Exclusive Article on Exchange Traded Futures Contracts
Copyright BusinessEconomics.com
A financial futures contract is an agreement between two counterparties to exchange a specified amount of a financial security (bond, bill, currency or stock) at a fixed future date at a predetermined price. The contract specifies the amount of the asset to be traded, the Exchange on which the contract is traded, the delivery date and the process for delivery of the asset and funds
Financial futures contracts were first traded on the Chicago Mercantile Exchange (CME) in the United States back in 1972, and a decade later in 1982 London opened the London International Financial Futures Exchange (LIFFE) which in 2001 was merged with the Amsterdam, Paris and Belgium exchanges to create Euronext.LIFFE. Since then Euronext has also merged with the Lisbon Stock Exchange.
Table Turnover of futures contracts traded on international exchanges
(Number of contracts in millions)
Instruments 1990 1995 2000 2005 2008
Interest rate 219.1 561.0 781.2 2110.4 2582.9
Currency 29.7 99.6 43.6 143.0 433.8
Equity index 39.4 114.8 225.2 918.7 2467.9
All Markets 288.2 775.4 1050 3172.1 5485.6
Source: Bank for International Settlements
Exchange-traded derivative contracts versus the over-the-counter market
One of the major advantages of exchange-traded futures and options is that the exchange guarantees every contract, thus relieving the holder of the risk of default by the writer. This means that potential option buyers are relieved of the burden of evaluating the creditworthiness of the writer. To protect itself against the risk of default by the writer for futures and options contracts, exchanges impose substantial capital and stringent margin requirements on option-writers. Membership requirements and standards are high and members’ positions are constantly monitored by the futures exchange. In addition, a futures exchange will maintain a large clearing fund to meet unforeseen circumstances.
Major international banks have for many years marketed the advantages and flexibility of futures and options contracts to their multinational corporate clients. Since multinational corporations have varied demands, not all of which can be matched by exchanges, banks have found it worthwhile to offer tailor-made futures and options contracts to meet the specific needs of their clients. This tailor-made market which allows for negotiation of the terms of the contract between the buyer and seller of an option is known as the over-the-counter market (OTC). The OTC market is dominated by major banks and securities houses, and contrasts with the standardized contracts on offer at the futures and options exchanges. The major advantage of the OTC market is that a client’s specific needs with regard to the size, exercise price and expiration date of the contract can be met.
However, there are a number of disadvantages of the OTC market:
1) The relatively small number of buyers and sellers means that the contract could be mispriced;
2) The lack of standardization of the contracts in the OTC market means that there is only a severely limited secondary market for OTC contracts, that is, OTC instruments lack the liquidity that is a vital part of exchange-traded futures and options
3) Each party to a contract runs the risk of default on the part of the other party whereas exchange-traded contracts are guaranteed by the exchange. For this reason, only high quality financial institutions tend to be involved in the OTC market.
Open interest and reversing trades
Two important but linked terms that crop up in connection with futures trades are the open interest in a contract and the concept of reversing trades.
Open interest is the outstanding number of contracts obligated for delivery. Consider four traders A, B, C and D, none of whom has any current position in a futures contract. If trader A takes a long position in a new contract with trader B taking a short position, then the open interest rises by one contract. Similarly, if trader C takes a long position in a futures contract with trader D taking the short position, then open interest rises by a further one contract.
For most futures contracts, especially those that involve physical commodities such as gold, cotton and so on, the physical delivery of the commodity would be a cumbersome process. To avoid getting involved in the actual delivery process most traders enter into what is known as a reversing trade prior to the maturity of the contract. That is, they will liquidate their position at the clearing house so that they neither have to actually deliver or actually receive the underlying commodity. In our example, traders A and C are committed to buying the underlying commodity upon expiry, while traders B and D are committed to delivering it upon expiry. Trader A may not actually wish to receive the underlying commodity and trader D may not wish to actually deliver it, and hence at some date prior to expiry trader A and trader D will take out reversing trades to liquidate their positions. Trader A will take out a contract to sell the underlying commodity (at the then prevailing market price). As far as the clearing house is concerned, then A will have no net position in the futures market since it has an identical futures contract to both receive and deliver the underlying instrument. If trader A sold his contract to a new party E then the open interest would have been left unaffected by A’s trade. If, however, trader A had sold his position to trader D who was also undertaking a reversing trade, then open interest would have declined by one since both A and D have effectively negated their positions with the clearing house.
