Futures market

The futures market is the economic place where the supply and demand for futures transactions meet. It complements the cash or spot market .

Main features

The transactions concluded on the futures market are to be performed by both parties within a fixed period of time, which must be at least three trading days after the conclusion of the transaction. This distinguishes the futures market from the cash market, in which the cash transactions are to be fulfilled on both sides after two trading days at the latest. Article 38 (2) of the EU regulation of 10 August 2006 (1287/2006) speaks of a forward transaction if, regardless of its express conditions, there is an agreement between the contracting parties that the delivery of the underlying is postponed beyond two trading days. The mutual fulfillment of the transaction with a period postponed beyond two trading days is decisive for the assignment to the futures market.

Objects to be traded on the futures markets are foreign exchange , securities , metals or other justifiable items in the form of standardized contracts for future transactions, which are referred to as derivative instruments (or derivatives for short). The price for the trading item (" base value ") to which a contract in the futures market refers is already set at the time the contract is concluded and applies regardless of the price development occurring during the term of the futures transaction.

Functions

Derivatives markets belong to the future markets that complement the spot or cash markets. Futures markets exist because economic uncertainties are unavoidable, future economic developments cannot be fully foreseen and people develop different expectations even with the same publicly available knowledge. In the foreign exchange market, it can be observed that the forward exchange rate normally deviates from the spot exchange rate because there is an interest rate difference between the currencies traded and / or market participants' expectations of future appreciation or depreciation of the currencies concerned are factored in. On the futures market, expectations of the market participants about data changes have a more intense effect than on the cash market, because the time until the trades are fulfilled is greater and therefore there is a higher probability of data changes.

Pricing

The prices on the futures markets are determined by supply and demand. However, this does not happen in isolation from price formation on the cash markets . For underlyings that are purely financial assets, the fair forward price can theoretically be derived from the spot price. At least an upper limit for the forward price can be derived for storable underlyings that have a utility value.

The derivation of the fair forward price is based on the comparison between two equivalent strategies:

You buy the underlying asset today at the spot rate and store it until maturity, financing the purchase price by borrowing.
An appointment was made today.

The first strategy simulates forward buying through cash transactions (replication).

Neither strategy should be financially advantageous over the other. If this were the case, one could make a profit by concluding a forward transaction and replicating the opposite position with cash transactions at the same time, without being exposed to a market price risk. It is also said that the forward price would no longer be arbitrage-free .

The derivation of the fair forward price is shown below for various constellations. The following symbols are used:

${\ displaystyle {t}}$ the time,
${\ displaystyle {t0}}$ the present time,
${\ displaystyle {T}}$ the exercise date (maturity of the futures contract),
${\ displaystyle {S_ {t}}}$ the price of the underlying at time t, in particular
${\ displaystyle {S_ {0}}}$ the price of the underlying asset now ( spot price ),
${\ displaystyle {S_ {T}}}$ the price of the underlying asset at maturity,
${\ displaystyle {F}}$ the fair forward price,
${\ displaystyle {K}}$ the exercise price agreed in the contract,
${\ displaystyle {z_ {t}}}$ the interest rate for the term up to time t

The formulas assume an exponential interest rate (see interest calculation ). With linear or constant interest, the compounding and discounting factors have a different form.

Futures on financial stocks with no income

The simplest case is a futures contract on a financial asset that does not pay any income, e.g. B. a dividend-free share.

If you buy the base value today according to the replication strategy, the purchase price must be financed through a loan.

An example: A share is bought for one year. The current price of the share is 40 EUR, the interest for 1 year 2%. For the implementation of the replication strategy, the purchase price would have to be financed for 1 year. The interest burden for this is 0.80 EUR (2% to 40 EUR for 1 year). After the year, a total of EUR 40.80 interest and repayment must be made.

This sum of the spot rate and holding costs is the fair forward price.

You can see that this price is arbitrage-free: If you carry out the described replication transaction and make a forward sale of the share as a counter-transaction, there are neither profits nor losses over the year:

The forward seller delivers the share that has now been purchased to the forward buyer when it is due.
For this he receives the forward price of EUR 40.80.
With this proceeds he can precisely repay the loan and pay the interest.

Expressed as a formula, the fair forward price is the compounded spot rate over the term of the forward transaction .

${\ displaystyle F = S_ {t0} {(1 + z_ {T}) ^ {T-t0}}}$

In the case of positive interest rates, the fair forward price is always higher than the spot price for financial stocks without income.

