Hedge ratio. Comparative analysis of the results of implementing hedging strategies Cash flow hedging

Hedge accounting (paragraphs 85–102)

AG102 An example of a fair value hedge is a hedge of the risk that the fair value of a fixed interest rate debt instrument will change as a result of changes in interest rates. Hedging of this type can be carried out by the issuer or the holder of such an instrument.

AG103 An example of a cash flow hedge is the use of a swap to convert a floating rate debt instrument into a fixed rate debt instrument (ie, a hedge of a future transaction in which the future cash flows being hedged represent future interest payments).

AG104 A firm commitment hedge (eg a fuel price hedge relating to an electric utility's unrecognized contractual obligation to purchase fuel at a fixed price in the future) is a hedge of fair value risk. Therefore, such a hedge constitutes a fair value hedge. However, paragraph 87 requires that a hedge of the foreign exchange risk to which a firm commitment is exposed may alternatively be accounted for in the same manner as a cash flow hedge.

AG105 A hedge is considered highly effective only if both of the following conditions are met:

(a) At the inception of the hedging relationship and in subsequent periods, the hedge should be expected to be highly effective in generating offsetting changes in fair value or cash flows attributable to the risk being hedged over the period for which the hedging relationship is designated. Such expectations can be demonstrated in a variety of ways, including comparing historical changes in the fair value or cash flows of the hedged item attributable to the risk being hedged with historical changes in the fair value or cash flows of the hedging instrument, or demonstrating a high statistical correlation between the fair value or cash flows of the item hedging and by hedging instrument. An entity may choose a hedge ratio other than one-to-one to improve the effectiveness of the hedge, as described in paragraph AG100.

(b) The actual results of the hedge should be in the range of 80 to 125 percent. For example, if the actual results are such that the loss on the hedging instrument is CU120 and the gain on the cash instrument is CU100, then the compensation could be estimated at 120/100, that is, 120 percent, or 100/120. that is, 83 percent. In this example, assuming that the hedge satisfies the condition in (a), the entity can conclude that the hedge was highly effective.



AG106 An assessment of the effectiveness of a hedge should be carried out, at a minimum, at the time the entity's annual or interim financial statements are prepared.

AG107 This Standard does not prescribe a single method for assessing the effectiveness of a hedge. The method an entity adopts to assess the effectiveness of a hedge depends on its risk management strategy. For example, if an entity's risk management strategy is to periodically adjust the amount of the hedging instrument to reflect changes in the hedged position, then the entity must demonstrate expected high hedge effectiveness only for the period until the next adjustment of the hedging instrument amount. In some cases, an entity adopts different methods for different types of hedges. An organization's internal documents establishing a hedging strategy should include a description of procedures for assessing effectiveness. This description of procedures should indicate whether the entire gain or loss on the hedging instrument is included in the measurement or whether the time component of the value of the hedging instrument is excluded from consideration.

AG107A If an entity hedges less than 100 percent of the risk in an item, such as 85 percent, it shall designate the hedged item as being equal to 85 percent of the risk and shall assess hedge ineffectiveness based on the change in that discretionary 85 percent risk. However, when hedging an 85 percent discretionary risk, an entity may use a hedge ratio other than one-to-one if this would improve the expected effectiveness of the hedge, as specified in paragraph AG100.

AG108 If the fundamental terms of the hedging instrument and the hedged item, which is an asset, liability, firm commitment or highly probable forecast transaction, are identical, changes in fair value and cash flows attributable to the risk being hedged are likely to offset each other in full as at the inception of the hedging relationship , and subsequently. For example, an interest rate swap is likely to be an effective hedging instrument if the principal and principal amounts, timing, repricing dates, collection and payment dates of interest and principal, and the basis for measuring interest rates are the same for the hedging instrument and the hedged item. In addition, hedging a highly likely forecast commodity purchase with a forward contract is likely to be highly effective if:

(a) the subject of the forward contract is the purchase of the same quantity of the same commodity at the same time and place as the hedged forecast purchase;

(b) the fair value of the forward contract at the inception of the hedging relationship is nil; And

(c) either the change in the discount or premium on the forward contract is excluded from the performance measurement and recognized in profit or loss, or the change in the expected cash flows of the highly probable forecast transaction is based on the forward price of the commodity.

