Let me first state the conclusion.

In the futures market, there is a way to play rolling positions. Taking a long position as an example, rolling positions involve buying more as the price rises until you can buy no more.

For example, if the initial capital is $100 and the leverage is set to 3 times, then under non-rolling positions, the maximum amount that can be opened is $300.

The strategy for rolling positions is: under 3x leverage, the initial can only open $300, as the stock price rises, the account shows floating profit, and the floating profit is used to continue to open long positions until no more can be opened.

If the stock price doubles, under a non-rolling strategy, the final profit can be $300. (After closing, the account balance is $300*2=$600, after repaying $200 of the loan, the account balance is $400, subtracting the principal of $100, yielding a net profit of $300.)

If the stock price doubles, how much can I ultimately earn in dollars under the rolling position strategy?

Let me first state the conclusion: You can earn $700.

The following table shows the difference between profits (including principal) in non-rolling positions and rolling positions under different leverage when the stock price doubles.

Calculation method

For non-rolling futures contracts, the profit formula is relatively easy to calculate.

Let a be the leverage, x be the multiple of the price, and y be the multiple of the account balance (including principal) after closing, then there is

For example, under 3x leverage, if the price is 2 times the original, then a=3, x=2, y=4, which means the account balance is 4 times the original.

What is the profit formula for rolling futures contracts?

(Note that the rolling position mentioned in this article defaults to a long rolling position, not a short rolling position. Also, once the initial leverage is set, it should not be changed.)

A very important property of rolling positions is: whenever a new high is created, when the price rises to a level where more can be purchased, execute the addition; at this point, it is equivalent to closing all positions and immediately opening a full position with the same leverage.

For example, with an initial $100, 3x leverage on a long position, the initial stock price is $10, and the minimum opening amount is $3 (the minimum opening amount is $3 for each trade, but with 3x leverage, only $1 capital is needed to open). When the stock price rises to $10.001, the account balance becomes $300.3, at this point there isn't enough profit to open a long position. When the stock price rises to $10.004, the account balance becomes $301.2, and at this point, I can use the $1.2 profit to continue opening a long position with 3x leverage. This is rolling position.

This corresponds to when I closed all positions at $10.004, at which point the account balance was $301.2. Then I opened a long position with the full amount.

This property is key to deriving the profit formula for rolling positions. Let me give a deeper example:

For example, at moment A, when the price rises to 1.2 times the original, the account balance becomes 1.4 times the original.

So when the price rises to 1.44 times the original, how many times is the account balance compared to the original? It’s equivalent to me closing all positions at moment A and then immediately restarting the rolling position, so the account balance is multiplied by 1.4 again on top of the initial 1.4 times.

Therefore, a property can be summarized: when x becomes x squared, y also becomes y squared. Only exponential functions satisfy this property.

Thus we assume that

What should the parameter b be? At this point, the idea of calculus can be referenced.

When the price rises very slightly, rolling positions have not yet been executed on a large scale, and thus the profits from rolling and non-rolling positions should be almost the same.

For example, with 3x leverage, when the price is 1.0001 times the initial price, the profit from non-rolling positions (including principal) is y=a*x-(a-1)=1.0003.

The profit from rolling positions (including principal) is

Letting the two be equal, we can derive b=3.

Exactly the leverage of 3.

Thus, it can be concluded that the profit formula for rolling positions is

Practical fitting

I wrote rolling position code, which is practically used in cryptocurrency contract trading.

The following chart shows the fitting curve for 3x leverage of wld, and it can be seen that the actual will be slightly lower than the fitting curve because opening positions is discrete and has a minimum opening precision.

The following chart shows the fitting curve for 4x leverage of xvg:

Theoretical profit curve

I listed the balance under different leverages (3/4/5) in relation to price changes (the horizontal axis is the price relative to the opening price, and the vertical axis is the total amount in the account (including floating profit and principal, in other words, the account balance immediately after closing) relative to the initial capital):

It can be seen that the power of exponential functions far exceeds that of linear functions. If the price doubles, a 5x leveraged rolling position can yield 32 times the profit!

However, the risks of rolling positions are also evident: taking 3x leverage as an example, the liquidation price in a rolling position mode is at 0.667 of the highest point since opening the position. This means that if the subsequent market experiences a spike followed by a pullback, rolling positions are likely to incur significant losses.

The essence of rolling positions is to transfer the risk of triggering a stop loss due to high leverage after opening a position.

Taking 3x leverage as an example, the risk of liquidation under non-rolling positions is: the price drops to 2/3 of the opening price.

Rolling positions bear the risk of liquidation, which happens when the price drops to 2/3 of the highest point after opening.

Some explorations

I also explored a question: after the price drops, if I immediately close the position and then open a full position with the same leverage, when the price returns, can the account break even?

If not rolling positions, it's clearly impossible to break even. For example, if the initial capital is $100 and a long position is taken with 3x leverage. After opening a position, if the price directly drops 10%, the account drops 30%, leaving a balance of $70. At this point, if closed, then opening a long position with $70 at 3x leverage. When the price returns (needs to rise 1/9), you earn 1/3 of the $70, which doesn't allow you to return to $100.

If rolling positions, can I break even?

Let a be the leverage and x be the drop percentage.

Thus, when the price returns, the balance as a percentage of the original initial capital is: (1-a*x)*(1-x)**(-a)

The following chart shows the account balance under different values of a and x. It can be seen that regardless of the combination, they are strictly less than 1, meaning that they cannot return to the principal.

If after the price drops, I immediately close the position and then roll with the same initial capital of $100. When the price returns, can I break even?

Not only can it, but it can also be profitable, with the profit amount being (1-x)**(-a)-a*x-1.

The quantity relationship is shown in the figure below. For example, with $100 at 3x leverage, if it drops 30%, it is close to liquidation. At this point, if I close and reopen with $100 in a rolling position, when the price returns to the original opening price, the profit amount (including principal) is about 2 times the original (around $201).

If it drops 20%, then executing a close and reopening with $100, when the price returns, I can earn an additional profit of about 0.35 (or $35).

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