Comparison of hedging costs in the foreign exchange and derivatives markets. Comparative analysis of the results of hedging strategies Hedging using forward contracts

Delta is the ratio of the price of a call option to the change in the price of the underlying asset, that is, the ratio of the value of futures contracts bought or sold to the current value of the commodity being hedged, or the ratio of the volatility of the portfolio to be hedged to the volatility return on the hedging instrument. From English Hege ratio.

• The meaning of the hedge ratio

Hedge ratios are required when the price movements of the futures contract and the hedged financial instrument do not coincide. A larger number of futures contracts are used to hedge less stable financial instruments. Basis risk can be measured by the correlation of prices in the cash and futures markets. The closer the correlation coefficient is to one, the greater the relationship between the price dynamics of the corresponding financial instruments.

For futures contracts and FRA, delta is the number of contracts required. This number is calculated as follows:

The risk for a hedged portfolio cannot be considered completely eliminated for the remainder of the time after its formation, because the delta will change as the stock price changes and the option's expiration date decreases.

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The thesis examined several strategies. The revenue of the Polyus Gold Group of Companies was calculated when selling products at the spot price. The company's income directly depends on market conditions. Therefore, in the event of a prolonged correction in the gold market or a change in the trend to a bearish one, the company may significantly reduce income, which will affect the efficiency of the enterprise.

Considering the possibility of a correction in the gold market and, consequently, a decrease in prices for these products, hedging instruments that could reduce the company’s price risks were considered. The simulation results are presented in table. 3.7.

Table 3.7

Simulation results

Based on the results of the sale of gold under the first contract, the strategy of combining a forward contract and a futures contract showed the best results. Due to the reduction in prices at the time of the first delivery, using a forward contract, the products were sold at a higher price. However, due to the use of futures, the loss on the futures reduced the profit on the forward. The opposite situation occurred at the time of the second delivery. Since the futures contract produced both gains and losses, another contract was considered.

Hedging a position under a forward contract with a put option led to the fact that the revenue for this strategy decreased in comparison with the previous strategy - forwards and futures. This is due to the increase in prices under the second contract. The use of a futures contract reduced losses on the forward contract due to the growth of the futures at market prices. In the case of an option, which only reduced the risk of a price decrease, when prices rose, the option was not exercised and the product was sold at the price of the forward contract. Due to the fact that in the second contract the possibilities of the forward contract were not realized, the option in the strategy with a spot price showed the best results. The option was exercised if prices on the spot market fell; if prices rose, it was not exercised and the goods were sold at the highest prices prevailing on the market.

Given the possibility of non-execution of a forward contract, the most attractive strategy is to sell products at spot prices and hedge these positions with a put option contract.

Thus, by determining the revenue received during correction periods, it was revealed that financial instruments of the exchange market, as well as the use of a forward contract, reduce the risk of price decline. The use of these tools requires certain costs and at a certain point reduces the possible profit. However, in the event of an approaching correction and a change in trend, companies that are already using hedging now insure themselves in the future against a change in trend. Certain costs associated with hedging will be insignificant compared to the losses that the company may incur if it does not use these strategies. Therefore, it is important for companies in the mineral resources complex, whose income depends on world prices for their products, to assess the dynamics and state of the stock market. It is very important to forecast in advance in order to take care of hedging against possible price declines in the future.

To hedge his position, the investor must determine the required number of futures contracts to buy or sell. With full hedging, the required number of futures contracts is determined by the formula:

A full hedge situation, however, is not common, so the above formula must be supplemented by a hedge ratio (or as it is sometimes called, an optimal hedge ratio). To approach the determination of the hedge ratio, imagine a portfolio consisting of the hedged asset and futures contracts used for insurance (the investor buys the hedged asset and sells the futures contracts). The portfolio value is:

To eliminate the risk of loss with a small price change, the following equality must be satisfied:

If the hedge ratio is equal to one, then we have the case of complete hedging (formula 4.4.19). The hedge ratio must take into account the standard deviation of the deviation of the price of the hedged asset AS and the futures price AF and the correlation between these quantities. Therefore, in its final form the hedge ratio takes the following form:

Graphically, the hedge ratio is the slope of the regression line AS relative to AF, as shown in the figure. The coefficient is calculated based on statistical data on the deviation of the spot price and futures price for the asset in question for previous periods. The length of time periods is chosen equal to the hedging period. So, if an asset is hedged for two months, then price deviations for a number of previous two-month periods are taken.

