Currency accepted regarded only as an object for speculation or as a means of international payments. However, modern markets allow synthesis of currencies and derivatives, synthetic products, whose behavior corresponds to the bonds. With the advent of computer technologies such opportunities have not only for large financial institutions, but also for small investors.
Inquisitive person asked in the letter ...
One day I received a letter in which the author asked the board: how to cover the price risk on the currency pair Pound / Yen? I must say, the trader, this is highly commendable: rare really inquisitive person engaged in commerce in the financial markets, strange as it sounds. The main incentive that motivates him to a deal where he was in a long position on the pound and the yen on short, were betting, or rather - their differential. Trader estimated that if the price will not move anywhere, then a year he gets a little more than nine "shapes" as a result of payments on swap of 2.5 points on a daily basis to the position of the two lots. This meant, he explained in a letter that the amount required to maintain the position, increased approximately seven times.
But miracles do not happen, prices fluctuate, and the market is unlikely to want to give the ability to easily get rich. Therefore, the trader and the question arose: how can we try to cover the risk of existing positions, using, for example, options? His question was rather curious, has no clear answer and solutions, and therefore it is interesting to explore the possibility of price risk management rates of currency exchange. The article shows the basic options and, therefore, emphasis is placed on a common methodology, which is illustrated by examples. Select a period which I consider here, is sporadic and not dictated by technical or fundamental analysis of the situation. For simplicity, I stopped at the interval, covering January - end of May 2002.
Purpose creates tools and - to no avail ...
First, find out the true purpose of the position of the pound / yen in the game on interest rates. The first idea that comes to mind is this: if we are going to benefit from the differential rates, not whether we should cover is interest rate risk, rather than price? This argument has a fundamental under the soil - a global effect of Fisher, which determines the relationship between rates and rates. If you follow the theory, to cover interest rate risk is to use interest instruments that are traded today in abundance on the stock and OTC markets [1]. Because in this case the exchange rate and the differential rates are determined by short-term rates, it is logical to assume the possibility of short sterling (short sterling) and the euro (euroyen). And on evroiene could explore the possibility of using different tools: LIBOR, TIBOR or 3-month.
I stress that while this is only a hypothesis, which we are discussing to have a full understanding of the object under study. But recourse to prices, rather, to their dynamics, showed the impossibility of using these instruments to cover losses that could arise as a result of price fluctuations. Although the theory of general law, but the real market does not want to follow it and demonstrates change of course, while interest rate futures are almost immobile. For example, in the individual periods when the pound / yen unchanged at 200 points, short sterling and the euro (futures) almost did not change in price. Thus, the original idea fails, and should more seriously explore the issue.
All the power in the simplicity
Turning to the market of futures contracts, we immediately face the problem of inconsistency of contracts used in the FOREX and futures market. Futures are a direct quotation, and the size of contracts correspond 62,500 pounds and 12,500,000 yen. In a randomly selected time, 14 January 2002, when the pound / dollar 1.4496, the dollar / yen 131.84, and the pound / yen 191.14 - the June futures are traded as follows: pounds 143.58 (multiplier 100), 76.38 yen (multiplier 10000), which gave the course pound / yen 187.98. In translating the dollar value of futures contract was a pound to almost $ 90,000, and on the yen - $ 95.5 thousand. Obviously, the use of futures, we will remain uncovered risk, if we trade on FOREX-billion dollar contracts for $ 100,000. If there is an opportunity to use the contracts of other, smaller size, this problem can be removed. A different solution is to increase the position size to such magnitude that the futures and cash positions consistent with each other. It makes sense to use the mini-contracts. Of course, there is always the option to assume the residual risk of having a meaning, if we feel confident about "upstairs". So, why has the situation when we bought a pound, sold the yen, trading originally $ 100 thousand, and the hedge position in the FOREX, a very short contract for a pound and one long on the yen (Figure 1 and 2)?
Fig. 1. Pound / dollar daily chart: from 14 January to 31 May 2002
Fig. 2. Dollar / yen, the daily schedule: from 14 January to 31 May 2002
By 31 May, we could get the loss on the pound / euro at $ 6058 (pound / dollar 1.4543, the dollar / yen 124.13, and the pound / yen 191.14). Proceeds from the swap would provide $ 2490 (Of course, if the broker charges a differential, in this case is about 3.15% per year), which do not cover the loss. However, oppositely directed positions in futures would bring a total profit of $ 4012 (on the yen - a gain 5200, and a pound - a loss in 1187). Summing up all together, we have a total profit of $ 445. It could take place only in the case of interest. Also note: in the analysis used prices at the end of the day, but hours trading session, the futures market and FOREX differ, so in reality, the results would be slightly worse. In addition, the influence spread in prices the demand-supply in this case is not taken into account.
