How to calculate the arbitrage profit virtual currency
Publish: 2021-04-23 05:03:49
1. Futures speculation and arbitrage
spread arbitrage
generally speaking, the profit and loss of spread arbitrage can be calculated with the following formula:
spread arbitrage profit and loss = Σ The profit and loss of each futures contract (30)
generally, spread arbitrage can be divided into buy arbitrage and sell arbitrage. Buying arbitrage refers to the arbitrage behavior that if the arbitrager expects the spread of futures contracts in different delivery months to expand, the arbitrager will buy the "leg" with higher price and sell the "leg" with lower price. Selling arbitrage means that if the arbitrager expects the price difference of futures contracts in different delivery months to narrow, the arbitrager will sell the "leg" with higher price and buy the "leg" with lower price
therefore, the arbitrage profit and loss can also be calculated by the following formula:
the profit and loss of buying arbitrage = the price difference when closing the position - the price difference when building the position (31)
the profit and loss of selling arbitrage = the price difference when building the position - the price difference when closing the position (32)
spread arbitrage
generally speaking, the profit and loss of spread arbitrage can be calculated with the following formula:
spread arbitrage profit and loss = Σ The profit and loss of each futures contract (30)
generally, spread arbitrage can be divided into buy arbitrage and sell arbitrage. Buying arbitrage refers to the arbitrage behavior that if the arbitrager expects the spread of futures contracts in different delivery months to expand, the arbitrager will buy the "leg" with higher price and sell the "leg" with lower price. Selling arbitrage means that if the arbitrager expects the price difference of futures contracts in different delivery months to narrow, the arbitrager will sell the "leg" with higher price and buy the "leg" with lower price
therefore, the arbitrage profit and loss can also be calculated by the following formula:
the profit and loss of buying arbitrage = the price difference when closing the position - the price difference when building the position (31)
the profit and loss of selling arbitrage = the price difference when building the position - the price difference when closing the position (32)
2. There are many ways of foreign exchange arbitrage, such as hedging arbitrage, triangle arbitrage, gift arbitrage, delay arbitrage, jump arbitrage and so on. In fact, any kind of arbitrage is not difficult. The principle is very simple. It depends on whether you are good at discovering the details
for example, arbitrage is to buy high interest currency and sell low interest currency to earn overnight interest difference between platforms. Is it very simple, but the principal required is relatively large, but the profit is very stable
the so-called triangle arbitrage is an arbitrage method of introcing three currencies. It uses the temporary deviation of three kinds of foreign exchange from reasonable cross price to realize arbitrage. Theoretically, if we have a low delay order platform and can get a low bid ask spread (, then we have a chance to realize risk-free arbitrage
it's even easier to arbitrage with free cash. For example, if you invest $10000 + 15% free cash on platform a, you'll get $11500; if you invest $10000 + 15% free cash on platform B, you'll get $11500. Platform a is long and platform B is short. If the market goes up, platform A's capital will become 23000, and platform B's loss will be 023000 - principal 20000 - free cash 1500 = 1500, There is a profit of about 1000 excluding the handling charge
compared with the above arbitrage methods, delay arbitrage is more technical. But the income is also more violent. It is to take advantage of the poor strength of each platform to find arbitrage opportunities. In short, it is the network delay of AB platform to carry out arbitrage, but this kind of opportunity is usually rare. It needs professional software to cooperate with the market
short jump arbitrage is based on the principle of closing at the weekend and possible short jump on Monday. Traders will place heavy orders on the platform near the closing time on Friday. That is to say, they will place heavy orders above the current price, place heavy short orders at the current price, set a stop loss position, and then after the short jump at the opening price on Monday, they will directly double their profits, It's better not to trade in one account. It's better to operate in two accounts. And it's best to choose the weekend when there is a major market announcement.