AG109 Sometimes the hedging instrument only partially offsets the risk being hedged. For example, a hedge may not be considered to be fully effective when the hedging instrument and the hedged item are denominated in different currencies that are not linked to each other. In addition, a hedge of interest rate risk with a derivative will not be fully effective if part of the change in the fair value of the derivative is attributable to the credit risk of the counterparty.

AG110 To qualify for hedge accounting, the hedge must be for a specific identifiable risk that is determined by the entity rather than for the entity's general business risks. In this case, the risk being hedged must ultimately affect the profit or loss of the organization. Hedging the risk of asset obsolescence or the risk of government seizure of property does not qualify for hedge accounting; in these cases, the effectiveness of such hedging cannot be assessed, since these risks cannot be reliably assessed.

AG110A Paragraph 74(a) permits an entity to separate the intrinsic value and time value of an option and designate as the hedging instrument only the change in the intrinsic value of the option contract. A hedging relationship so designated may be fully effective in generating offsetting changes in cash flows associated with a hedged one-sided risk for a forecast transaction, if the main terms of the forecast transaction coincide with the main terms of the hedging instrument.

AG110B If an entity designates the entire purchased option as a hedge of one-sided risk arising from a forecast transaction, the hedging relationship will not be highly effective. This is because the premium paid for the option includes time value, whereas, as stated in paragraph AG99BA, the discretionary one-sided risk does not include the time value of the option. Therefore, in such a situation, there will be no offsetting effect between the cash flows associated with the time value of the premium paid on the option and the cash flows associated with the discretionary risk being hedged.

AG111 In the case of interest rate risk, the effectiveness of the hedge can be assessed by preparing a table of maturities for financial assets and financial liabilities that shows the net interest rate risk position at each time period, provided that the net position is associated with a specific asset or liability (or a particular group of assets or liabilities, or a particular part thereof) that form that net position, and the effectiveness of the hedge will be assessed in relation to that asset or liability.

AG112 When assessing the effectiveness of a hedge, an entity generally considers the time value of money. The fixed interest rate on the hedged item need not be the same as the fixed interest rate on the swap designated as a fair value hedge. Similarly, the floating interest rate The rate on the interest-bearing asset or liability does not have to be the same as the floating interest rate on the swap designated as a cash flow hedge. The fair value of the swap is determined based on the net settlement amounts of the swap. change by the same amount, such a change will not affect the net settlement amounts.

AG113 If an entity's designated hedge relationships do not meet the criteria for effectiveness, it shall discontinue hedge accounting from the last date at which the hedge was demonstrated to be effective. However, if an entity identifies an event or change in circumstances that causes the hedging relationship to no longer meet the criteria for effectiveness, and demonstrates that the hedge was effective before the occurrence of that event or change in circumstances, it discontinues hedge accounting from the date on which the event or change occurs. circumstances.

AG113A For the avoidance of doubt, the effect of replacing the original counterparty with a clearing counterparty and making the corresponding changes as required by paragraphs 91(a)(ii) and 101(a)(ii) shall be reflected in the measurement of the hedging instrument and, consequently, in the assessment of hedge effectiveness and determining the amount of hedging effectiveness.

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 is 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 brokerage 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 results 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.

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 bearish, the company may significantly reduce revenues, 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 by 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 - forward 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 a 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.

Let's assume that the hedge ratio is calculated during the life of the hedge. It would be logical to check how the results of hedging using this ratio compare with the results that would have been obtained without hedging. Market conditions change and unusual events may occur, so there is no certainty about how good our hedge will be. However, in general, a hedge can be expected to reduce losses that would have occurred without it.

Consider the following example.