By the way, recently opened a futures contract for trading the pound / yen, which eliminates the need to use different contracts (with the same success we could apply the currency pair euro / pound and the euro / yen). Finally, an important question: how many more need of money to hold these positions? If you focus on practice (shoulder on the FOREX market is 1:100), then a lot more than the very cash position. Last but not least, will the agent take into account the available positions in the aggregate. Although the major brokerage houses are now without any problems provide access from one account and the market FOREX, and to derivative instruments.
Next option - options
I can not ignore the options markets, providing the opportunity to speculate as well as cover the risks. The options here may be countless. Let us just some of them having bright features. First, let's see how options behave themselves "in the money". We choose June-150-Put a pound (in futures) traded on Jan. 14 at 7.30 ($ 4562), and the yen in June-72-call cost 5.00 ($ 6250). By the end of May first brought us to a loss of $ 1750, and the second - profit $ 4425. The total profit of $ 2,675 does not cover the loss on the spot position. Strategy in the amount of loss turned into $ 892. As we see, the desire to reduce risk through stock options has turned a small, but a loss. This does not mean that if we used other option series, we would have made the same result. The most obvious advantage - the possibility of early retirement with a greater benefit than using futures as a tool to cover the risk.
For example, if the pound / yen rose rapidly after a month or two after the creation of positions, we felt the need to get out of it early. Options, not having time to experience the corrosive influence of the decay time [2], could be of great value. In the proposed version to cover the risk, we need additional resources amounting to $ 10.776, that given the margin for positions in FOREX very unattractive. So let us turn to a strategy that attracts novice players, since it does not require such a significant capital.
It is a strategy which combines "cap" ("ceiling") and "Flo" (floor), in other words - buying and selling of options "outside money". While the price of the asset being hedged is between the price of performance options, the strategy does not manifest itself, except for the need to divert margin. But when the price rushes outside exercise prices, the strategy begins to behave similar to the position in the underlying asset. More attractive point is the possibility of selection of exercise prices at which the strategy will itself fund, if not take into account the margin. Selected for the strategy options (on the principle of "debit = credit") are presented in Table 1, while showing the results for the period.
Note: in this case the result was 24% more efficient than using futures. In this case as a whole would have less margin of at least two times, which suggests a much more substantial. Of course, this does not cover the loss in position on the pound / yen, but it provides an aggregate gain of $ 1,382 as a result of cash inflows from the swap. The third option - the most difficult of all, since it requires thorough preparation and understanding of the mechanism of dynamic risk management. Such strategies are adopted to determine how the purchase or sale of volatility. In fact, they are based on the retention of the main positions in options, which are regularly hedged underlying asset in the amount necessary to establish neutrality on the market.
In general, these strategies are fairly simple, but they are fraught with many pitfalls. The greatest difficulty lies in choosing the principles of rebalancing, on which, in fact, depends, the result will be positive or negative. In our case, the strategy calls for buying at least two options "at the money": Put to the pound and the call for the yen. Accordingly, the maximum amount of position on the currency increase to at least $ 180,000. Because risk management strategies volatility requires a minimum trade reasonable lots, in this version there is a need for lots of $ 10,000. If this is not possible, and we have to sell 100-thousand contracts, the maximum position on FOREX swell to $ 1,800,000, and we need at least 20 options contracts.
We are now more interested in the result, so forget about the amount of positions and see what would such a risk-management when trading the 10-thousand contracts.
Thus, the initial position - we use $ 90,000 for a position on the pound / yen. Coverage risk is through the purchase of two June-144-Put a pound (3.35 = $ 2031, which requires the position of $ 4062) and two 76-June-Call for yen (2.19 = $ 2,737, to the position - $ 5475). Calculating the rebalancing options, changing the volume of foreign exchange position for every pound of 100 points and over 200 points on the yen (it is substantially more volatile in terms of standard deviation), shows: the pound brought the final loss of about $ 1000. Profits on the FOREX in the amount of $ 3000 does not cover the loss in options, is $ 4000. Ian gives the best result, which depends on the principle of risk management can range from zero to + $ 2000, will assess the likely outcome of a $ 1000 prize [3].