for example, arbitrage is to buy high interest currency and sell low interest currency to earn overnight interest difference between platforms. Is it very simple, but the principal required is relatively large, but the profit is very stable
the so-called triangle arbitrage is an arbitrage method of introcing three currencies. It uses the temporary deviation of three kinds of foreign exchange from reasonable cross price to realize arbitrage. Theoretically, if we have a low delay order platform and can get a low bid ask spread (, then we have a chance to realize risk-free arbitrage
it's even easier to arbitrage with free cash. For example, if you invest $10000 + 15% free cash on platform a, you'll get $11500; if you invest $10000 + 15% free cash on platform B, you'll get $11500. Platform a is long and platform B is short. If the market goes up, platform A's capital will become 23000, and platform B's loss will be 023000 - principal 20000 - free cash 1500 = 1500, There is a profit of about 1000 excluding the handling charge
compared with the above arbitrage methods, delay arbitrage is more technical. But the income is also more violent. It is to take advantage of the poor strength of each platform to find arbitrage opportunities. In short, it is the network delay of AB platform to carry out arbitrage, but this kind of opportunity is usually rare. It needs professional software to cooperate with the market
short jump arbitrage is based on the principle of closing at the weekend and possible short jump on Monday. Traders will place heavy orders on the platform near the closing time on Friday. That is to say, they will place heavy orders above the current price, place heavy short orders at the current price, set a stop loss position, and then after the short jump at the opening price on Monday, they will directly double their profits, It's better not to trade in one account. It's better to operate in two accounts. And it's best to choose the weekend when there is a major market announcement.
3. Futures arbitrage refers to a kind of futures contract, when there is a price gap between the futures market and the spot market, so as to make use of the price gap between the two markets, buy low and sell high and make profits. Theoretically, the futures price is the future price of the commodity, and the spot price is the current price of the commodity. According to the same price theory in economics, the gap between the two, namely "basis" (basis = spot price futures price), should be equal to the holding cost of the commodity. Once the basis deviates greatly from the cost of holding, there is a chance of arbitrage. Among them, the price of futures is higher than the price of existing goods, and exceeds the costs used for delivery, such as transportation costs, quality inspection costs, storage costs, the increased costs of issuing invoices, and so on. Futures arbitrage mainly includes forward buying futures arbitrage and reverse buying futures arbitrage
implementation steps
1. Calculate the theoretical price of stock index futures, and estimate the upper and lower boundaries of no arbitrage range of stock index futures contract. The upper and lower bounds of no arbitrage range are related to many parameters, such as the loan interest rate, market liquidity, market shock cost, transaction fees and so on. After determining the parameters and substituting into the formula, we can get the suitable non arbitrage interval. Because the arbitrage opportunity is fleeting, the calculation of no arbitrage interval should be completed in time. In practice, it is often carried out with the help of computer programmed trading
2. Judge whether there are arbitrage opportunities. By monitoring the price trend of futures contract and comparing with no arbitrage range, we can judge whether there is arbitrage opportunity. Only when the futures price falls above or below the upper bound of no arbitrage range, can there be operational arbitrage opportunity
3. To determine the transaction scale, we should consider the expected profit level when determining the transaction scale. The impact of the transaction scale on the market, too large transaction scale will cause high impact cost, which will rece the arbitrage profit. In addition, we should also consider the possibility of financing and securities lending. We can do reverse basis arbitrage
4. Conct stock index futures contract and stock trading at the same time
5. Monitor the profit and loss of arbitrage position to determine whether to increase or decrease positions.
implementation steps
1. Calculate the theoretical price of stock index futures, and estimate the upper and lower boundaries of no arbitrage range of stock index futures contract. The upper and lower bounds of no arbitrage range are related to many parameters, such as the loan interest rate, market liquidity, market shock cost, transaction fees and so on. After determining the parameters and substituting into the formula, we can get the suitable non arbitrage interval. Because the arbitrage opportunity is fleeting, the calculation of no arbitrage interval should be completed in time. In practice, it is often carried out with the help of computer programmed trading
2. Judge whether there are arbitrage opportunities. By monitoring the price trend of futures contract and comparing with no arbitrage range, we can judge whether there is arbitrage opportunity. Only when the futures price falls above or below the upper bound of no arbitrage range, can there be operational arbitrage opportunity
3. To determine the transaction scale, we should consider the expected profit level when determining the transaction scale. The impact of the transaction scale on the market, too large transaction scale will cause high impact cost, which will rece the arbitrage profit. In addition, we should also consider the possibility of financing and securities lending. We can do reverse basis arbitrage