The Figure below shows the typical profile of open interest on futures contracts from the day trading in the contract is started (contract originates) to the time that the contract expires.
Figure Typical Open Interest Profile
Copyright BusinessEconomics.com
A financial futures contract is an agreement between two counterparties to exchange a specified amount of a financial security (bond, bill, currency or stock) at a fixed future date at a predetermined price. The contract specifies the amount of the asset to be traded, the Exchange on which the contract is traded, the delivery date and the process for delivery of the asset and funds
Financial futures contracts were first traded on the Chicago Mercantile Exchange (CME) in the United States back in 1972, and a decade later in 1982 London opened the London International Financial Futures Exchange (LIFFE) which in 2001 was merged with the Amsterdam, Paris and Belgium exchanges to create Euronext.LIFFE. Since then Euronext has also merged with the Lisbon Stock Exchange.
Table Turnover of futures contracts traded on international exchanges
(Number of contracts in millions)
Instruments 1990 1995 2000 2005 2008
Interest rate 219.1 561.0 781.2 2110.4 2582.9
Currency 29.7 99.6 43.6 143.0 433.8
Equity index 39.4 114.8 225.2 918.7 2467.9
All Markets 288.2 775.4 1050 3172.1 5485.6
Source: Bank for International Settlements
Exchange-traded derivative contracts versus the over-the-counter market
One of the major advantages of exchange-traded futures and options is that the exchange guarantees every contract, thus relieving the holder of the risk of default by the writer. This means that potential option buyers are relieved of the burden of evaluating the creditworthiness of the writer. To protect itself against the risk of default by the writer for futures and options contracts, exchanges impose substantial capital and stringent margin requirements on option-writers. Membership requirements and standards are high and members’ positions are constantly monitored by the futures exchange. In addition, a futures exchange will maintain a large clearing fund to meet unforeseen circumstances.
Major international banks have for many years marketed the advantages and flexibility of futures and options contracts to their multinational corporate clients. Since multinational corporations have varied demands, not all of which can be matched by exchanges, banks have found it worthwhile to offer tailor-made futures and options contracts to meet the specific needs of their clients. This tailor-made market which allows for negotiation of the terms of the contract between the buyer and seller of an option is known as the over-the-counter market (OTC). The OTC market is dominated by major banks and securities houses, and contrasts with the standardized contracts on offer at the futures and options exchanges. The major advantage of the OTC market is that a client’s specific needs with regard to the size, exercise price and expiration date of the contract can be met.
However, there are a number of disadvantages of the OTC market:
1) The relatively small number of buyers and sellers means that the contract could be mispriced;
2) The lack of standardization of the contracts in the OTC market means that there is only a severely limited secondary market for OTC contracts, that is, OTC instruments lack the liquidity that is a vital part of exchange-traded futures and options
3) Each party to a contract runs the risk of default on the part of the other party whereas exchange-traded contracts are guaranteed by the exchange. For this reason, only high quality financial institutions tend to be involved in the OTC market.
Open interest and reversing trades
Two important but linked terms that crop up in connection with futures trades are the open interest in a contract and the concept of reversing trades.
Open interest is the outstanding number of contracts obligated for delivery. Consider four traders A, B, C and D, none of whom has any current position in a futures contract. If trader A takes a long position in a new contract with trader B taking a short position, then the open interest rises by one contract. Similarly, if trader C takes a long position in a futures contract with trader D taking the short position, then open interest rises by a further one contract.