If our goal - to receive income from interest payments on the swap, very bad, that managed to neutralize the risk of exchange rate fluctuations and to obtain a result rehedzhirovaniya zero result. Accordingly, interest income deduce strategy in the category of successful, providing a $ 2250 profit for every $ 90,000 of seed capital used to create foreign exchange position.
Yield similar to interest payments
What is the relative yield of all investigated operations? Simple answer to this question is difficult because from different brokers margin varies. Estimated - yield ranged from -20% to +90% per annum (if we trade on FOREX 100000th contract, with $ 1000), and it is determined the selected method of risk management. Successful transactions confidently yield may reach 20-75% per annum. The range is great enough. Much, if not all, depends on the correct choice of tools covering the risks as well as management positions.
Placed in the very early goal was to find opportunities to eliminate price risk in order to safely receive interest income from the differential rates. We have achieved this goal. Naturally, simple methods have the lowest incomes, sophisticated techniques to provide increased yield, comparable to the norm for operations with derivatives of the active risk management. Please note: we are not talking about the limits traditionally used when exiting unprofitable trades, because there are all too intuitive.
Abstracting from the speculative components of the strategy, which has in its composition FOREX-position and a set of instruments covering the risk, we find: it provides a regular incoming cash flow, which resembles the interest payments on bonds. The difference is that here the coupons are redeemed each day. Since the price risk in general is eliminated, the price behavior of a synthetic instrument, which includes spot position and instruments cover the risk, similar to a bond, decreasing in price as the coupon redemption.
If you do not resort to the neutralization of price risk, you can expect: the pound / yen will fall exactly on the value of interest payments. This tendency is quite clear, if you do not pay attention to the speculative fluctuations.
Fig. 3. Synthetic bond created by foreign exchange and futures positions.
Figure 3 illustrates the behavior of the strategy used to cover the risk of futures contracts on the yen and the pound. Since our goal - to get the maximum dollar profit, then created synthetics represented in dollar terms for the appropriate courses. Of course, if the broker does not charge interest on the swap, the strategy turns out to be unprofitable. By the way, in this case the opposite position on all the components could provide a positive result when playing on exchange rate fluctuations.
Maximizing capital - a new approach
Is there any other way to limit the risk? Yes, it exists, but we partially deprived of the possibility of gain from the differential rates between the pound and the yen. At the heart of risk management, which uses only two tools, which correlate with each other, is the need to eliminate the risk of using oppositely directed positions, whose size is calculated as the product of the correlation coefficient for the private use of the standard deviations of assets [4]. This principle works quite well in the futures markets.
For example, 9 of long futures pound fully cover the loss on the 2 short yen during the analyzed period of time. If we try to apply the same principle in FOREX, we find: exchange rate risk on the one hundred thousandth contract dollar / yen will be covered position in the pound / dollar rate of not less than $ 4 million.
It would seem that this question has been: it is enough to calculate the correlation, standard deviation, and then find out hedge ratio. But the correlation behaves quite unstable, constantly fluctuating widely. For example, a 21-day correlation for the period under discussion ranged from -0.66 to +0.98 with a mean of +0.27 (Fig. 4).
Fig. 4. Pound / yen with 21-day correlation between the pound / dollar and dollar / yen.
Increase in the period although it smooths out the behavior, but does not improve the understanding: oscillations 50-period correlation from January to June ranged from -0.01 to 0.86. In addition, the task is complicated by the nature of the behavior of the standard deviation, especially for highly varying rates of pound / dollar.
Actual market behavior indicates: hedge ratio should be constantly changing, if we seek the most optimal variant of risk management. The problem of dynamic hedging, and there is very similar re-balancing to be applied in strategies for volatility. Can I still somehow determine the size of the required items? To answer this question, had to investigate the behavior of the hedge, which proved to be quite closely related to the correlation between the exchange rates.
We call attention to a simple fact: the cross-trading the pound / yen, in reality we are dealing with the spread between the dollar value of the position of the yen and the pound. Since the natural purpose of a speculator and investor is to maximize the dollar value (at least, so we assume), then should we not pay attention to this aspect?
The answer given two graphs showing the dependence of the dollar value of futures positions on the yen and the pound on the coefficient of correlation and hedge ratio, calculated according to the traditionally used method of hedging (Fig. 5 and 6).