Forward transactions on financial stocks with steady income

Financial stocks with steady income are e.g. B. Bonds and Foreign Exchange .

The income from the underlying reduces the holding costs for the underlying and reduces the forward price. The example from the previous section must be modified accordingly.

$ 100 will be purchased for one year in advance. The current exchange rate is 0.8000 euros per US dollar, expressed as a price quotation (see exchange rate ; the quantity quotation is common for US dollars, the price quotation was chosen here for reasons of comprehensibility). The euro interest rate for 1 year is again 2%.

Since USD can be invested in an account with interest, an amount of US dollars must be purchased in order to carry out the replication strategy, which, including interest, results in the sum of 100 US dollars in one year. The interest rate for US dollars is 1.4%. If you buy 98.62 USD today and invest it at 1.4% for 1 year, you will receive 1.38 USD interest in one year and thus have the 100 USD required (rounding differences were neglected).

For the purchase of 98.62 US dollars at the exchange rate mentioned, 78.90 EUR have to be spent. The financing costs for 1 year are EUR 1.58 (2% to EUR 78.90 for 1 year). To have 100 US dollars in one year, you have to pay 80.48 EUR (78.90 EUR + 1.58 EUR) in one year. Accordingly, the fair forward rate is 0.8048 euros per US dollar.

The fact that the underlying security generates income reduces the holding costs for foreign exchange, since a smaller amount has to be financed in the replication business.

This relationship can be calculated using the formula

${\ displaystyle F = S_ {t0} {\ frac {(1 + z_ {T}) ^ {T-t0}} {(1 + r_ {T}) ^ {T-t0}}}}$

be expressed, wherein the interest rate on the foreign currency and the spot rate designated for foreign currency. ${\ displaystyle {r_ {t}}}$ ${\ displaystyle {S_ {t0}}}$

Forward deal on shares with dividend payment

The fair forward price for shares that pay a dividend during the term of the forward transaction can be determined in the same way as the fair forward price of a financial asset with steady income. The dividend is income that reduces the cost of holding the underlying asset. The fair forward price is

${\ displaystyle F = (S_ {t0} -I) {(1 + z_ {T}) ^ {T-t0}}}$ ,

where is the present value of the dividend payment. ${\ displaystyle I}$

Forward transactions on real goods

Forward transactions on real goods (" commodities ") can differ from the examples given so far in that, with real goods, it can be advantageous to actually dispose of them.

Whether and to what extent this is the case depends on the type of goods. Gold and silver, while having certain industrial uses, are mostly held by investors such as financial stocks. The fair forward price is calculated in the same way as for shares with dividend payments. The storage costs are treated like a negative dividend:

${\ displaystyle F = (S_ {t0} + U) {(1 + z_ {T}) ^ {T-t0}}}$ ,

U is the present value of the storage costs. Alternatively, storage costs can be expressed as relative annual storage costs. Then the formula for financial stocks with steady income is applicable, whereby the storage costs are shown as negative income in the formula.

In the case of goods such as crude oil, construction timber or agricultural products, the utility cannot be neglected. Therefore the arbitrage arguments used so far are only valid to a limited extent; as a result, the previous derivation of the fair forward price provides an upper limit.

If the forward price traded on the market is greater than ${\ displaystyle M}$ ${\ displaystyle F}$

${\ displaystyle M> F = (S_ {t0} + U) {(1 + z_ {T}) ^ {T-t0}}}$ ,

it is still true that the arbitrageur can borrow the amount of money, buy the goods and store them. If he sells the good on the futures market at the same time at the futures price , he will make a sure profit when the futures contract is due. The execution of this arbitrage strategy increases the demand for the good on the cash market and the supply on the futures market, whereby the spot price (and thus ) increases and the futures price decreases until it applies again . ${\ displaystyle S_ {t0} + U}$ ${\ displaystyle M}$ ${\ displaystyle S_ {t0}}$ ${\ displaystyle F}$ ${\ displaystyle M}$ ${\ displaystyle M = F}$

On the other hand, it is quite possible that the forward price traded on the market will be lower than . In order to use this price difference, the arbitrageur would have to borrow the good (analogous to securities lending ) and sell it short . However, market participants who have stocks of the good hold it in order to use it up, which is why short selling is generally not possible and the arbitrage strategy is not feasible. As a result, there is an upper limit for the forward price of a good with utility ${\ displaystyle M}$ ${\ displaystyle F}$

${\ displaystyle F \ leq (S_ {t0} + U) {(1 + z_ {T}) ^ {T-t0}}}$

Availability premium

The difference in the above inequality can be obtained by the so-called availability premium be expressed (conveniance yield):

${\ displaystyle F {(1 + y) ^ {T-t0}} = (S_ {t0} + U) {(1 + z_ {T}) ^ {T-t0}}}$ .