4. Conct stock index futures contract and stock trading at the same time
5. Monitor the profit and loss of arbitrage position to determine whether to increase or decrease positions.
4. This question type is the most common arbitrage calculation. The author of the question is ing other topics, ing the wrong sentence order, causing your misunderstanding
this question should be written as follows
if the quoted price of a stock is 30 yuan, the stock will not pay any dividends within two years. If the quoted price of 2-year futures is 35 yuan, arbitrage can be carried out as follows: purchase 1000 shares, borrow 3000 yuan at 5% annual interest rate, and sell 1000 shares of 2-year futures. Two years later, the delivery of futures contract will get 3500 yuan in cash. What is the profit after repaying the loan
this makes it clear that the process of arbitrage is (there is an implicit assumption in this question, that is, you originally have money to buy stocks) borrowing money to do futures, and paying interest after closing the futures position. So the calculation method of this problem is:
method 1
final stock price = 35-500 / 1000 = 34.5
futures profit = 3500 final value - 3000 principal - 300 interest = 200 profit
spot profit = (34.5-30) × 1000 = 4500
total profit = 4500 + 200
method 2
arbitrage profit = (35-30) × 1000 = 5000
interest = 300
total profit = 5000-300
as for why to borrow 3000 instead of 30000, that is because futures trading is margin trading, you only need a sum of money to guarantee the performance of the contract, as long as your floating loss does not exceed the margin ring this period, in this question, if the futures price rises to more than 38 yuan, (38-35) * 1000 = 3000, The margin is insufficient. The futures company will let you make up the margin. This problem does not examine this point, later exercises may encounter.
this question should be written as follows
if the quoted price of a stock is 30 yuan, the stock will not pay any dividends within two years. If the quoted price of 2-year futures is 35 yuan, arbitrage can be carried out as follows: purchase 1000 shares, borrow 3000 yuan at 5% annual interest rate, and sell 1000 shares of 2-year futures. Two years later, the delivery of futures contract will get 3500 yuan in cash. What is the profit after repaying the loan
this makes it clear that the process of arbitrage is (there is an implicit assumption in this question, that is, you originally have money to buy stocks) borrowing money to do futures, and paying interest after closing the futures position. So the calculation method of this problem is:
method 1
final stock price = 35-500 / 1000 = 34.5
futures profit = 3500 final value - 3000 principal - 300 interest = 200 profit
spot profit = (34.5-30) × 1000 = 4500
total profit = 4500 + 200
method 2
arbitrage profit = (35-30) × 1000 = 5000
interest = 300
total profit = 5000-300
as for why to borrow 3000 instead of 30000, that is because futures trading is margin trading, you only need a sum of money to guarantee the performance of the contract, as long as your floating loss does not exceed the margin ring this period, in this question, if the futures price rises to more than 38 yuan, (38-35) * 1000 = 3000, The margin is insufficient. The futures company will let you make up the margin. This problem does not examine this point, later exercises may encounter.
5. The arbitrage of stock index futures is mainly divided into two types: futures arbitrage and cross month arbitrage
let's talk about futures arbitrage first
futures arbitrage refers to the arbitrage between stock index futures and spot index
there are two kinds of arbitrage opportunities:
1. If the point of stock index futures is larger than that of spot index and exceeds a certain range, it can carry out forward arbitrage of buying spot index and selling stock index futures
2. If the point of stock index futures is less than that of spot index and exceeds a certain range, reverse arbitrage can be carried out to buy stock index futures and sell spot index
to sell spot index, we need to use securities lending to achieve the purpose of selling emerging goods. The operation is complex and not very convenient. Therefore, in practice, the reverse arbitrage of stock index futures is difficult to implement< In other words, when the point of stock index futures is less than that of spot index, arbitrage operation will be more difficult
we mainly study the forward arbitrage technology of "the point of stock index futures is larger than that of spot index"
arbitrage on commodity futures is low risk, but not completely zero risk. The risk of arbitrage is mainly caused by the difficulty of spot delivery. And the arbitrage of stock index futures, because it is cash delivery, delivery is very convenient, and everyone can deliver, completely breaking the barrier of delivery, which makes the arbitrage between stock index futures and spot index become completely zero risk
because of the cash delivery system, the arbitrage technology of stock index futures is much simpler than that of commodity futures. Because the arbitrage of stock index futures can be calculated by mathematical formula. Now let's talk about how to calculate