For most futures contracts, especially those that involve physical commodities such as gold, cotton and so on, the physical delivery of the commodity would be a cumbersome process. To avoid getting involved in the actual delivery process most traders enter into what is known as a reversing trade prior to the maturity of the contract. That is, they will liquidate their position at the clearing house so that they neither have to actually deliver or actually receive the underlying commodity. In our example, traders A and C are committed to buying the underlying commodity upon expiry, while traders B and D are committed to delivering it upon expiry. Trader A may not actually wish to receive the underlying commodity and trader D may not wish to actually deliver it, and hence at some date prior to expiry trader A and trader D will take out reversing trades to liquidate their positions. Trader A will take out a contract to sell the underlying commodity (at the then prevailing market price). As far as the clearing house is concerned, then A will have no net position in the futures market since it has an identical futures contract to both receive and deliver the underlying instrument. If trader A sold his contract to a new party E then the open interest would have been left unaffected by A’s trade. If, however, trader A had sold his position to trader D who was also undertaking a reversing trade, then open interest would have declined by one since both A and D have effectively negated their positions with the clearing house.
The Figure below shows the typical profile of open interest on futures contracts from the day trading in the contract is started (contract originates) to the time that the contract expires.
Figure Typical Open Interest Profile
Each contract starts with zero open interest and during the early days of the opening of a futures contract open interest in the contract slowly builds up as the number of new contracts increases. However, eventually open interest in the contract peaks. Thereafter, as the expiry date of the contract nears, the number of traders involved in trade reversals increases so that open interest rapidly declines until the expiry date when open interest falls to zero.
Example Using Stock Index Futures
Table S&P 500 Index Futures $250 per index point
Open Sett Price Change High Low Est Vol Open int
Sep 998 1005 +8 1008 995 12,372 375,374
Dec 991 1000 +8 1002 990 1,640 13,315
Source: Chicago Mercantile Exchange August 20 2009
(a) Previous futures settlement prices on August 19 were September 997, December 992
(b) The cash S&P 500 on close of business 20 August was 1007 up 9 points on the day. Hence the September futures settlements price is at a discount of 2 points and the December contract at a discount of 7 points.
(c) There is an S&P 500 mini futures contract that trades with much higher volumes and very similar prices but at only $50 a point.
If Mr Bull buys the December futures at 1000 and Ms Bear Sells the December futures at 1000.
Both now make an initial margin payment say 50 points each at $250 so that is $12,500 each initial margin.
The initial margin is a deposit against potential losses – it is not the cost of the contract which is rather low eg $25.
Table The profit and loss from speculation on S&P 500 Futures
Cash S&P 500 index 3rd Friday MR BULL MS BEAR
of December equals futures profit/loss profit/loss
price on expiration. long futures short futures
700 -$75,000 +$75,000
750 -$62,500 +$62,500
800 -$50,000 +$50,000
850 -$37,500 +$37,500
900 -$25,000 +$25,000
950 -$12,500 +$12,500
1000 $0 $0
1050 +$12,500 -$12,500
1100 +$25,000 -$25,000
1150 +$37,500 -$37,500
1200 +$50,000 -$50,000
1250 +$62,500 -$62,500
1300 +$75,000 -$75,000
Figure The Profit/Losses on a Forward/Futures Contract
Example Using Stock Index Futures
Table S&P 500 Index Futures $250 per index point
Open Sett Price Change High Low Est Vol Open int
Sep 998 1005 +8 1008 995 12,372 375,374
Dec 991 1000 +8 1002 990 1,640 13,315
Source: Chicago Mercantile Exchange August 20 2009
(a) Previous futures settlement prices on August 19 were September 997, December 992
(b) The cash S&P 500 on close of business 20 August was 1007 up 9 points on the day. Hence the September futures settlements price is at a discount of 2 points and the December contract at a discount of 7 points.
(c) There is an S&P 500 mini futures contract that trades with much higher volumes and very similar prices but at only $50 a point.
If Mr Bull buys the December futures at 1000 and Ms Bear Sells the December futures at 1000.
Both now make an initial margin payment say 50 points each at $250 so that is $12,500 each initial margin.
The initial margin is a deposit against potential losses – it is not the cost of the contract which is rather low eg $25.