Fig. 5. The dollar value of futures yen / dollar and pound / dollar, as compared with the 20-day correlation coefficient (used splines).
Inquisitive person asked in the letter ...
One day I received a letter in which the author asked the board: how to cover the price risk on the currency pair Pound / Yen? I must say, the trader, this is highly commendable: rare really inquisitive person engaged in commerce in the financial markets, strange as it sounds. The main incentive that motivates him to a deal where he was in a long position on the pound and the yen on short, were betting, or rather - their differential. Trader estimated that if the price will not move anywhere, then a year he gets a little more than nine "shapes" as a result of payments on swap of 2.5 points on a daily basis to the position of the two lots. This meant, he explained in a letter that the amount required to maintain the position, increased approximately seven times.
But miracles do not happen, prices fluctuate, and the market is unlikely to want to give the ability to easily get rich. Therefore, the trader and the question arose: how can we try to cover the risk of existing positions, using, for example, options? His question was rather curious, has no clear answer and solutions, and therefore it is interesting to explore the possibility of price risk management rates of currency exchange. The article shows the basic options and, therefore, emphasis is placed on a common methodology, which is illustrated by examples. Select a period which I consider here, is sporadic and not dictated by technical or fundamental analysis of the situation. For simplicity, I stopped at the interval, covering January - end of May 2002.
Purpose creates tools and - to no avail ...
First, find out the true purpose of the position of the pound / yen in the game on interest rates. The first idea that comes to mind is this: if we are going to benefit from the differential rates, not whether we should cover is interest rate risk, rather than price? This argument has a fundamental under the soil - a global effect of Fisher, which determines the relationship between rates and rates. If you follow the theory, to cover interest rate risk is to use interest instruments that are traded today in abundance on the stock and OTC markets [1]. Because in this case the exchange rate and the differential rates are determined by short-term rates, it is logical to assume the possibility of short sterling (short sterling) and the euro (euroyen). And on evroiene could explore the possibility of using different tools: LIBOR, TIBOR or 3-month.
I stress that while this is only a hypothesis, which we are discussing to have a full understanding of the object under study. But recourse to prices, rather, to their dynamics, showed the impossibility of using these instruments to cover losses that could arise as a result of price fluctuations. Although the theory of general law, but the real market does not want to follow it and demonstrates change of course, while interest rate futures are almost immobile. For example, in the individual periods when the pound / yen unchanged at 200 points, short sterling and the euro (futures) almost did not change in price. Thus, the original idea fails, and should more seriously explore the issue.
All the power in the simplicity
Turning to the market of futures contracts, we immediately face the problem of inconsistency of contracts used in the FOREX and futures market. Futures are a direct quotation, and the size of contracts correspond 62,500 pounds and 12,500,000 yen. In a randomly selected time, 14 January 2002, when the pound / dollar 1.4496, the dollar / yen 131.84, and the pound / yen 191.14 - the June futures are traded as follows: pounds 143.58 (multiplier 100), 76.38 yen (multiplier 10000), which gave the course pound / yen 187.98. In translating the dollar value of futures contract was a pound to almost $ 90,000, and on the yen - $ 95.5 thousand. Obviously, the use of futures, we will remain uncovered risk, if we trade on FOREX-billion dollar contracts for $ 100,000. If there is an opportunity to use the contracts of other, smaller size, this problem can be removed. A different solution is to increase the position size to such magnitude that the futures and cash positions consistent with each other. It makes sense to use the mini-contracts. Of course, there is always the option to assume the residual risk of having a meaning, if we feel confident about "upstairs". So, why has the situation when we bought a pound, sold the yen, trading originally $ 100 thousand, and the hedge position in the FOREX, a very short contract for a pound and one long on the yen (Figure 1 and 2)?
Fig. 1. Pound / dollar daily chart: from 14 January to 31 May 2002
Fig. 2. Dollar / yen, the daily schedule: from 14 January to 31 May 2002
By 31 May, we could get the loss on the pound / euro at $ 6058 (pound / dollar 1.4543, the dollar / yen 124.13, and the pound / yen 191.14). Proceeds from the swap would provide $ 2490 (Of course, if the broker charges a differential, in this case is about 3.15% per year), which do not cover the loss. However, oppositely directed positions in futures would bring a total profit of $ 4012 (on the yen - a gain 5200, and a pound - a loss in 1187). Summing up all together, we have a total profit of $ 445. It could take place only in the case of interest. Also note: in the analysis used prices at the end of the day, but hours trading session, the futures market and FOREX differ, so in reality, the results would be slightly worse. In addition, the influence spread in prices the demand-supply in this case is not taken into account.
