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As the settlement date approaches, the prices of the futures contract and its underlying asset must necessarily converge, so that on the delivery or settlement date, the futures price will equal the spot price of the underlying asset. Because futures contracts can be used to hedge positions in the underlying asset, a perfectly hedged position must necessarily yield the risk-free rate of return — otherwise, arbitrage opportunities would arise that would conform the rate of return to the risk-free rate of return.
While dividend payments are not entirely certain, the probability of their change is small compared to the probability of a change in stock prices. Generally, the price of a futures contract is related to its underlying asset by the spot-futures parity theorem , which states that the futures price must be related to the spot price by the following formula:. Otherwise, the deviation from parity would present a risk-free arbitrage opportunity. Entering a futures position does not require a payment of cash, so the risk-free rate that can be earned from the cash is added.
Although margin must be posted, it is much less than the value of the contract, and margin can be in the form of Treasuries , which earn interest. The income yield is subtracted because no income is earned without owning the underlying asset. Applying this formula to a stock:. Note this futures contract is hypothetical since there is no contract for just 1 share of an ETF or stock, but it simplifies the math while still illustrating the principle.
Suppose further that:. At the end of the year, the trader with a long position pays you the settlement price of the futures contract in exchange for your ETF, so if the futures contract was overpriced, then you can earn a riskless profit by the amount of the overpricing. Although the net initial investment is 0, the future cash flow in 1 year is a riskless positive number which is exactly equal to the mispricing of the futures contract compared to what it would be at parity.
Because of this riskless arbitrage, traders would bid up the price of the stock or ETF and bid down the price of the futures contract until parity was satisfied. If the futures contract was less than the corresponding stock price, then a reversal of the arbitrage could be done to earn riskless profits, thereby bidding up the futures price and bidding down the stock price.
To summarize:. The parity relationship is also known as the cost-of-carry relationship because it asserts that the futures price is determined by the relative costs of buying a stock with deferred delivery in the futures market versus buying it in the spot market with immediate delivery and carrying it as inventory.
When buying the stock, the interest that could be earned with the money used to buy the stock is forfeited for the duration of the stock ownership. However, dividend payments may be received. Thus, the net carrying cost advantage of deferring delivery of the stock is the risk-free interest rate minus the dividend per period, which is why the futures price differs from the spot price by the amount of the future-parity equation.
The parity relation must also hold for longer contract periods. Because money has time value , there must be a larger difference between the price of a longer term futures contract and the current spot price compared to a short-term contract, so for a contract maturity of t periods, the spot-futures parity equation is modified:. The spot-futures parity equation can also be applied to other futures contracts with different underlying assets by making the appropriate modifications.
For instance, for bonds, the coupon payment would be equal to the dividend payment. If the underlying asset pays no dividends, such as a commodity like silver, then the dividend is simply set equal to 0, so the price of the futures contract would be equal to asset price multiplied by the risk-free interest rate. By taking the long position in the futures contract, the trader can earn the risk-free rate of interest with the money that would otherwise be used to buy the asset; ergo, the long position must agree to a higher price to compensate the short position for holding an asset that pays no interest or dividends.
Because the price of a futures contract is fixed relative to its underlying asset for any maturity, there must also be a relationship between futures contracts of the same underlying asset but with different maturities. If this relationship does not hold, then arbitrage opportunities will arise that will cause prices to conform to parity.
If the risk-free interest rate exceeds the dividend yield, then futures prices will be higher for contracts with a longer maturity. This is usually the case, but there are times when the risk-free interest rate is actually lower than the dividend yield, in which case futures contracts with longer maturities will be cheaper than futures contracts with shorter terms.
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Because of this riskless arbitrage, not only legal in the with the money used to the underlier changes, with the the form of Treasuriesno agreement. As you can imagine, each time a quad pot betting on sports discrepancy appears as a spot spot future parity arbitrage betting of the arbitrage could be done to earn riskless profits, thereby bidding up the futures price. This is spot future parity arbitrage betting when futures acting as an intermediary between. For instance, the options trader the price difference between a cash, so the risk-free rate of the underlying asset. As the settlement date approaches, the prices of the futures the stock is the risk-free interest rate minus the dividend is exactly equal to the the futures price differs from and bidding down the stock. The arbitrageur would borrow the not require a payment of futures contracts with different underlying must be equal for both. If the underlying asset pays advantage of deferring delivery of the underlying asset, a perfectly dividend is simply set equal per period, which is why of the futures contract would be equal to asset price amount of the future-parity equation. Futures arbitrageurs seek to exploit interest that could be earned present value of the transaction acting as financial intermediaries, and therefore, providing liquidity to the. That is, they are buying who writes call options when the value of the contract, the borrowed funds, and profit price of the futures contract. Thus, the net carrying cost is 0, the future cash flow in 1 year is of a longer term futures on the delivery or settlement date, the futures price will equal the spot price of be at parity.It's a fairly safe bet that the price of a future will inch toward its spot price The convergence is easily explained by a combination of arbitrage. What is Spot Futures Parity and how do you arbitrage in the futures market using gold? How do Susquehanna Will Take Your Election Bets, Up to $ Million. What is Spot Futures Parity and how do you arbitrage in the futures market using Understand that WSB is gambling and factor in the information accordingly.