- Examples of Futures Contracts
- An Example of Currency Futures
- An Example of Interest Futures
- An Example of Futures for Government Bonds
- An Example of Stock Index Futures
- An Example of Volatility Futures
Examples of Futures Contracts
The following section provides several examples of futures for better orientation on how this instrument is used in practice.
An Example of Currency Futures
We are exporters of American sporting goods. It´s summer but we know that in December we will receive one million euro. In order to plan our future business, we’d like to ensure an exchange rate with which we’ll exchange euros for dollars. At the moment, one contract for 125,000 euro due in December has a value of 150,000 USD. This corresponds to an exchange rate of 1:1.2. We would receive 1,200,000 USD for our million euros. We are satisfied with this exchange rate and we will sell eight contracts (1,000,000/125,000). We are now in a ‘short’ position, which means we are committed to sell one million euro in three months. We deposit the initial margin to our broker’s (bank) account, in the minimal amount of 32,400 USD (8*4,050).
In three months, one euro costs 1.3 dollars. In this case, we lost 100,000 USD on our contracts, because if we hadn’t bought them, we would receive 1,300,000 USD at the spot/cash market instead of the agreed 1,200,000 USD. On the other hand, for three months we were sure that we would receive exactly one million two hundred thousand dollars for our million euros. Technically the process means we must deposit an additional 100,000 USD over the course of the contract to our broker’s account to top up our margin. On the day our position closes (contract expiration), we sell our million euro on the spot market for the 1,300,000 USD. We lost 100,000 USD and received 1,200,000 USD for our million euros.
The following table illustrates a case where the exchange rate remained the same (Scenario 2) or dropped to 1.1 USD per euro (Scenario 3).
|A||Value of 8 contracts at in the summer||1 200 000||1 200 000||1 200 000|
|B||Value of 8 contracts on the expiration date||1 300 000||1 200 000||1 100 000|
|C||Profit/loss from the 8 contracts, position short (A-B)||-100 000||0||100 000|
|D||The price per million euro on the current market in December||1 300 000||1 200 000||1 100 000|
|Resulting price (D+C)||1 200 000||1 200 000||1 200 000|
An Example of Interest Futures
The Specifics of Interest Futures
- Interest futures are always issued for a three-month term. Therefore they usually expire after a quarter. A month-long expiration only exists for the closest upcoming months.In interest futures for the EURIBOR (Euro Interbank Offered Rate) it is possible to trade on 28 different expirations. The first six are based on months (if it’s the beginning of January, the first month will be February, the last June), the others expire by quarter, always in March, June, August and December. The last of them therefore expire in December, after six years.
- For example, if we wanted to ensure a five-year loan with a variable tied to a LIBOR or EURIBOR interest rate, we must arrange twenty quarterly futures in a row. Each quarter we would collect the profit (or loss) from one of them to compensate the fluctuation of the interest rate.
- If we had contracted a loan for five years, with an interest rate that will be stipulated in three months for the entire period of the loan, dependent on one of the most commonly used interest rates, we might again use futures. Just as in the previous circumstance, we would purchase 20 quarterly contracts. On the date establishing the interest rate, the profit/loss from their sale would balance out the change of the interest rate that occurred over the course of those three months prior to establishing the rate.
It’s August and we know that in September we will borrow a million euro for three months. We now want to know the value of the variable interest rate. The bank establishes 1% plus the EURIBOR rate on the date of signing the loan, let’s say September 17th. In order to fix the interest rate, we will sell one contract to EURIBOR in the nominal value of one million euro (as if committing that in September we will borrow one million euro for three months with the given interest rate). The price of the contract is 99, which corresponds to the annual interest rate of 1% (this means that the market expects that in three months the given EURIBOR rate will be 1%). We deposit a margin of 800 € to the exchange account and wait until September 17th.
On the expiration date, the price of the futures dropped to 98. This corresponds to an interest rate of 2% (100–98). Therefore we made money on the futures and received 2,500 € to our exchange account (the price dropped by 100 base points, hundreds of percent – we received 25 euro for each, because we were in the short position). The bank loans us a million euro at 3% (1% + the current EURIBOR rate in the amount of 2%). Therefore we will pay a total of 7,500 € in interest (30,000/4 – our loan is only for a quarter of the year). But the futures contract earned us 2,500 €, so the actual costs of the interest rate will be five thousand. This corresponds to the 2% interest rate from the bank (that is the EURIBOR interest rate in the amount of 1%, which is precisely the rate we were securing in September).