By the way, recently opened a futures contract for trading the pound / yen, which eliminates the need to use different contracts (with the same success we could apply the currency pair euro / pound and the euro / yen). Finally, an important question: how many more need of money to hold these positions? If you focus on practice (shoulder on the FOREX market is 1:100), then a lot more than the very cash position. Last but not least, will the agent take into account the available positions in the aggregate. Although the major brokerage houses are now without any problems provide access from one account and the market FOREX, and to derivative instruments.
Next option - options
I can not ignore the options markets, providing the opportunity to speculate as well as cover the risks. The options here may be countless. Let us just some of them having bright features. First, let's see how options behave themselves "in the money". We choose June-150-Put a pound (in futures) traded on Jan. 14 at 7.30 ($ 4562), and the yen in June-72-call cost 5.00 ($ 6250). By the end of May first brought us to a loss of $ 1750, and the second - profit $ 4425. The total profit of $ 2,675 does not cover the loss on the spot position. Strategy in the amount of loss turned into $ 892. As we see, the desire to reduce risk through stock options has turned a small, but a loss. This does not mean that if we used other option series, we would have made the same result. The most obvious advantage - the possibility of early retirement with a greater benefit than using futures as a tool to cover the risk.
For example, if the pound / yen rose rapidly after a month or two after the creation of positions, we felt the need to get out of it early. Options, not having time to experience the corrosive influence of the decay time [2], could be of great value. In the proposed version to cover the risk, we need additional resources amounting to $ 10.776, that given the margin for positions in FOREX very unattractive. So let us turn to a strategy that attracts novice players, since it does not require such a significant capital.
It is a strategy which combines "cap" ("ceiling") and "Flo" (floor), in other words - buying and selling of options "outside money". While the price of the asset being hedged is between the price of performance options, the strategy does not manifest itself, except for the need to divert margin. But when the price rushes outside exercise prices, the strategy begins to behave similar to the position in the underlying asset. More attractive point is the possibility of selection of exercise prices at which the strategy will itself fund, if not take into account the margin. Selected for the strategy options (on the principle of "debit = credit") are presented in Table 1, while showing the results for the period.
Note: in this case the result was 24% more efficient than using futures. In this case as a whole would have less margin of at least two times, which suggests a much more substantial. Of course, this does not cover the loss in position on the pound / yen, but it provides an aggregate gain of $ 1,382 as a result of cash inflows from the swap. The third option - the most difficult of all, since it requires thorough preparation and understanding of the mechanism of dynamic risk management. Such strategies are adopted to determine how the purchase or sale of volatility. In fact, they are based on the retention of the main positions in options, which are regularly hedged underlying asset in the amount necessary to establish neutrality on the market.
In general, these strategies are fairly simple, but they are fraught with many pitfalls. The greatest difficulty lies in choosing the principles of rebalancing, on which, in fact, depends, the result will be positive or negative. In our case, the strategy calls for buying at least two options "at the money": Put to the pound and the call for the yen. Accordingly, the maximum amount of position on the currency increase to at least $ 180,000. Because risk management strategies volatility requires a minimum trade reasonable lots, in this version there is a need for lots of $ 10,000. If this is not possible, and we have to sell 100-thousand contracts, the maximum position on FOREX swell to $ 1,800,000, and we need at least 20 options contracts.
We are now more interested in the result, so forget about the amount of positions and see what would such a risk-management when trading the 10-thousand contracts.
Thus, the initial position - we use $ 90,000 for a position on the pound / yen. Coverage risk is through the purchase of two June-144-Put a pound (3.35 = $ 2031, which requires the position of $ 4062) and two 76-June-Call for yen (2.19 = $ 2,737, to the position - $ 5475). Calculating the rebalancing options, changing the volume of foreign exchange position for every pound of 100 points and over 200 points on the yen (it is substantially more volatile in terms of standard deviation), shows: the pound brought the final loss of about $ 1000. Profits on the FOREX in the amount of $ 3000 does not cover the loss in options, is $ 4000. Ian gives the best result, which depends on the principle of risk management can range from zero to + $ 2000, will assess the likely outcome of a $ 1000 prize [3].