Taking into account the hedging ratio, the formula for determining the number of futures contracts takes the following form:

If we take the data presented in the figure as an example, then from the slope of the regression line we determine that the hedging ratio is equal to:

This means that the futures position must be 98.73% of the value of the hedged asset. Let’s assume that the volume of one futures contract is 10 GKO bonds. The hedger expects to insure the purchase of 300 bonds. He needs to buy:

7. Hedging with a stock index futures contract

Let's consider an example of hedging an investor's position using a futures contract for the AK&M100 agency stock index. Let's assume that in August an investor has a portfolio of shares worth 570 million rubles, the beta of the portfolio is 1.2. He plans to insure the portfolio for the period until the end of December. The price of the December contract for the index is 2100.

Since the investor is long the stock, he needs to sell futures contracts. The number of futures contracts is determined by the formula:

8. Hedging with a bond futures contract a) Hedging the cheapest bond

Bond futures contracts can be used to hedge bond positions. Let's first consider the example of hedging the cheapest bond. As you know, to execute a bond futures contract for delivery, the investor will choose the cheapest bond. The relationship between the change in the futures price and the price of the cheapest bond can be written as follows:

As follows from formula (4.4.26), the change in the futures price is equal to the change in the spot price of the cheapest bond, adjusted for the conversion rate. Formula (4.4.26) can be rewritten as follows:

As can be seen from the above formula, the conversion ratio for hedging the cheapest bond is nothing more than a hedge ratio. If K K >1 this suggests that to hedge a spot position, more futures contracts must be opened relative to the spot position because the futures price moves less than the spot price. If TO To <1, then you should open fewer futures contracts compared to the spot position, since the futures price changes more than the spot price. The total number of futures contracts that need to be opened is determined by the formula:

In formula (4.4.28), the ratio of the hedged amount to the price of the cheapest bond is nothing more than the sum of the par values ​​of the cheapest bond.

Let us examine in general terms the impact of the basis on the results of hedging. An ideal hedge assumes a situation where the basis does not change.

The entity buys 10 units of the commodity at $2.50 on October 15 and immediately hedges by selling 10 units of the December futures contract at $2.75. Thus, the basis at the time of the hedge is -25 cents. A month later, the business sells 10 units at $2.0, with a cash market loss of 50 cents. If futures prices also fell by 50 cents, the loss was exactly offset by the profit (Table 1).

Table 1 No change in basis

Because the basis did not change, the futures market provided ideal protection. But real practice provides few such opportunities. If futures market prices had fallen more than cash prices, the outcome would have been different (Table 2). [4, 152]

Table 2 Favorable change in basis

In this case, changing the basis by $0.05 resulted in a profit. Broadening the basis would have the opposite effect, as shown in Table 3. In this case, the hedge provided incomplete protection against losses in the cash market.

Table 3 Unfavorable change in basis

At the same time, even with an unfavorable change in the basis, the hedge can significantly reduce losses.

The merchant bought 25 thousand tons of gasoline for the purpose of resale in the near future. However, considering the market not very stable, he sells futures contracts to protect against falling prices. After a transaction with a physical commodity is completed, futures are liquidated (Table 4).

hedging stock speculation

Table 4 Liquidation of futures

As you can see, the hedging was not perfect, but it saved the trader $350 thousand in possible losses. Of course, there will be broker commission costs, but they will be less than $0.30/t, including deposit and margin costs and the commission itself.

Let us now give a similar example of a long hedge.

The film production company expects to buy 20 thousand ounces of silver in November-December. Expecting prices to rise, the firm should buy silver immediately, but is unable to do so. The current price of silver futures contracts for December delivery is $5.71 per ounce in June, and spot prices are $5.21. A firm purchases 20 silver futures contracts for December delivery. In November, real silver was purchased at a price of $9.0, while futures contracts were simultaneously sold at a price of $9.45 (Table 5).