The table with calculations for situations when the value of the futures remains the same (Scenario 2) and in case it drops (Scenario 3).
|A||Price of the contract in August||99||99||99|
|- Corresponding to the annual EURIBOR interest rate in the amount of||1%||1%||1%|
|B||Price of the contract on the day if expiration, September 17||98||99||100|
|- Corresponding to the annual EURIBOR interest rate in the amount of||2%||1%||0%|
|C||Profit/loss from the contract, position short (in €)||2 500||0||- 2 500|
|An annual interest rate for which the bank loans me (EURIBOR + 1 %)||3%||2%||1%|
|D||I will pay to the bank (in €)||7 500||5 000||2 500|
|Overall costs of the interest rate (D-C) (in €)||2 500||0||-2 500|
An Example of Futures for Government Bonds
We are the administrators of an investment fund that buys German government bonds. We know that in approximately a month (let’s say in September), a new client will appear who will deposit 10 million euro into the fund. We decide that for this amount we will buy a selection of government bonds with an expiration date around 2 years. We want to ensure their price by purchasing futures contracts (Schatz). The value of one of them with delivery in September is now 98,000 €. We decide to purchase 102 contracts in the total value of 9,996,000 euro. We deposit the margin to the exchange account in the amount of 102*360 €.
We are now in the long position and in September are supposed to receive 102 Schatz bonds in the value of 98,000 € each. Because our counterparty (in the short position) can supply us with any bond with a maturity period of 1.75–2.25 year, we decide that we would rather close our position through an opposite operation - to sell. In the decisive moment, the value of one Schatz contract is 99,000 euro. Therefore, we made a thousand euro on each, totaling 102,000 euro. In practice, this means that upon closing the position, we didn’t ‘get anything extra’. The thousands we made were already deposited in our margin account by the exchange.
Right now, one Schatz costs 99,000 € on the market. However, it seems that for the 10 million we received from our new investor we can no longer buy 102 bonds, as we planned (we are missing 98,000). However, this is deceptive. We made 102,000 on the futures that cover the increased costs (that actually leaves us with 4,000 extra). We can purchase precisely as many Schatz bonds as we planned. We will also be able to buy the selection we want.
The following table illustrates a situation where the value of futures remained the same (Scenario 2) and dropped (Scenario 3).
|A||The value of the contract in August||98||98||98|
|B||The value of the contract upon closing the position||99||98||97|
|C||Profit/loss from 102 contracts, position long (A-B*102)||102||0||-102|
|D||Purchase price of 102 bonds in September||10 098||9 996||9 894|
|Resulting price for 102 contracts (D-C)||9 996||9 996||9 996|
An Example of Stock Index Futures
Imagine that we hold shares of European companies that are included in the Euro Stoxx 50 index and are concerned that their price will drop. Unfortunately, we can’t immediately sell them. A possible solution is the sale of futures for the Euro Stoxx 50 stock index (version of use A). Or, we can use this type of contract for investing into European companies (European economy), if we don’t have enough funds to buy the portfolio that would specifically correspond to the composition of the index. In the case of futures, it’s enough to initially deposit the margin (version of use B). Additionally, unlike classic shares, futures are more liquid– it’s easier to buy and sell them. Another option is to use futures contracts for speculation (version of use C).
Version of Use A
We can secure ourselves against the drop of European shares by selling the respective contracts (we will be in a short position). We want to secure the value of the portfolio to a maximum 100,000 euro. The value of the futures is calculated as the price of the index multiplied by 10 euro. It’s August and the value of the futures with expirations in December is 25,000 € (this corresponds to the value of the Euro Stoxx 50 index in the amount of 2,500 points). Therefore, we sell four contracts. After opening the position, we deposit the margin in the amount of 1,842 euro per contract.
Let’s say our concerns were correct and the shares of the European companies in fact dropped. The Stock index Euro Stoxx 50 now has a value of only 2,000 points (a drop by 20% as opposed to the value for which we purchased the futures), and therefore each contract we hold has a value of 20,000 €. Because we are in the short position, we must buy the contracts in order to close the position. Therefore, we made 5,000 euro on each contract (their value during the sale minus the purchase value). Overall we therefore received 20,000 €, which should cover our losses from the shares held. It’s evident that, in order to secure the 100,000 euro portfolio, in this case, we ‘scored.’ We needed nothing beyond depositing 7,368 € (the initial margin is, in this case of course, returned).