Table The profit and loss from speculation on S&P 500 Futures
Cash S&P 500 index 3rd Friday MR BULL MS BEAR
of December equals futures profit/loss profit/loss
price on expiration. long futures short futures
700 -$75,000 +$75,000
750 -$62,500 +$62,500
800 -$50,000 +$50,000
850 -$37,500 +$37,500
900 -$25,000 +$25,000
950 -$12,500 +$12,500
1000 $0 $0
1050 +$12,500 -$12,500
1100 +$25,000 -$25,000
1150 +$37,500 -$37,500
1200 +$50,000 -$50,000
1250 +$62,500 -$62,500
1300 +$75,000 -$75,000
Figure The Profit/Losses on a Forward/Futures Contract
Open Interest Further Explanation
Imagine we get to November 20th and the S&P cash market is reading 804 while the December futures is reading 800.
Let pretend that November 20th
Estimated Volume Open interest
15,000 450,000
Note the futures discount is now only 4 point not 7 points – the discount/premium narrows as we get closer to expiration and futures=cash/spot price on expiration.
Mr Bull is very unhappy he is down 200 point @ $250 a point is minus -$50,000.
Ms Bear is very unhappy she is up 200 point @ $250 a point is a profit of $50,000.
Mr Bull might decide to close his position
He can close by selling at 800 (having previously bought at 1000) making a loss of $50,000.
If he sells to a new third party Mr Stag who is bullish and buys at 800 then there is one new contract traded that day but open interest is unaffected:
Estimated Volume Open interest
15,001 450,000
Mr Stag is now long the market and has replaced Mr Bull who is now out of the market. Ms Bear is short the market and Mr Stag the long position.
But say both Mr Bull and Ms Bear decide to close their positions at the same time !
He can close by selling at 800 (having previously bought at 1000) making a loss of $50,000.
She can close by buying at 800 (having previously sold at 1000) making a profit of $50,000.
There is one new contract traded that day but open interest declines by one unaffected:
Estimated Volume Open interest
15,001 449,999
Both Mr Bull and Ms Bear have closed their positions. Mr Bull at a loss of $50,000 and Ms Bear at a profit of $50,000.
Variation Margin Payments
Both Mr Bull and Ms Bear make initial margin payments of 50 points x $250 per point = $12,500.
If the futures moves from 1000 to 970 Mr Bull is losing -30 points at $250 = -$7,500 but there is no need to chase him since they have the initial margin of $12,500 which is more than sufficient to cover his losses.
However, once the futures falls to 950 then the exchange will chase Mr Bull for variation margin payments roughly equivalent to his losses, that is a further 50 points x $250 = $12,500. If the futures market falls to 900 then the exchange will seek variation payments equal to 100x$250 = $25,000.
The variation margin payments ensure that the winning party can close their position and be credited with funds
Also it means the losing party is marked to market on a daily basis so reducing the risk of them disappearing if their losses become unmanageable.
Failure to come up with variation margin payments will mean the exchange will close out the losing party’s position so as to minimise the risk of further losses accumulating.
Risk Management
The use of a stop loss:
Say you can afford to lose more than $12,500 –you can place a stop loss on the futures at 950. Let us suppose Mr Bull places a stop-loss at 950.
Cash S&P 500 index 3rd Friday MR BULL MS BEAR
of December equals futures profit/loss profit/loss
price on expiration. long futures short futures
700 Stopped +$75,000
750 Stopped +$62,500
800 Stopped +$50,000
850 Stopped +$37,500
900 Stopped +$25,000
Stop loss 950 -$12,500 +$12,500
1000 $0 $0
1050 +$12,500 -$12,500
1100 +$25,000 -$25,000
1150 +$37,500 -$37,500
1200 +$50,000 -$50,000
1250 +$62,500 -$62,500
1300 +$75,000 -$75,000
The stop loss means that Mr Bull’s loss will be limited to $12,500 since the exchange or his broker will automatically generate a sell order once the market hits 950. In this case it generates a sell order for Mr Bull.
There are some things to note with regard to the stop loss if the futures fall to 949 then Mr Bull will be stopped out but if the futures then rebound to 1100 Mr Bull will not have a profit of 100x $250 = $25,000 instead he will have a loss of $12,500 ! (if stopped out at 950).