Table 5

Final purchase price: 9.0 -- 3.74 = $5.26/oz. In the end, the company paid only an additional 5 cents per ounce instead of the possible $3.79.

Having considered the effect of basis on a hedge, the outcome of any hedge can be simply determined by measuring changes in basis at the beginning of the hedge and at the end. In the example presented in Table 2, narrowing the basis by 5 cents gave the same amount of profit to the hedger, and in a situation with expanding the basis by the same 5 cents (Table 3), this gave the same amount of loss. Therefore, we can conclude.

final price = target price (+ or -) change in basis.

This means that the main task in hedging is the correct forecasting of the basis at a given target price. Of course, the correct determination of the target price is also the most important problem for the hedger, but this is already beyond the scope of hedging. The result of the insurance operation as such depends on the correctness of the basis forecast.

To understand the effects of hedging in different circumstances, here are eight possible combinations of short and long hedges in terms of expanding and narrowing the basis.

• 1. Short hedge in a normal market with a narrowing basis. The hedger takes a short position in the futures market at a premium to spot prices. If prices fall and the basis narrows, the gains in the futures contract will exceed the losses in the cash market. The result is profitable. If prices rise, the shrinking basis means that the loss on the futures contract is less than the gain on the cash market. The result is net profit.
• 2. Short hedge in a normal market when the basis expands. A futures contract produces smaller profits (or larger losses) than the cash market.
• 3. Short hedge when the market is inverted and the basis is narrowing. A futures contract produces a smaller profit (or a larger loss) than the cash market.
• 4. Short hedge when the market is inverted and the basis is expanding. A futures contract produces a greater profit (or a smaller loss) than the cash market.
• 5. Long hedge in a normal market when the basis narrows. A futures contract produces a smaller profit (or a larger loss) than the cash market.
• 6. Long hedge in a normal market when the basis expands. This results in a larger profit (or smaller loss) on the futures contract.
• 7. Long hedge in an inverted market when the basis narrows. In this case, the profit (loss) on the futures position is greater (less) than on the cash position.
• 8. Long hedge in an inverted market when the basis expands. Here, the futures contract will produce a greater loss (or less profit) than the cash position.

Let's return to the example of hedging for an importing company from the first part of the course. At the initial point in time, the company receives an invoice to pay for the goods in foreign currency. Then the goods arrive at the company’s warehouse and begin selling them to customers for rubles with deferred payment. Domestic prices in rubles are fixed at the time of receipt of the invoice based on the exchange rate, and the conversion of rubles received from customers occurs at the rate on the date of receipt of money from customers. Thus, the company faces the risk of an increase in the exchange rate during this period.

Hedging period is 60 days. If the exchange rate increases from 62 to 66 rubles, the company receives a loss from exchange differences of 4 million rubles. In case of a decrease from 62 to 58 rubles, income from exchange rate differences is 4 million rubles. If a decision is made to hedge the risk with a futures contract, then when prices are fixed based on the exchange rate, the futures are purchased with a deadline of 90 days, after 60 days when funds are received from buyers and currency conversion, the futures are sold, but there are already 30 days left until its execution . With a swap rate of 15% per annum, futures at a spot rate of 62 rubles will cost 64.29, and at a spot rate of 66 rubles - 66.81 rubles. As a result, over 60 days, the premium in the futures price decreased by 1.48 kopecks, the result was exchange rate differences of minus 1,480 thousand rubles, in the event of a depreciation of the currency, exchange rate differences would amount to −1,570,000 rubles, that is, positive exchange rate differences from the imported goods , were compensated by the loss from the futures transaction. And in the event of an increase in the exchange rate, the profit on the futures position of 2,520 thousand rubles will compensate for exchange rate differences on imported goods minus 4 million rubles.

Comparison of hedging costs in the foreign exchange and derivatives markets

Currency hedging makes it possible to completely eliminate currency risk, but for a slight increase in ruble liabilities equal to the swap rate. In the derivatives market, this rate is taken into account in the futures price; as the date of its execution approaches, the amount of the premium relative to the spot rate decreases.