(1) calculation method of reasonable price difference between futures and cash
as long as the point of stock index futures is higher than that of spot index, and the higher point is greater than the handling fee and capital interest fee, arbitrage of "buying spot index fund and selling stock index futures contract" can be carried out
the specific formula is:
(contract point spot index) × As long as this condition is met, risk-free arbitrage can be carried out
at present, it needs 200000 yuan to sell stock index futures and 1 million yuan to buy spot Index ETF funds, which is 1.2 million yuan in total. The annual loan interest of 1.2 million is about 58300 According to the half year loan interest rate)
the daily interest of 58300 divided by 365 days is 160 yuan
the Commission of futures is 150 yuan for opening and 150 yuan for closing
the transaction fee of ETF in the secondary market is the same as that of stock transaction, except that there is no stamp ty and transfer fee. The minimum charge is 5 yuan. We charge one thousandth of the transaction fee and two thousandth of the transaction fee. Buy 1 million ETF index fund, need 2000 yuan Commission
the specific formula is: 2000 + 300 + 160 × Days. For example, there are 30 days left for delivery, which is 2000 + 300 + 160 × 30=7100
each point of stock index futures represents 300 yuan, and 7100 divided by 300 = 23.6 points
in other words, if the point between the recent month contract to be delivered in 30 days and the CSI 300 index exceeds 23.6, arbitrage will not lose money, which is the arbitrage break even point in 30 days
however, there is no money to earn. To earn money, the price difference should be more than 23.6. If it is more than double, such as 50 points, it is a good arbitrage opportunity
break even point of 2 months and 60 days: (2000 + 300 + 160) × 60) divided by 300 = 40 points
3 months, 90 day breakeven point: (2000 + 300 + 160) × 90) divided by 300 = 56 points
6 months, 180 day breakeven point: (2000 + 300 + 160) × 180) divided by 300 = 104 points
7 months, 210 day breakeven point: (2000 + 300 + 160) × When dividing by 300 = 120 points
arbitrage, we need to pay attention to two points:
1. The delivery date of each month is different, and the specific days need to be calculated
2. All the above price differences are reasonable. Arbitrage can only be carried out if the price difference exceeds this point. If the point is more than twice the reasonable point, the annual zero risk arbitrage profit will exceed 10%
you can talk to me for details
let's talk about futures arbitrage first
futures arbitrage refers to the arbitrage between stock index futures and spot index
there are two kinds of arbitrage opportunities:
1. If the point of stock index futures is larger than that of spot index and exceeds a certain range, it can carry out forward arbitrage of buying spot index and selling stock index futures
2. If the point of stock index futures is less than that of spot index and exceeds a certain range, reverse arbitrage can be carried out to buy stock index futures and sell spot index
to sell spot index, we need to use securities lending to achieve the purpose of selling emerging goods. The operation is complex and not very convenient. Therefore, in practice, the reverse arbitrage of stock index futures is difficult to implement< In other words, when the point of stock index futures is less than that of spot index, arbitrage operation will be more difficult
we mainly study the forward arbitrage technology of "the point of stock index futures is larger than that of spot index"
arbitrage on commodity futures is low risk, but not completely zero risk. The risk of arbitrage is mainly caused by the difficulty of spot delivery. And the arbitrage of stock index futures, because it is cash delivery, delivery is very convenient, and everyone can deliver, completely breaking the barrier of delivery, which makes the arbitrage between stock index futures and spot index become completely zero risk
because of the cash delivery system, the arbitrage technology of stock index futures is much simpler than that of commodity futures. Because the arbitrage of stock index futures can be calculated by mathematical formula. Now let's talk about how to calculate
(1) calculation method of reasonable price difference between futures and cash
as long as the point of stock index futures is higher than that of spot index, and the higher point is greater than the handling fee and capital interest fee, arbitrage of "buying spot index fund and selling stock index futures contract" can be carried out
the specific formula is:
(contract point spot index) × As long as this condition is met, risk-free arbitrage can be carried out
at present, it needs 200000 yuan to sell stock index futures and 1 million yuan to buy spot Index ETF funds, which is 1.2 million yuan in total. The annual loan interest of 1.2 million is about 58300 According to the half year loan interest rate)
the daily interest of 58300 divided by 365 days is 160 yuan
the Commission of futures is 150 yuan for opening and 150 yuan for closing