If our goal - to receive income from interest payments on the swap, very bad, that managed to neutralize the risk of exchange rate fluctuations and to obtain a result rehedzhirovaniya zero result. Accordingly, interest income deduce strategy in the category of successful, providing a $ 2250 profit for every $ 90,000 of seed capital used to create foreign exchange position.
Yield similar to interest payments
What is the relative yield of all investigated operations? Simple answer to this question is difficult because from different brokers margin varies. Estimated - yield ranged from -20% to +90% per annum (if we trade on FOREX 100000th contract, with $ 1000), and it is determined the selected method of risk management. Successful transactions confidently yield may reach 20-75% per annum. The range is great enough. Much, if not all, depends on the correct choice of tools covering the risks as well as management positions.
Placed in the very early goal was to find opportunities to eliminate price risk in order to safely receive interest income from the differential rates. We have achieved this goal. Naturally, simple methods have the lowest incomes, sophisticated techniques to provide increased yield, comparable to the norm for operations with derivatives of the active risk management. Please note: we are not talking about the limits traditionally used when exiting unprofitable trades, because there are all too intuitive.
Abstracting from the speculative components of the strategy, which has in its composition FOREX-position and a set of instruments covering the risk, we find: it provides a regular incoming cash flow, which resembles the interest payments on bonds. The difference is that here the coupons are redeemed each day. Since the price risk in general is eliminated, the price behavior of a synthetic instrument, which includes spot position and instruments cover the risk, similar to a bond, decreasing in price as the coupon redemption.
If you do not resort to the neutralization of price risk, you can expect: the pound / yen will fall exactly on the value of interest payments. This tendency is quite clear, if you do not pay attention to the speculative fluctuations.
Fig. 3. Synthetic bond created by foreign exchange and futures positions.
Figure 3 illustrates the behavior of the strategy used to cover the risk of futures contracts on the yen and the pound. Since our goal - to get the maximum dollar profit, then created synthetics represented in dollar terms for the appropriate courses. Of course, if the broker does not charge interest on the swap, the strategy turns out to be unprofitable. By the way, in this case the opposite position on all the components could provide a positive result when playing on exchange rate fluctuations.
Maximizing capital - a new approach
Is there any other way to limit the risk? Yes, it exists, but we partially deprived of the possibility of gain from the differential rates between the pound and the yen. At the heart of risk management, which uses only two tools, which correlate with each other, is the need to eliminate the risk of using oppositely directed positions, whose size is calculated as the product of the correlation coefficient for the private use of the standard deviations of assets [4]. This principle works quite well in the futures markets.
For example, 9 of long futures pound fully cover the loss on the 2 short yen during the analyzed period of time. If we try to apply the same principle in FOREX, we find: exchange rate risk on the one hundred thousandth contract dollar / yen will be covered position in the pound / dollar rate of not less than $ 4 million.
It would seem that this question has been: it is enough to calculate the correlation, standard deviation, and then find out hedge ratio. But the correlation behaves quite unstable, constantly fluctuating widely. For example, a 21-day correlation for the period under discussion ranged from -0.66 to +0.98 with a mean of +0.27 (Fig. 4).
Fig. 4. Pound / yen with 21-day correlation between the pound / dollar and dollar / yen.
Increase in the period although it smooths out the behavior, but does not improve the understanding: oscillations 50-period correlation from January to June ranged from -0.01 to 0.86. In addition, the task is complicated by the nature of the behavior of the standard deviation, especially for highly varying rates of pound / dollar.
Actual market behavior indicates: hedge ratio should be constantly changing, if we seek the most optimal variant of risk management. The problem of dynamic hedging, and there is very similar re-balancing to be applied in strategies for volatility. Can I still somehow determine the size of the required items? To answer this question, had to investigate the behavior of the hedge, which proved to be quite closely related to the correlation between the exchange rates.
We call attention to a simple fact: the cross-trading the pound / yen, in reality we are dealing with the spread between the dollar value of the position of the yen and the pound. Since the natural purpose of a speculator and investor is to maximize the dollar value (at least, so we assume), then should we not pay attention to this aspect?
The answer given two graphs showing the dependence of the dollar value of futures positions on the yen and the pound on the coefficient of correlation and hedge ratio, calculated according to the traditionally used method of hedging (Fig. 5 and 6).
Fig. 5. The dollar value of futures yen / dollar and pound / dollar, as compared with the 20-day correlation coefficient (used splines).
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