Using Stock Index Futures to Hedge Risk
Consider the case of a Pension Fund Manager in August that has a $50 million pension fund mainly invested in S&P 500 shares, the fund manager fears the pension fund could be adversely affected by a fall in the S&P 500 index in the period up to December.
The value of the fund is tends to move very much in line with the S&P 500 index.
The current level of the S&P 500 is 1007
December S&P 500 futures index is reading 1000
The fund manager fearing that by December the S&P 500 index could be around the 800 level.
The fund manager fears that if the S&P 500 index falls from 1007 to 800 then the $50 million pension fund may be worth only:
800 x $50 million = $39,721,945
1007
NOTE – we use the cash index of 1007 for this part of the calculation.
Hence the fund could lose potentially $10,278,055 of its value.
In this instance the fund manager could protect his fund by selling December futures contracts at 1000 and then buy them back at 800 making a profit of 200 x $250 = $50,000 per contract sold.
To calculate the number of contracts that need to be sold to hedge against the risk of stock market fall we take the potential loss and divide it by the corresponding profit per contract, that is:
$10,278,055 = 206 contracts.
$50,000
In this instance, the fund manager needs to sell approximately 206 S&P 500 futures contracts.
If the S&P 500 index has fallen in December to 800, then the value of the shares held by the fund will be worth approximately $39,721,945 ($50 million x 800/1007).
However, the fund manager will be able to close the S&P 500 contract by buying 206 contracts at 800 (on expiry the futures and cash market index coincide) so gaining 206 x $50,000 = $10,300,000
The total portfolio is worth
$39,721,945 + $10,300,000 = $50,021,945
The fund will have been protected from a fall in the S&P 500 index.
We should note that in the above example the fund manager having taken a short position in the futures index is still entitled to dividends on the underlying fund in the interim, and hence the fund will be worth more than we have suggested.
Also, the fund manager is not necessarily achieving a perfect hedge by using stock-index futures, his portfolio may differ from the S&P 500 index and changes in the dividend-yield and interest rate relationship may mean that the forward index does not move exactly in line with the underlying cash market.
We should also note, of course, that if the S&P 500 index actually rises to say 1,200 by December then the fund manager will have a loss on the futures contracts sold:
206 x -$50,000 = -$10,300,000
Against this the value of the shares held by the pension fund will have risen to approximately
1200 x $50 million = $59,582,219
1007
Enabling virtually all the losses on the futures contract to be covered giving a net position of approximately $49,282,915.
Of course, the fund will not then have participated in the rise of the stockmarket but the hedging activity was designed to protect it against losses.
The Pricing of Stock Index Futures
In a normal futures contract, the futures price exceeds the spot price by the rate equivalent to the cost of financing a position in the cash market.
In the case of the futures index we have to look at the net financing cost. Holders of the underlying stock receive dividends which reduces the cost of financing a position in the underlying stocks.
Hence, it is possible for a futures stock index to be priced at a discount to the cash price when the expected dividend yield on holding the stock is less than the cost of financing the cash position as represented by the rate of interest on borrowing.
The appropriate arbitrage model for the pricing of the futures index is given by:
Imagine we get to November 20th and the S&P cash market is reading 804 while the December futures is reading 800.
Let pretend that November 20th
Estimated Volume Open interest
15,000 450,000
Note the futures discount is now only 4 point not 7 points – the discount/premium narrows as we get closer to expiration and futures=cash/spot price on expiration.
Mr Bull is very unhappy he is down 200 point @ $250 a point is minus -$50,000.
Ms Bear is very unhappy she is up 200 point @ $250 a point is a profit of $50,000.
Mr Bull might decide to close his position
He can close by selling at 800 (having previously bought at 1000) making a loss of $50,000.
If he sells to a new third party Mr Stag who is bullish and buys at 800 then there is one new contract traded that day but open interest is unaffected:
Estimated Volume Open interest
15,001 450,000
Mr Stag is now long the market and has replaced Mr Bull who is now out of the market. Ms Bear is short the market and Mr Stag the long position.