the transaction fee of ETF in the secondary market is the same as that of stock transaction, except that there is no stamp ty and transfer fee. The minimum charge is 5 yuan. We charge one thousandth of the transaction fee and two thousandth of the transaction fee. Buy 1 million ETF index fund, need 2000 yuan Commission
the specific formula is: 2000 + 300 + 160 × Days. For example, there are 30 days left for delivery, which is 2000 + 300 + 160 × 30=7100
each point of stock index futures represents 300 yuan, and 7100 divided by 300 = 23.6 points
in other words, if the point between the recent month contract to be delivered in 30 days and the CSI 300 index exceeds 23.6, arbitrage will not lose money, which is the arbitrage break even point in 30 days
however, there is no money to earn. To earn money, the price difference should be more than 23.6. If it is more than double, such as 50 points, it is a good arbitrage opportunity
break even point of 2 months and 60 days: (2000 + 300 + 160) × 60) divided by 300 = 40 points
3 months, 90 day breakeven point: (2000 + 300 + 160) × 90) divided by 300 = 56 points
6 months, 180 day breakeven point: (2000 + 300 + 160) × 180) divided by 300 = 104 points
7 months, 210 day breakeven point: (2000 + 300 + 160) × When dividing by 300 = 120 points
arbitrage, we need to pay attention to two points:
1. The delivery date of each month is different, and the specific days need to be calculated
2. All the above price differences are reasonable. Arbitrage can only be carried out if the price difference exceeds this point. If the point is more than twice the reasonable point, the annual zero risk arbitrage profit will exceed 10%
you can talk to me for details
6. There are many ways of foreign exchange arbitrage
, such as hedging arbitrage, triangle arbitrage, gift arbitrage, delay arbitrage, jump arbitrage and so on. In fact, any kind of arbitrage is not difficult, the principle is very simple, it depends on whether you are good at finding the details carefully
for example, arbitrage is to buy high interest currency and sell low interest currency to earn overnight interest difference between platforms. Is it very simple, but the principal required is relatively large, but the profit is very stable
the so-called triangle arbitrage is an arbitrage method of introcing three currencies. It uses the temporary deviation of three kinds of foreign exchange from reasonable cross price to realize arbitrage. Theoretically, if we have a low delay order platform and can get a low bid ask spread (, then we have a chance to realize risk-free arbitrage
it's easier to arbitrage with free cash. For example, if you invest $10000 + 15% free cash on platform a, you'll get $11500; if you invest $10000 + 15% free cash on platform B, you'll get $11500. Platform a is long and platform B is short. If the market goes up, platform A's capital will turn to 23000, and platform B will lose to 0.
23000 - principal 20000 - platform free cash 1500 = 1500 profit, There is a profit of about 1000 excluding the handling charge
compared with the above arbitrage methods, delay arbitrage is more technical. But the income is also more violent. It is to take advantage of the poor strength of each platform to find arbitrage opportunities. In short, it is the network delay of AB platform to carry out arbitrage, but this kind of opportunity is usually rare. It needs professional software to cooperate with the market
short jump arbitrage is based on the principle of closing at the weekend and possible short jump on Monday. Traders will place heavy orders on the platform near the closing time on Friday. That is to say, they will place heavy orders above the current price, place heavy short orders at the current price, set a stop loss position, and then after the short jump at the opening price on Monday, they will directly double their profits, It's better not to trade in one account. It's better to operate in two accounts. And it's best to choose the weekend when there is a major market announcement.
, such as hedging arbitrage, triangle arbitrage, gift arbitrage, delay arbitrage, jump arbitrage and so on. In fact, any kind of arbitrage is not difficult, the principle is very simple, it depends on whether you are good at finding the details carefully
for example, arbitrage is to buy high interest currency and sell low interest currency to earn overnight interest difference between platforms. Is it very simple, but the principal required is relatively large, but the profit is very stable
the so-called triangle arbitrage is an arbitrage method of introcing three currencies. It uses the temporary deviation of three kinds of foreign exchange from reasonable cross price to realize arbitrage. Theoretically, if we have a low delay order platform and can get a low bid ask spread (, then we have a chance to realize risk-free arbitrage
it's easier to arbitrage with free cash. For example, if you invest $10000 + 15% free cash on platform a, you'll get $11500; if you invest $10000 + 15% free cash on platform B, you'll get $11500. Platform a is long and platform B is short. If the market goes up, platform A's capital will turn to 23000, and platform B will lose to 0.