In the example discussed earlier, the rate at the initial moment of time was 62 rubles, and the futures price was 64.29.

At the end of the period, the spot rate is 66 rubles, and the futures price is 66.81.

The premium in the futures price decreased over 60 days from 2.29 rubles to 81 kopecks. The result of hedging was minus 1 ruble 48 kopecks, which in terms of annual interest is 14.52%.

In the foreign exchange market, the main costs arise from the cost of borrowed money.

If the currency exchange rate increases from 62 to 66 rubles and the use of borrowed funds in the amount of 80% of the hedged amount at an annual rate of 22%, the cost of hedging will be equal to −1.79 rubles, which in terms of the annual percentage rate is 17.56%. Using the derivatives market for hedging purposes in this example turned out to be 3% per annum cheaper than using the foreign exchange market.

Let's say a company received a loan in the amount of $100 thousand for a period of 12 months at a rate of 5% per annum. Quarterly payments will be $25,785.66, exchange rate changes during the period are shown in the table

The increase in the exchange rate caused an increase in the planned ruble overpayment from 103 thousand rubles to 913 thousand rubles, that is, exchange rate differences amounted to 810 thousand rubles.

Now suppose that the company hedged this loan with futures contracts. For this purpose, futures were initially purchased for $103 thousand - $100 thousand loan and $3 thousand the amount of the planned overpayment. Every three months the hedge position was reduced by the amount of the payment to the bank.

Each time, the position was opened in a futures contract with an expiration date of 3 months, and after it expired, it was transferred to the next futures contract with an expiration date, but minus the loan payment to the bank. For example, on December 15, 103 futures were purchased at a price of 33.83, and they were executed on March 16 at 36.63, that is, for the first three months, the hedging result amounted to 288,400 rubles, while only 78 futures were purchased again at a price of 37.73 . The loan payment is the product of the exchange rate at the time of payment and the payment amount. The resulting exchange rate differences were offset by the results of the futures transaction. And the overpayment amounted to 370 thousand rubles or approximately 17% per annum, that is, the company managed to switch from a foreign currency loan with a rate of 5% to a ruble loan, and since during hedging the swap rate in the futures price was equal to 12%, the final rate was equal to 17%.

To open such a hedge position in the initial period, a guarantee in the amount of 300 thousand rubles would be required.

Hedging currency risks using options

Previously, we discussed instruments that protect a position from an unfavorable exchange rate change, but do not allow a positive result in the event of a favorable one.

The ability to hedge currency risks from an increase in the exchange rate while maintaining profits in the event of a decline in the exchange rate is provided by another derivative financial instrument - an option.

An option is an instrument that gives the buyer the right to buy or sell an underlying asset at a predetermined price on or at any time before a predetermined date. An option can be either an exchange-traded or over-the-counter instrument. The buyer transfers the option premium to the seller upon conclusion of the transaction - the premium amount is non-refundable.

The graph shows the dependence of the financial result when purchasing an option on changes in the value of the underlying asset. As we can see, such an option will allow you to hedge the risk of an increase in the exchange rate, and leaves the possibility of making a profit from a decrease in the exchange rate.

To compare the results of hedging for an option and a futures, we can plot them on a chart along with profit and loss, for example, for a foreign currency loan.

The financial result of the revaluation of the obligation depending on the exchange rate on the futures chart is highlighted in red, the profit and loss from a transaction with a futures is in green, the final result of hedging is in blue, and as we can see, it does not depend on changes in the exchange rate and always remains at the same level

If we use an option, then, due to the presence of a non-refundable premium, the result of hedging in the event of a rise in the currency exchange rate turns out to be slightly lower than in a futures transaction, however, in the event of a decline in the currency exchange rate, the option allows us to receive part of the positive revaluation of the foreign exchange obligation.

I would like to separately note that working with derivatives market instruments does not limit us to hedging currency risk: a wide range of underlying assets allows us to work with both interest rate risk and price risks for currencies, stocks, precious metals, agricultural crops and energy.