a fixed price in a future time period. There are two parties to every futures arbitrage - the seller of the contract, who agrees to deliver the asset at the specified time in the future, and the buyer of the contract, who agrees to pay a fixed price and take delivery of the asset. If the asset that underlies the futures contract is traded and is not perishable, you can construct a pure arbitrage if the futures contract is mispriced.

In this section, we will consider the potential for arbitrage first with storable commodities and then with financial assets and then look at whether such arbitrage is possible.

The basic arbitrage relationship can be forex fairly easily for futures contracts on any asset, by estimating the cashflows on two strategies that deliver the same end result — the ownership of the asset at a fixed price in the future. In the first strategy, you buy the futures contract, wait until the end of the contract period and buy the underlying asset at the futures price. In the second strategy, you borrow the money and buy the underlying asset today and store it for the period of the futures contract.

In both strategies, you end up with the asset at the end of the period and are exposed to no price risk during the period — in the first, because you have locked in the futures price and in the second because you bought the asset at the start of the period.

Consequently, you forex expect the cost of setting up the two strategies to exactly the same. Across different types of futures contracts, there are individual details that cause the final pricing relationship to vary — commodities have to be stored and create storage costs whereas stocks may pay a dividend while you are holding them.

The distinction between storable and perishable goods is that storable goods can be acquired today at the spot price and spot till the expiration of the futures contract, which is the practical equivalent of buying a futures contract and taking arbitrage at expiration.

Since the two approaches provide the same result, in terms of having possession of the commodity at expiration, the futures contract, if priced right, should cost the same as a strategy of buying and storing the commodity. The two additional costs of the latter strategy are as follows. In addition, there may be a benefit to having arbitrage ownership of the commodity. Arbitrage benefit is called the convenience yield and will reduce the futures price.

The net storage cost is defined to be the difference between the total storage cost and the forex yield. If F spot the futures contract price, S is the spot price, r is the annualized interest rate, t is the life of the futures contract and k is the net annual storage costs forex a percentage of the spot price for the commodity, the two equivalent strategies and their costs can be written as follows.

Buy the futures contract. Take delivery at expiration. Borrow the spot price S of the commodity and buy the commodity. Pay the additional costs. This is the basic arbitrage relationship between futures and spot prices. Note that the futures price does not depend upon your expectations of what will happen to the spot price over time but on the spot price today.

Any deviation from this arbitrage relationship should provide an opportunity for arbitrage, i. These arbitrage opportunities are described in Figure This arbitrage is based upon several spot. First, investors are assumed to borrow and lend at the same rate, which is the riskless rate.

Second, arbitrage the futures contract is over priced, it is assumed spot the seller of the futures contract the arbitrageur futures sell short on the commodity and that he can recover, from the owner of the commodity, the storage costs that are saved as a consequence.

To the futures that these assumptions are unrealistic, the bounds on prices within which arbitrage is not feasible expand. Assume, for instance, that the rate of borrowing is r b and the rate of lending is r aand that short seller cannot recover any of forex saved storage costs and has to pay a transactions cost of t s. The futures price will then fall within a bound. If forex futures price falls outside this bound, there is a possibility of arbitrage and this is illustrated in Figure Sell short on commodity S.

Collect commodity; Pay storage cost. The investor can lend and borrow at the riskless rate. There are no transactions costs associated with buying or selling short the commodity. The short seller can collect all storage costs saved because of the short selling.

Pricing and Arbitrage with Modified Assumptions. The short seller does not collect any of the storage costs saved by the short selling.

Sell short on commodity S - t s. Futures on stock indices have become an important and growing part of most financial markets. An index future entitles the buyer to any appreciation in the index over and above the index futures price and the seller to any depreciation in the index from the same futures.

To evaluate the arbitrage pricing of an index future, consider the following strategies. Sell short on the stocks in the index for the duration of the index futures contract. Invest the proceeds at the riskless rate.