23000 - principal 20000 - platform free cash 1500 = 1500 profit, There is a profit of about 1000 excluding the handling charge
compared with the above arbitrage methods, delay arbitrage is more technical. But the income is also more violent. It is to take advantage of the poor strength of each platform to find arbitrage opportunities. In short, it is the network delay of AB platform to carry out arbitrage, but this kind of opportunity is usually rare. It needs professional software to cooperate with the market
short jump arbitrage is based on the principle of closing at the weekend and possible short jump on Monday. Traders will place heavy orders on the platform near the closing time on Friday. That is to say, they will place heavy orders above the current price, place heavy short orders at the current price, set a stop loss position, and then after the short jump at the opening price on Monday, they will directly double their profits, It's better not to trade in one account. It's better to operate in two accounts. And it's best to choose the weekend when there is a major market announcement.
7. If the futures price is much higher than the spot, you can buy the spot and short the futures. When the futures are delivered, you make a profit on the futures price spot price. This kind of arbitrage basically has no risk and only pays the time cost of capital
for example, the current spot price is 100, and the futures price next month is 150. Then one month later, the futures delivery, you can make 150-100 = 50.
for example, the current spot price is 100, and the futures price next month is 150. Then one month later, the futures delivery, you can make 150-100 = 50.
8. Take silver as an example:
traditional theory: futures price = spot price + holding cost + premium, etc. according to the delivery period, storage and transportation expenses, the holding cost + premium can be roughly calculated. If the total holding and delivery cost of silver futures 1406 contract and spot silver delay Shanghai T + D is 100, then theoretically, the price of futures 1406 should be higher than TD100 points. If one day's market fluctuation leads to the futures price higher than td150 points, then you can buy TD, sell futures, wait until the delivery period, use td to collect the spot, deliver to the futures for performance, the cost is 100 points, and the price difference is 150, you can get 50 points of risk-free profit
now, after the opening of futures night trading, arbitrage trading can be realized completely by closing positions without delivery. There is an assumption that the futures and spot prices maintain an equilibrium position in the short term. If the spread deviates, the reverse opening can be synchronized and arbitrage profits can be obtained after the spread returns. As mentioned above, if the price difference between futures 1406 and TD is 100 in the short term, if the market suddenly changes one day and the price difference becomes 120, you can short futures and long TD. When the price difference returns to 100, you can close the position. The gross profit is 20 points, the handling fee is about 5 points, and the net profit is 15 points. This kind of arbitrage transaction is convenient, simple, low risk and stable.
traditional theory: futures price = spot price + holding cost + premium, etc. according to the delivery period, storage and transportation expenses, the holding cost + premium can be roughly calculated. If the total holding and delivery cost of silver futures 1406 contract and spot silver delay Shanghai T + D is 100, then theoretically, the price of futures 1406 should be higher than TD100 points. If one day's market fluctuation leads to the futures price higher than td150 points, then you can buy TD, sell futures, wait until the delivery period, use td to collect the spot, deliver to the futures for performance, the cost is 100 points, and the price difference is 150, you can get 50 points of risk-free profit
now, after the opening of futures night trading, arbitrage trading can be realized completely by closing positions without delivery. There is an assumption that the futures and spot prices maintain an equilibrium position in the short term. If the spread deviates, the reverse opening can be synchronized and arbitrage profits can be obtained after the spread returns. As mentioned above, if the price difference between futures 1406 and TD is 100 in the short term, if the market suddenly changes one day and the price difference becomes 120, you can short futures and long TD. When the price difference returns to 100, you can close the position. The gross profit is 20 points, the handling fee is about 5 points, and the net profit is 15 points. This kind of arbitrage transaction is convenient, simple, low risk and stable.
9. First of all, the problem of this topic should not be asking you to ask for delivery cash in two years
secondly, "the stock will not pay any dividends within two years", which can be calculated directly by 35 * 1000 hands
finally, in reality, there are basically no quotations for indivial stock futures in the past two years, and it doesn't matter how this 3500 is obtained
don't try to be a bull's horn, but look at your body shape. It should be the type that will benefit you in the end.
secondly, "the stock will not pay any dividends within two years", which can be calculated directly by 35 * 1000 hands
finally, in reality, there are basically no quotations for indivial stock futures in the past two years, and it doesn't matter how this 3500 is obtained
don't try to be a bull's horn, but look at your body shape. It should be the type that will benefit you in the end.
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