On December 1, the fuel dealer signs a contract to deliver 420,000 gallons of heating oil on the 16th day of each of the next six months. The price for each supply is 51.5 cents per gallon. The current cash price is 52.50 cents. The trader believes spot prices will fall over the next 6 months as the weather gets warmer and demand falls. Accordingly, he plans to purchase the required fuel for deliveries just before each delivery date, avoiding any storage costs. He is ready to pay any cash price that emerges at the time of purchase.

To protect himself from a possible increase in cash prices, the trader decides to hedge using a heating oil futures contract. It assumes a regression equation similar to the one above, but uses daily price data for only 11 months of the year. The results of his analysis show that the minimum risk hedge ratio is approximately equal to 1 (p = 1).

Accordingly, the trader hedges by purchasing futures contracts to the extent necessary to minimize risk. In cha-!| In fact, he takes long positions that are synchronized with his forward delivery obligations: 10 January futures contracts at 52.00 cents to cover December delivery; 10 contracts for February at 51.41 cents to cover January delivery; 10 March futures at 48.96 cents; 10 April futures at 46.83 cents; 10 May futures at 45.58 cents and 10 June futures at 1 44.58 cents - a total of 60 contracts.

In table Figure 11.3 shows the results of this hedging strategy along with the results without hedging. Column 1 - cash price of fuel on the corresponding delivery date when the merchant actually purchased fuel for delivery; gr. 2 - income from each delivery; gr. 3 - costs of purchasing fuel for delivery; gr. 4 - net profit (loss) from delivery without hedging.

The results of the trader's futures positions are shown in graph. 5-7: 5th column - purchase price of 10 futures contracts; gr. 6 - futures prices for position liquidation; gr. 7 - profit (loss) on the futures position. The 8th column shows the net profit (loss) for hedging the position (column 4 + column 7).

In Fig. Figure 11.1 shows the monthly cash flow balance for unhedged and hedged positions (columns 4 and 8 of Table 11.3). It can be seen that the cash flow on the hedged position is more stable. The hedge manages to reduce cash flow fluctuations: the standard deviation falls from $9,437 to $7,653 (see Table 11.3). This means a reduction in volatility of 18.90%. However, it is clear that this does not remove all price risk. Why? Was the hedge ratio we used (p = 1) really giving minimal risk?

Profit (loss), dollars

In answering this question, it should be noted that, firstly, even if the calculated value of p turns out to be exactly equal to its final value calculated on the basis of real data for the hedge period, i.e. data from 1.12 to 16.05, all the same, the very technique of opening and closing a hedge on specific days contains a basis risk that cannot be eliminated. Second, the trader's ratio of 1 (or p = 1) was not the best hedge ratio to use to reduce risk.

This can be clearly seen from the table. 11.4, which shows changes in the average and standard deviation values ​​for cash flows obtained in the example under consideration for various hedge ratios. In particular, these data show that, based on actual prices, the optimal hedging ratio turned out to be 0.60. If the trader had used a factor of 0.60 instead of 1, the standard deviation of his net cash flow would have dropped to $5,594. This would have resulted in a 40.72% reduction in volatility instead of the 18.90% reduction obtained. However, even a hedge ratio of 0.60 would not eliminate all fluctuations in net cash flows because there are changes in basis.

Table Figure 11.4 also shows the result that occurs when a position is overhedged: when a larger ratio is used than that obtained from historical data (p = 0.60). As the ratio increases (from 0.60 to 1.10), the risk (or standard deviation) increases (from $5,594 to $8,580) while the average return falls (from $5,985 to $5,723). When a position is overhedged, the hedger effectively has two positions: a hedged cash position and a speculative futures position. The latter may result in greater or lesser profits depending on actual price changes. In this case, this led to a decrease in profits. In all cases, however, the overhedged position will result in greater risk. Because volatility in futures prices is often greater than volatility in cash prices, under-hedging is often more effective than over-hedging.

As a result, developing a hedging strategy requires caution and careful calculation. The main component here will be to estimate the expected minimum risk hedge ratio, which will be close to the actual ratio calculated over the planning period. This requires an accurate prediction of the relationship between cash and futures prices that will occur over the life of the hedge.

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 entire remaining 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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