Reading 38 : DETERMINATION OF FORWARD AND FUTURES PRICES

Investment and Consumption Assets

An investment asset is an asset that is held for the purpose of investing. A consumption asset is an asset that is held for the purpose of consumption.

Short-Selling and Short Squeeze

Short sales are orders to sell securities that the seller does not own. A short squeeze results if the broker runs out of securities to borrow.

Forward and Futures Contracts

        Forward and futures contracts are similar because they are both future obligations to transact an asset on some future date. Forward contracts do not trade on an exchange, are not standardized, and do not normally close out prior to expiration.
        The relationship between forward and spot prices is as follows:
                 F = S₀e^rT

        The futures price or cost-of-carry model is easily accommodated for interim cash flows from the underlying asset. If the underlying asset pays a known amount of cash, I, over the life of the forward contract, a simple adjustment is made to the cost-of-carry model:
                 F = (S₀ − I)e^rT
         When the underlying asset pays a dividend, q, we assume that the dividend is paid continuously:
                 F = S0e^{(r – q)T}

Cost-Of-Carry Model

        The cost-of-carry model is used to price forward and futures contracts. It states that the total cost of carrying the underlying asset to expiration must be the futures price. Any other price results in arbitrage.

Forward Prices vs. Futures Prices

        When interest rates are known over the life of a contract, forward and futures prices can be shown to be the same. Various relationships can be derived, depending on the assumptions made between the value of the underlying and the level of change in interest rates.

Stock Index Futures

        If the futures price is greater than the cost of carry, an arbitrage profit is generated by shorting the futures contracts and going long stocks underlying the index at the spot price. Conversely, if the futures price is lower than the cost of carry, an arbitrage profit is generated by shorting stocks underlying the index and going long the futures contracts.

Currency Futures

        Interest rate parity states that the forward exchange rate, F [measured in domestic currency (DC) per unit of foreign currency (FC)], must be related to the spot exchange rate, S, and to the interest rate differential between the domestic and the foreign country:
         F=S₀exp[(r_DC−r_FC)T]

Commodity Futures

        Consumption assets have actual storage costs (known as carrying costs) associated with them. If there is a benefit to owning the underlying consumable asset compared to owning the futures, the futures price will incorporate a convenience yield.

        Futures price with storage costs, u: F = S₀e^{(r + u)T}
        Futures price with convenience yield, y: F = S₀e^{(r + u – y)T}

Delivery Options in the Futures Market

        Physical assets, such as gold or corn, may offer a choice of delivery locations to the short. These options can be of significant value to the holder of the short position in a futures contract. Futures contracts are typically “offset” by buying or selling a contract before the delivery date. Only a small percentage of contracts result in physical delivery.

Futures Prices And Expected Future Spot Prices

        The expectations model states that the current futures price for delivery at time T is equal to the expected spot price at time T. This model acts to keep the current futures price in line with the expected spot rate at that time.

Contango and Backwardation

Contango is the situation in which the futures price is above the current spot price. Backwardation is the opposite relationship.