Version of Use B
In case we wanted to invest into the Euro Stoxx 50 stock index, specifically into the shares of which it’s composed and didn’t have sufficient funds in order to buy all its components in the correct ratio (which would be very difficult with a ‘mere’ hundred thousand euro), we may also use futures for this index. If we want to invest 100,000 €, we purchase contracts in this amount. In our case (an index value of 2,500 points), it will again be four contracts (100,000/25,000). We will deposit the margin in the amount 7,368 € and put the balance into secure government bonds.
At the expiration of our contracts, the result will be the same as if we had purchased a hundred-thousand € worth of shares in the correct ratio from the index. The difference is that, unlike direct investment into the shares, profits and losses are not only calculated every day, but also subtracted or added every day to our exchange account. It is also easier to close the opened position.
Version of Use C
If we wanted to risk a lot, we could use our 100,000 euro to sell 54 contracts (100,000/1,848, leaving us with 532 €). If we risked this much and the Euro Stoxx 50 index drops to 2,000 points, we would be 270,000 euro in plus. That’s a serious profit, given that we only had to deposit 99,468 euro at the beginning.
The challenges of risk strategies are clear. If, instead, the value of the Euro Stoxx 50 index, instead of dropping by 500 points, rises by the same amount, we would lose 270,000 euro.* Using a ‘conservative’ strategy, by merely selling four contracts, we would only lose the entire 100,000 should the value of the stock index rise to 5,000 points, which is highly unlikely. Using the risky strategy, the losses would reach a dizzying 1,350,000 euros.
* In practice, we would be required to continue topping up the margin with the decreasing value of the index. At the moment the index reaches 2,686 points, we would have lost our entire hundred-thousand. If we failed to continue topping up the margin, the exchange would automatically close our position.
The following table summarizes the results of the ‘conservative’ strategy by selling four contracts (I) and the risky strategy by selling 54 contracts (II) under various scenarios – stock index drop (Scenario 1), no change (Scenario 2), increase by 500 points (Scenario 3) and doubling the stock index (Scenario 4). If we invested into the shares of the Euro Stoxx 50 index, that is if we purchased futures contracts, we would be in the long position and the results would be entirely the opposite.
|A||Value of a December contract in August (in thousands of euros)||25||25||25||25||25||25||25||25|
|B||Number of contracts||4||54||4||54||4||54||4||54|
|Margin (rounded to thousands of euros)||7||100||7||100||7||100||7||100|
|C||Price of the contract at the moment of closing the position (in thousands of euros)||20||20||25||25||30||30||50||50|
|D||Profit/Loss per single contract, position short (in thousands of euros) (A-C)||5||5||0||0||-5||-5||-25||-25|
|Overalls profit/loss (in thousands of euros) (D*B)||20||270||0||0||-20||-207||-100||-1 350|
An Example of Volatility Futures
A rather extravagant example from the stable of futures contracts are volatility futures, meaning the fluctuation of prices (specifically a determinant deviation over a certain period of time).
The contract is based on the VIX Index (Chicago Board Options Exchange Market Volatility Index) that is, in fact, the only traded futures contract of this type and highlights the options market volatility to the S&P 500 Index. It’s particularly used for securing against high volatility in this market. Contract expirations are issued month-to-month.
The value of the contract for January was 20,000 USD – corresponding to the value of the VIX index at the level of 20 points, because each point always has the value of 1,000 USD. Let’s say that a change in the volatility index by one point up will cost us 10,000 USD. Because one point corresponds to 1,000 USD, we will purchase ten contracts. However, for now, we will only deposit the margin to the exchange account in the amount of 57,750 USD.
In January the contracts expired. The VIX value for this month was 22. Therefore, we sold the contracts for 220,000 USD. An increase of value by 20,000 USD occurred. Our margin account at the exchange now has an additional 20,000 USD more to cover any losses caused by increased market volatility. Naturally, this is only under the assumption that we correctly estimated the sensitivity of our portfolio to the change in volatility. The following table shows the results of our purchase, where the VIX value for January remained at the level of 20 (Scenario 3) and when it dropped to 18 (Scenario 3).
|A||Value of ten January contracts at the time of purchase||200||200||200|
|VIX value at the end of January||22||20||18|
|B||Value of ten contracts at the end of January||220||200||180|
|Overall profit/loss from ten contracts, position long (B-A)||+20||0||-20|