But say both Mr Bull and Ms Bear decide to close their positions at the same time !
He can close by selling at 800 (having previously bought at 1000) making a loss of $50,000.
She can close by buying at 800 (having previously sold at 1000) making a profit of $50,000.
There is one new contract traded that day but open interest declines by one unaffected:
Estimated Volume Open interest
15,001 449,999
Both Mr Bull and Ms Bear have closed their positions. Mr Bull at a loss of $50,000 and Ms Bear at a profit of $50,000.
Variation Margin Payments
Both Mr Bull and Ms Bear make initial margin payments of 50 points x $250 per point = $12,500.
If the futures moves from 1000 to 970 Mr Bull is losing -30 points at $250 = -$7,500 but there is no need to chase him since they have the initial margin of $12,500 which is more than sufficient to cover his losses.
However, once the futures falls to 950 then the exchange will chase Mr Bull for variation margin payments roughly equivalent to his losses, that is a further 50 points x $250 = $12,500. If the futures market falls to 900 then the exchange will seek variation payments equal to 100x$250 = $25,000.
The variation margin payments ensure that the winning party can close their position and be credited with funds
Also it means the losing party is marked to market on a daily basis so reducing the risk of them disappearing if their losses become unmanageable.
Failure to come up with variation margin payments will mean the exchange will close out the losing party’s position so as to minimise the risk of further losses accumulating.
Risk Management
The use of a stop loss:
Say you can afford to lose more than $12,500 –you can place a stop loss on the futures at 950. Let us suppose Mr Bull places a stop-loss at 950.
Cash S&P 500 index 3rd Friday MR BULL MS BEAR
of December equals futures profit/loss profit/loss
price on expiration. long futures short futures
700 Stopped +$75,000
750 Stopped +$62,500
800 Stopped +$50,000
850 Stopped +$37,500
900 Stopped +$25,000
Stop loss 950 -$12,500 +$12,500
1000 $0 $0
1050 +$12,500 -$12,500
1100 +$25,000 -$25,000
1150 +$37,500 -$37,500
1200 +$50,000 -$50,000
1250 +$62,500 -$62,500
1300 +$75,000 -$75,000
The stop loss means that Mr Bull’s loss will be limited to $12,500 since the exchange or his broker will automatically generate a sell order once the market hits 950. In this case it generates a sell order for Mr Bull.
There are some things to note with regard to the stop loss if the futures fall to 949 then Mr Bull will be stopped out but if the futures then rebound to 1100 Mr Bull will not have a profit of 100x $250 = $25,000 instead he will have a loss of $12,500 ! (if stopped out at 950).
Using Stock Index Futures to Hedge Risk
Consider the case of a Pension Fund Manager in August that has a $50 million pension fund mainly invested in S&P 500 shares, the fund manager fears the pension fund could be adversely affected by a fall in the S&P 500 index in the period up to December.
The value of the fund is tends to move very much in line with the S&P 500 index.
The current level of the S&P 500 is 1007
December S&P 500 futures index is reading 1000
The fund manager fearing that by December the S&P 500 index could be around the 800 level.
The fund manager fears that if the S&P 500 index falls from 1007 to 800 then the $50 million pension fund may be worth only:
800 x $50 million = $39,721,945
1007
NOTE – we use the cash index of 1007 for this part of the calculation.
Hence the fund could lose potentially $10,278,055 of its value.
In this instance the fund manager could protect his fund by selling December futures contracts at 1000 and then buy them back at 800 making a profit of 200 x $250 = $50,000 per contract sold.
To calculate the number of contracts that need to be sold to hedge against the risk of stock market fall we take the potential loss and divide it by the corresponding profit per contract, that is:
$10,278,055 = 206 contracts.
$50,000
In this instance, the fund manager needs to sell approximately 206 S&P 500 futures contracts.
If the S&P 500 index has fallen in December to 800, then the value of the shares held by the fund will be worth approximately $39,721,945 ($50 million x 800/1007).