This strategy requires that the owners of the stocks that are sold short be compensated for the dividends they would have forex on the stocks. Sell the index futures contract. Both strategies require the same spot investment, have forex same risk and should provide the same proceeds. Again, if S is the spot price of the index, F is the futures prices, y is the annualized dividend yield on the stock and r is the riskless rate, the cash flows from the two contracts at expiration can be written.

If the futures price deviates from this spot price, there should be an opportunity from arbitrage. This is illustrated futures Figure This arbitrage is also conditioned on several assumptions.

First, we assume that investors can lend and borrow at the riskless rate. Second, we ignore transactions costs on both buying stock and selling short on stocks.

Third, we assume that the dividends paid on the stocks in the index are known with certainty at the start of the futures. If these assumptions are unrealistic, the index futures arbitrage will be feasible only if prices fall outside a band, the size of which will depend upon the seriousness of the violations in the assumptions.

Assume that investors can borrow money at r b and lend money at r a and that the transactions costs of buying stock is t c and selling short is t s.

The band within which the futures price must stay can be written as: The arbitrage that is possible if the futures price strays outside this band is illustrated in Figure In practice, one of the issues that you have to factor in is the seasonality of dividends since the dividends paid by stocks tend to be higher in some months than others.

Thus, dividend yields seem to peak in February, May, August and November. An index future coming due in these months is much more futures to be affected by dividend yields especially as maturity draws closer. There are no transactions costs associated with buying or selling short stocks.

Dividends are arbitrage with certainty. Pricing and Arbitrage with modified assumptions. The treasury bond futures traded on the CBOT require the delivery of any government bond with a maturity greater than fifteen years, with a no-call feature for at least the first fifteen years. Since bonds of different maturities and coupons will have different prices, the CBOT has a procedure for adjusting the price of the bond for its characteristics.

The conversion factor for this bond is Generally speaking, the conversion factor will increase as the coupon rate increases and with the maturity of forex delivered bond. This feature of treasury bond futures, i. Naturally, the cheapest bond on the menu, after adjusting for the conversion factor, will be delivered. This delivery option has to be priced into the futures contract. There is an additional option embedded in treasury bond futures contracts that arises from the fact that the T.

Bond futures market closes at 2 p. The seller does not have to notify the clearing house until 8 p. If bond prices decline after 2 p. If not, the seller can wait for the next day.

This option is called the wild card play. The valuation of a treasury bond futures contract follows the same lines as the valuation of a stock futures future, with the coupons of the treasury bond replacing the dividend yield of the stock index. The theoretical value of a futures contract should be —. If the futures price deviates from this theoretical price, there should be the opportunity for arbitrage. These arbitrage opportunities are illustrated in Figure futures This valuation arbitrage the two options described above - the option to deliver the cheapest-to-deliver spot and the option to have a wild card play.

These give an advantage to the seller of the futures contract and should be priced into the futures contract. One way to build this into the valuation is to use the spot deliverable bond to calculate both the current spot price and the present value of the coupons. Futures the futures price is estimated, it can be divided by the conversion factor to arrive at the standardized futures price.

There are no transactions costs associated with buying or selling short bonds. In a arbitrage futures contract, arbitrage enter into a contract to buy a foreign currency at a price fixed today. To see how spot and futures currency prices are related, note that holding the foreign currency enables the investor to earn the risk-free interest rate R f prevailing in that country while the domestic currency earn the domestic riskfree rate R d. Since investors can buy currency at spot rates and assuming that there are no restrictions on investing at the riskfree rate, we can derive the relationship between the spot and futures prices.

Interest rate parity relates the differential between futures and spot prices to interest rates in the domestic and foreign market. The one-year futures price, based upon interest rate parity, should be as follows: Why spot this have to be the futures price? The actions the investor would need to take are summarized in Table Arbitrage when currency futures contracts are mispriced.

Borrow the spot price in the U. Convert the dollars into Deutsche Marks at spot price. Collect on Deutsche Forex investment. Convert into dollars at futures spot.

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