How We Built FactorIQ: Our Methodology Explained

Why Methodology Matters

Every portfolio analysis tool shows you numbers. Few explain where those numbers come from.

We built FactorIQ differently. We believe you should understand exactly how your risk metrics are calculated, what assumptions underlie them, and where the data comes from.

This isn't just about transparency—it's about making informed decisions. A Sharpe ratio is only meaningful if you know how it was computed. A stress test is only useful if you understand its limitations.

Our Guiding Principles

Three principles guide our methodology:

1. Academic Foundation

Every calculation in FactorIQ is grounded in peer-reviewed financial research. We don't invent our own metrics—we implement established ones correctly. This includes foundational work like the Fama-French factor models that explain why certain stocks outperform.

2. Practical Relevance

Academic rigor matters, but so does usefulness. We focus on metrics that help you make better decisions, not ones that look impressive but confuse more than they clarify.

3. Honest Limitations

Every model has limitations. We state ours clearly. You'll never see false precision or overconfident predictions.

The Core Framework: Modern Portfolio Theory

Our risk calculations build on Modern Portfolio Theory (MPT), the framework developed by Harry Markowitz that won him a Nobel Prize.

MPT's key insights:

• Expected portfolio return is the weighted average of individual returns
• Portfolio risk is not the weighted average of individual risks—diversification matters
• Correlations between assets determine how much diversification helps

The math:

Expected Return: E[Rₚ] = Σᵢ wᵢ × E[Rᵢ]

Portfolio Variance: σₚ² = Σᵢ Σⱼ wᵢwⱼσᵢσⱼρᵢⱼ

Where:

• wᵢ = weight of asset i
• E[Rᵢ] = expected return of asset i
• σᵢ = standard deviation of asset i
• ρᵢⱼ = correlation between assets i and j

Data Sources

Quality analysis requires quality data. Here's where ours comes from:

Stock Data

• Price history: 10 years of daily closing prices
• Beta: Individual stock sensitivity to market movements
• Sector classification: GICS sector assignments

Economic Indicators

• Federal Reserve Economic Data (FRED): VIX, yield curves, consumer sentiment, economic activity indices
• OECD: Leading economic indicators

Fallback Values

When individual stock data is unavailable, we use conservative defaults:

• Expected return: 8% (long-term equity average)
• Volatility: Estimated from beta × market volatility × 1.3 (idiosyncratic risk factor)
• Beta: 1.0 (market-neutral assumption)

We flag when fallbacks are used so you know the data quality for each holding.

Risk Metrics Methodology

Expected Return

We calculate expected return using arithmetic annualization: daily average return × 252 trading days.

Why arithmetic (not geometric)? For forward-looking projections, arithmetic returns better represent the expected value of future wealth. Geometric returns are more conservative but understate expected growth.

Volatility (Standard Deviation)

We use the full Markowitz covariance calculation, not simplifications. This accounts for:

• Individual stock volatilities
• Correlations between each pair of holdings
• The actual risk reduction from diversification

Sharpe Ratio

Our implementation uses a configurable "hurdle rate" rather than the traditional risk-free rate:

Sharpe = (Expected Return - Hurdle Rate) / Volatility

Default hurdle: 4% (representing a reasonable alternative investment)

This approach lets you compare your portfolio against your personal required return, not just Treasury yields.

Learn more: Sharpe Ratio methodology

Stress Testing Methodology

We apply historical market scenarios to your current portfolio using a three-component model:

1. Market Impact

The base scenario decline (e.g., -57% for 2008)

2. Beta Adjustment

Each holding's market sensitivity (beta) amplifies or dampens the impact:

Adjusted Impact = Market Impact × Beta

A beta-1.5 stock would fall 1.5× the market decline.

