What is Portfolio Dependency Score?

1. The Core Concept: True vs. Superficial Diversification

Investors often believe they are well-diversified simply because they own a large number of stocks (e.g., 10 or 15 holdings). However, if most of those stocks belong to the same sector, or if the capital is heavily concentrated in one or two positions, the portfolio is highly vulnerable to a single point of failure.

The Portfolio Dependency Score translates your nominal number of holdings into the number of independent, equally weighted bets you are actually making.

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2. How It is Calculated

The score is calculated using the reciprocal of the Herfindahl-Hirschman Index (HHI) of the portfolio's sectors:

Calculate the Sector HHI (Decimal):

$\text{Sector HHI} = \sum_{i} \left( \frac{\text{Sector Allocation \%}}{100} \right)^2$ (This sums the squared capital weights of all sectors in your portfolio. A higher HHI indicates higher concentration).

Compute the Dependency Score (Effective Bets):

$\text{Dependency Score} = \frac{1}{\text{Sector HHI}}$

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3. Example Scenario

Consider a portfolio with 10 holdings:

• Manufacturing: 86% capital allocation
• Banking: 2% capital allocation
• Other: 12% capital allocation

Even though you own 10 different stocks, the math shows:

• Sector HHI: $(0.86)^2 + (0.02)^2 + (0.12)^2 = 0.7396 + 0.0004 + 0.0144 = 0.7544$
• Dependency Score: $\frac{1}{0.7544} \approx 1.3$

The Verdict: 10 Holdings $\rightarrow$ 1.3 Independent Bets. Despite owning 10 stocks, the extreme concentration in Manufacturing means your portfolio risk profile behaves as if you only own 1.3 equally sized independent bets. A downturn in Manufacturing will affect almost your entire capital simultaneously.

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4. Diversification Quality Rating

Flagium classifies the Dependency Score into three categories:

• Very Low (Score $< 2.5$): High risk. The portfolio is highly dependent on a single theme or sector.
• Moderate (Score $2.5$ to $4.0$): Average risk. The portfolio has some concentration but has started building exposure to other areas.
• High (Score $\ge 4.0$): Low risk. Capital is broadly and evenly distributed across 4 or more independent sector regimes.