The availability premium, expressed like an interest rate, is first of all a measure of the difference between the two sides of the inequality. It can be interpreted as a measure of how strongly the market prefers actually holding the goods over participation in the futures market. It can therefore also be seen as a market expectation of future delivery bottlenecks. ${\ displaystyle y}$

Summary

In general, one comes to the conclusion that the fair forward price is the spot rate, increased by the costs of holding the underlying asset (refinancing costs, any storage costs), reduced by income generated by the underlying asset (e.g. interest income). This balance is also known as the “cost of carry”.

If the compounding and discounting factors are expressed using the constant interest rate, the fair forward price can be specified uniformly for all financial base values:

${\ displaystyle {F = S_ {t0} -e ^ {(z_ {T} -r_ {T}) (T-t0)}}}$ .

The following relationships can be derived from the formula:

The fair forward price rises as the spot price of the underlying rises.
The fair forward price is higher than the spot rate if the holding costs are higher than the holding income (i.e. if ), otherwise lower . ${\ displaystyle (z_ {T} -r_ {T})> 0}$
The forward price increases when the difference increases. ${\ displaystyle (z_ {T} -r_ {T})}$
With longer deadlines ${\ displaystyle (T-t0)}$ ${\ displaystyle (T-t0)}$
- the fair forward price increases if the difference is positive and ${\ displaystyle (z_ {T} -r_ {T})}$
- the fair forward price decreases if the difference is negative and ${\ displaystyle (z_ {T} -r_ {T})}$

Risks

According to the Federal Court of Justice, the particular danger of futures transactions and thus the risk on the futures market is that they - unlike cash transactions in which the investor must immediately use cash or a loan amount - due to the postponed fulfillment time, they can speculate on a favorable, but uncertain Seduce the development of the market price in the future, which is intended to enable the termination of the term commitment without using your own assets and without taking out a loan through a profitable close-out transaction . Exchange futures are typically associated with the risks of leverage and the total loss of the invested capital, as well as the risk of having to use additional funds contrary to plan. For this reason, under Section 26 (1) of the Stock Exchange Act , investment services companies are prohibited from concluding forward transactions with people who are not familiar with the subject matter. The BörsG understands stock exchange speculation transactions in particular buying and selling transactions with postponed delivery times, even if they are concluded over the counter (Section 26 Paragraph 2 BörsG) and options thereon if they are aimed at making a profit.

In the futures markets in particular, market participants act who, for the above reasons, are not interested in an effective fulfillment - such as delivery of the goods to be purchased, securities or foreign exchange - but instead plan to close them out during the term of the futures contract in order to make a profit.

Others

Derivatives markets offer the savvy investor numerous additional investment alternatives, each of which can be adapted to personal market expectations and psyche, but in particular to individual risk appetites.

If contracts are continuously concluded in standardized form on the futures markets for a predefined, standardized selection of trading objects, one speaks of futures exchanges . The derivatives exchange Eurex is the world market leader in trading futures and options .

Remarks

↑ For a market participant with stocks, there would be an analog arbitrage strategy: He could sell his stock and buy it back in advance. He pays interest on the sales proceeds for the term, and also saves storage costs for a long time. If M <F there is a sure gain. This strategy is also opposed by the desire to use the good.

Individual evidence

↑ BGHZ 103, 84, 87
↑ ^a ^b BGHZ 150, 164, 169
↑ BGHZ 139, 1, 6

[1] For a market participant with stocks, there would be an analog arbitrage strategy: He could sell his stock and buy it back in advance. He pays interest on the sales proceeds for the term, and also saves storage costs for a long time. If M <F there is a sure gain. This strategy is also opposed by the desire to use the good.

[2] BGHZ 103, 84, 87

[BGHZ_150,_164,_169-3] BGHZ 150, 164, 169

[4] BGHZ 139, 1, 6