The Exponential Nature of Compound and Decay in Position Sizing

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The Anti-Martingale Approach in Position Sizing and the Exponential Nature of Compounding and Decay

When using 1% of your capital per trade, both exponential compounding and exponential decay are essentially two sides of the same coin. This is because your position size always adjusts in proportion to your total capital, whether it increases due to profits or decreases due to losses. Let's break it down further and explore its connection to the Anti-Martingale strategy.

1. Compounding Exponentially in Position Sizing
This occurs when your capital grows, leading to a larger 1% allocation per trade. Every time your capital increases, the 1% used in the next trade is larger, which results in compounding growth.

Example of Compounding:

Initial Capital: $10,000
Position Size: 1% of $10,000 = $100 per trade
If you have a successful trade and gain 10%:

Profit: $100 * 10% = $10
New Capital: $10,000 + $10 = $10,010
Now, for the next trade:

New Position Size: $10,010 * 1% = $100.10
With each gain, your position size grows because 1% of a growing total is larger, meaning you're "compounding" your returns.

2. Exponential Decay in Position Sizing
Exponential decay happens when your capital shrinks, leading to a smaller 1% allocation per trade. This automatically reduces the size of your position on each subsequent trade, which minimizes further losses as your capital declines.

Example of Exponential Decay:

Initial Capital: $10,000
Position Size: 1% of $10,000 = $100 per trade
If you experience a 10% loss:

Loss: $100 * 10% = $10
New Capital: $10,000 - $10 = $9,990
For the next trade:

New Position Size: $9,990 * 1% = $99.90
With each loss, your position size decreases, preserving more capital and protecting against steep drawdowns.

3. Why Are They Essentially the Same?
In both cases, you're simply adjusting your position size based on the size of your current capital, which grows with profits and shrinks with losses. This constant adjustment—whether increasing or decreasing—creates an exponential relationship between your capital and your position size over time. You are always taking 1% of your capital, which means:

When you profit, your position size grows exponentially.
When you lose, your position size decays exponentially.

Thus, both processes—whether the capital is increasing or decreasing—are based on the same principle: you are continuously adjusting 1% of your capital, leading to exponential growth or decay depending on the trade outcomes.

4. Detailed Example:
Scenario 1: Winning Trades (Compounding)

Initial Capital: $10,000

Position Size: $10,000 * 1% = $100

Profit: 10% = $10

New Capital: $10,000 + $10 = $10,010

New Position Size: $10,010 * 1% = $100.10

Profit: 10% = $10.01

New Capital: $10,010 + $10.01 = $10,020.01

New Position Size: $10,020.01 * 1% = $100.20

Profit: 10% = $10.02

New Capital: $10,020.01 + $10.02 = $10,030.03

Here, each trade builds upon the last, increasing the capital and therefore increasing the size of 1%.

Scenario 2: Losing Trades (Decay)

Initial Capital: $10,000

Position Size: $10,000 * 1% = $100

Loss: 10% = $10

New Capital: $10,000 - $10 = $9,990

New Position Size: $9,990 * 1% = $99.90

Loss: 10% = $9.99

New Capital: $9,990 - $9.99 = $9,980.01

New Position Size: $9,980.01 * 1% = $99.80

Loss: 10% = $9.98

New Capital: $9,980.01 - $9.98 = $9,970.03

Here, each loss reduces the capital, and therefore the size of 1% decreases accordingly.

5. The Anti-Martingale Connection
The Anti-Martingale strategy is inherently reflected in this position sizing approach. In this strategy:

When Winning: You increase your position size as your capital grows, just like in the Anti-Martingale approach where you increase your bet size after a win.

When Losing: You decrease your position size as your capital shrinks, mirroring the Anti-Martingale approach where you reduce your bet size after a loss.

By following this principle, you capitalize on winning streaks by gradually increasing your exposure, while simultaneously protecting your capital during losing periods by reducing your risk. This dynamic adjustment aligns with the core philosophy of the Anti-Martingale strategy, ensuring that you maximize gains during favorable market conditions and minimize losses during downturns.

This approach, rooted in the principles of Anti-Martingale, provides a robust framework for managing risk and optimizing returns through disciplined, adaptive position sizing.