3. Sector Multiplier

Historical sector-specific performance during each crisis:

Final Impact = Adjusted Impact × Sector Multiplier

Example 2008 multipliers:

• Financials: 1.5× (epicenter of crisis)
• Healthcare: 0.6× (defensive)
• Technology: 1.1× (slightly worse than market)

The final stressed value:

Stressed Value = Current Value × (1 + Market Impact × Beta × Sector Multiplier)

Learn more: Stress Testing methodology

Monte Carlo Simulation

Our Monte Carlo projections use Geometric Brownian Motion (GBM) with the critical Ito correction:

S(t+dt) = S(t) × exp[(μ - σ²/2) × dt + σ × √dt × Z]

Where:

• μ = expected return
• σ = volatility
• dt = time step
• Z = random draw from normal distribution

The -σ²/2 term (Ito correction) is essential. Without it, simulations overestimate future wealth, especially for volatile portfolios. This correction ensures the median simulation path matches mathematical expectation.

We run 1,000 simulations and report:

• 5th percentile (pessimistic)
• 25th percentile (conservative)
• 50th percentile (median)
• 75th percentile (optimistic)
• 95th percentile (best case)
• Probability of loss (chance of ending below starting value)

Learn more: Monte Carlo methodology

Correlation Analysis

We use a sector-based correlation model:

• Individual stock correlations approximated by their sector
• Pre-computed sector correlation matrix from historical S&P 500 sector data
• Regime adjustment for market stress

Market Regime Detection

Correlations increase during market stress. We adjust for this using VIX:

| VIX Level | Regime | Correlation Multiplier | |-----------|--------|----------------------| | < 20 | Normal | 1.0× | | 20-30 | Elevated | 1.15× | | > 30 | Crisis | 1.3× |

This provides more realistic risk estimates during stressed markets.

Learn more: Correlation methodology

Risk Decomposition

We use Euler decomposition to attribute total portfolio risk to individual holdings:

MCRᵢ = wᵢ × (Σⱼ wⱼσᵢσⱼρᵢⱼ) / σₚ

This satisfies the adding-up property: the sum of all marginal contributions equals total portfolio volatility.

The risk-to-value ratio identifies inefficient holdings:

• Ratio > 1.3: Contributing disproportionately more risk than value
• Ratio ≈ 1.0: Proportional contribution
• Ratio < 0.8: Providing diversification benefits

Learn more: Risk Decomposition methodology

Economic Sentiment

Our sentiment score aggregates five indicators:

| Indicator | Weight | Source | |-----------|--------|--------| | VIX | 30% | CBOE via FRED | | CFNAI | 25% | Chicago Fed | | Consumer Sentiment | 15% | University of Michigan | | Yield Curve | 15% | Treasury data via FRED | | OECD Leading Index | 15% | OECD |

Each indicator is normalized to a -100 to +100 scale, then weighted to produce the composite score.

Learn more: Sentiment methodology

What We Don't Do

Being clear about limitations is part of intellectual honesty:

• We don't predict the future. Projections show possible outcomes, not guaranteed ones.
• We don't provide investment advice. FactorIQ is an educational tool, not a financial advisor.
• We don't guarantee accuracy. Data can be delayed, fallback values may be used, and models have inherent limitations.
• We don't capture all risks. Market risk isn't the only risk—liquidity, concentration, currency, and company-specific risks matter too.

The Full Methodology Library

For complete technical documentation on every metric we calculate, visit our Learn section:

• Risk Metrics — Sharpe ratio, expected return, volatility
• Risk Decomposition — Risk contribution, diversification benefit
• Stress Testing — Historical scenarios, beta adjustment
• Monte Carlo — GBM, Ito correction, percentile projections
• Correlation — Sector correlation, market regime
• Sentiment — Economic indicators, composite scoring

Each page includes formulas, data sources, interpretation guides, and academic citations.

Our Commitment

FactorIQ is built on the belief that understanding your portfolio's risk shouldn't require a finance degree—but the methodology should be there for those who want to dig deeper.

We'll continue improving our models, expanding our data sources, and maintaining full transparency about how everything works.

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