However, the fund manager will be able to close the S&P 500 contract by buying 206 contracts at 800 (on expiry the futures and cash market index coincide) so gaining 206 x $50,000 = $10,300,000
The total portfolio is worth
$39,721,945 + $10,300,000 = $50,021,945
The fund will have been protected from a fall in the S&P 500 index.
We should note that in the above example the fund manager having taken a short position in the futures index is still entitled to dividends on the underlying fund in the interim, and hence the fund will be worth more than we have suggested.
Also, the fund manager is not necessarily achieving a perfect hedge by using stock-index futures, his portfolio may differ from the S&P 500 index and changes in the dividend-yield and interest rate relationship may mean that the forward index does not move exactly in line with the underlying cash market.
We should also note, of course, that if the S&P 500 index actually rises to say 1,200 by December then the fund manager will have a loss on the futures contracts sold:
206 x -$50,000 = -$10,300,000
Against this the value of the shares held by the pension fund will have risen to approximately
1200 x $50 million = $59,582,219
1007
Enabling virtually all the losses on the futures contract to be covered giving a net position of approximately $49,282,915.
Of course, the fund will not then have participated in the rise of the stockmarket but the hedging activity was designed to protect it against losses.
The Pricing of Stock Index Futures
In a normal futures contract, the futures price exceeds the spot price by the rate equivalent to the cost of financing a position in the cash market.
In the case of the futures index we have to look at the net financing cost. Holders of the underlying stock receive dividends which reduces the cost of financing a position in the underlying stocks.
Hence, it is possible for a futures stock index to be priced at a discount to the cash price when the expected dividend yield on holding the stock is less than the cost of financing the cash position as represented by the rate of interest on borrowing.
The appropriate arbitrage model for the pricing of the futures index is given by:
The equation indicates that when the annualized cost of finance exceeds the expected dividend yield then the futures index price will exceed the cash index, that is it will be at a premium to the cash index.
When the annualized cost of finance is less than the expected dividend yield then the futures index price will be less than the cash index, that is it will be at a discount to the cash index.
Since interest rates are usually higher than dividend yields, the futures index usually trades at a premium to the spot index.
Another point to note is that as the time to maturity approaches, that is T – t reduces, then the difference between the cash price and the futures price reduces (assuming the interest rate and dividend yield is unchanged) and on the day of expiry the futures price will coincide with the cash price.
Numerical example of Pricing of Futures
On August 20, 2009 the S&P 500 cash Index is 1007, the borrowing cost of funds based on the 3 month Treasury bill rate is approximately 0.2%. The expected annualized dividend rate yield is approximately 2.5% based upon the historical dividend yield and the carrying period (T-t ) is 120 days
When the annualized cost of finance is less than the expected dividend yield then the futures index price will be less than the cash index, that is it will be at a discount to the cash index.
Since interest rates are usually higher than dividend yields, the futures index usually trades at a premium to the spot index.
Another point to note is that as the time to maturity approaches, that is T – t reduces, then the difference between the cash price and the futures price reduces (assuming the interest rate and dividend yield is unchanged) and on the day of expiry the futures price will coincide with the cash price.
Numerical example of Pricing of Futures
On August 20, 2009 the S&P 500 cash Index is 1007, the borrowing cost of funds based on the 3 month Treasury bill rate is approximately 0.2%. The expected annualized dividend rate yield is approximately 2.5% based upon the historical dividend yield and the carrying period (T-t ) is 120 days
The actual December futures price of 1000 very close to the results we
would expect. In the above example, the stock index futures is below the cash
index because the assumed rate of interest is greater than the dividend yield.
Normally interest rates are higher than the dividend yield so stock index futures are normally higher than the related cash index.
(The extraordinarily low US interest rate of only 0.2% in this example being because of the monetary easing by the Federal Reserve in response to the credit crunch).
Copyright BusinessEconomics.com
Normally interest rates are higher than the dividend yield so stock index futures are normally higher than the related cash index.
(The extraordinarily low US interest rate of only 0.2% in this example being because of the monetary easing by the Federal Reserve in response to the credit crunch).
Copyright BusinessEconomics.com
