Sigmoid Allocation Indicator & Dashboard

TL;DR This sigmoid-based allocation indicator tells you percentage of your portfolio to invest based on how much the market has dropped.

Market at all-time high? → Stay defensive, invest less (e.g., 30%)
Market crashed hard? → Get aggressive, invest more (e.g., 100%)

The "sigmoid" part just means the transition between these two extremes follows a smooth S-shaped curve.

Description
This indicator is a sigmoid-based allocation system that dynamically adjusts a portfolio exposure based on market drawdown.
It compares multiple steepness curves (K values) to find your optimal risk profile for leveraged ETF strategies, but it can also be used to scale in-out from stocks, crypto and to understand whether to use leverage or not.

The Sigmoid Allocation Dashboard helps you to dynamically adjust a portfolio allocation based on how much a market has dropped from its all-time high.
I've implemented it using a sigmoid (S-curve) function, that dynamically calculates the optimal allocation percentages. Depending on the market conditions, the S curves transition between defensive and aggressive allocations.

The Math Behind It (if you are a geek like me)
This indicator uses the sigmoid function to create smooth S-curve transitions:

α(D) = α_min + (α_max - α_min) × σ(k × (D - D_mid))
Where:
σ(x) = 1 / (1 + e^(-x)) ← Standard sigmoid function

You can also check it here:

// Sigmoid function: σ(x) = 1 / (1 + e^(-x))
sigmoid(float x) =>
    1.0 / (1.0 + math.exp(-x))

// Alpha calculation: α(D) = α_min + (α_max - α_min) × σ(k × (D - D_mid))
calcAlpha(float drawdown, float k, float a_min, float a_max, float d_midpoint) =>
    sig_input = k * (drawdown - d_midpoint) / 100.0
    a_min + (a_max - a_min) * sigmoid(sig_input)

User parameters (you can tweak this):

• Allocation Min (%): Your baseline allocation when markets are at ATH (default: 30%)
  
• Allocation Max (%): Your maximum allocation during deep drawdowns (default: 100%)
  
• D_mid (%): The drawdown level where you want to be at the midpoint (default: 25%)
  

Why do I like sigmoid and not a linear line?
Unlike linear models, the sigmoid creates "floors" and "ceilings" for your allocation. It transitions smoothly, no sudden jumps, and you never exceed your defined min/max bounds.

Understand the K Values (Steepness)
The K parameter controls how quickly your allocation shifts from defensive to aggressive.
Lower K (for example K=5) will give you a gradual transition, but at 0% drawdown you are already at a 46% allocation.
A higher like (like K=40) will give you a sharp transition, but at 0% drawdown you are close to the minimum allocation. On the other hand, a higher K will give close to 100% allocation when the markets are at new lows.
The example below illustrates this well, then the S&P 500 reached new lows in October 2022:

Different K values will affect the sigmoid curves (and you allocations differently). The chart below illustrates well how K affects the sigmoid curves:

Read the Dashboard
The main dashboard shows:

• Current drawdown from ATH
  
• Allocation % for each K value
  
• Suggested action (Defensive → MAX LONG)
  
• Use the Reference Chart
  

The static reference panel shows what your allocation would be at various drawdown levels (0%, 10%, 20%, 30%, 40%, 50%), helping you plan ahead.

Identify Zones
The color-coded chart background shows:
- 🟢 Green Zone: Aggressive positioning - "Buy the Dip"
- 🟡 Yellow Zone: Transition zone - Scaling in/out
- 🔴 Red Zone: Defensive positioning - Protect ya gains

Use Cases
Use case 1: Leveraged ETF Portfolio Management (this is my main use case)
When holding leveraged ETFs like TQQQ or UPRO, volatility makes it important to:
- Reduce exposure near all-time highs (when crashes hurt most)
- Increase exposure during drawdowns (when recovery potential is highest)

Example Strategy:
- At ATH: Hold 30% TQQQ, 70% cash/bonds or other uncorrelated assets
- At 25% drawdown: Hold 65% TQQQ, 35% cash/bonds
- At 40%+ drawdown: Hold 100% TQQQ

Use case 2: Diversified Leveraged Portfolio
Compare different K values for different assets:
- Use K = 10 for broad market (QQQ/SPY exposure via TQQQ/UPRO)
- Use K = 25 for sector bets (TECL, SOXL, TMF) that you want to scale into faster

Use case 3: Systematic Rebalancing Signals
Use the alerts to trigger rebalancing:
- Alert when K3 allocation crosses above 90% (time to add)
- Alert when drawdown exceeds your D_mid threshold
- Alert when market returns to within 5% of ATH

Tips for Best Results

• It works best in longer time frames
  
• Adjust the ATR lookback window
  
• Match your risk tolerance level
  
• I use this for index investing and stocks and haven't tried with crypto
  

Thanks for using the indicator and let me know if you have any feedback :)
- Henrique Centieiro