GAU Calculator Methodology

GAU (Global Asset Unit) Methodology

Overview

The Global Asset Unit (GAU) is a unitless index designed to provide a neutral benchmark for comparing asset performance. Unlike traditional price indices that are denominated in a specific fiat currency, the GAU uses a basket of diverse global assets to create a more balanced reference point that minimizes currency bias.

Calculation Methodology

Base Formula

The GAU is calculated as a weighted geometric mean of the prices of the assets in the basket:

GAU(t) = exp( Σ w_i * ln(P_i(t)) )

Where: - GAU(t) is the value of the GAU at time t - w_i is the weight of asset i - P_i(t) is the price of asset i at time t - Σ represents summation over all assets i in the basket

Weighting Schemes

The GAU supports multiple weighting schemes:

1. Market Cap Weighting (Default)

Weights are assigned proportionally to each asset's market capitalization:

w_i = MarketCap_i / Σ MarketCap_j

This approach better represents the global allocation of wealth and provides a more realistic benchmark for comparing asset performance.

Market Cap Data Sources

Market cap data is primarily obtained through Yahoo Finance API. If market cap data is unavailable for an asset, a fallback mechanism is used based on estimated global asset class sizes:

Asset Class Approximate Global Market Cap
Stocks $116 trillion
Bonds $137 trillion
Commodities $20 trillion
Real Estate $382 trillion
Gold $13 trillion
Bitcoin $1.2 trillion

These fallback values are updated periodically to maintain accuracy.

2. Equal Weighting

Each asset receives the same weight:

w_i = 1/n

Where n is the number of assets in the basket.

Asset Basket

The GAU basket includes six major asset classes to create a diversified representation of global wealth:

  1. Global Stocks: Vanguard Total World Stock ETF (VT)
  2. Represents global equity markets
  3. Includes developed and emerging markets

  4. Global Bonds: Vanguard Total World Bond ETF (BNDW)

  5. Represents the global fixed income market
  6. Includes government and corporate bonds

  7. Commodities: Invesco DB Commodity Index Tracking Fund (DBC)

  8. Represents a broad basket of commodities
  9. Includes energy, precious metals, industrial metals, and agricultural products

  10. Real Estate: iShares Global REIT ETF (REET)

  11. Represents global real estate investment trusts
  12. Provides exposure to the real estate sector

  13. Gold: SPDR Gold Shares (GLD)

  14. Represents gold as a traditional store of value
  15. Acts as an inflation hedge and safe haven asset

  16. Bitcoin: Bitcoin in USD (BTC-USD)

  17. Represents the digital asset class
  18. Provides exposure to cryptocurrency markets

Data Handling

Data Sources

The GAU currently uses adjusted closing prices from Yahoo Finance. These are price returns rather than total returns (which will be implemented in Phase 2).

Missing Data Handling

To ensure continuous GAU calculation even with occasional missing data points:

  1. Forward Fill: Missing values are filled with the last available value
  2. Backward Fill: If forward fill is insufficient, backward fill is applied
  3. Data Validation: Assets with more than 30% missing values trigger a warning
  4. Critical Threshold: If all values for an asset are missing, calculation is halted

Date Range Flexibility

The calculator supports flexible date ranges: - Default analysis period: 5 years - User-selectable time frames: 1, 2, 3, 5, or 10 years - Custom date ranges can be specified

Rebalancing Procedure

Schedule

The GAU basket is rebalanced semi-annually: - End of June (June 30) - End of December (December 31)

Drift Limits

Between rebalancing dates, the weights are allowed to drift naturally with market movements, subject to the following constraints: - Maximum drift: ±3 percentage points from target weight - If any asset exceeds these drift limits, an exceptional rebalancing is triggered

Implementation

  1. At rebalancing dates, new market cap data is collected for each asset
  2. New target weights are calculated based on the chosen weighting scheme
  3. The index is rebalanced to match these target weights
  4. A record of the rebalancing is published with the new weights

Versioning and Transparency

Version Control

All changes to the GAU methodology are version-tagged and publicly announced: - Major version changes (e.g., v1.0 to v2.0) represent significant methodology updates - Minor version changes (e.g., v1.1 to v1.2) represent smaller adjustments or corrections

Data Publication

The following data is published daily: - GAU index level - Component weights - Price data for all assets in the basket - CSV exports for research and analysis

The historical records are maintained in a structured format that allows for easy analysis and verification.

Normalization for Comparison

When comparing assets against the GAU, the following normalization process is applied:

  1. Calculate the ratio of asset price to GAU value at each time point
  2. Normalize all ratios to 100 at the beginning of the analysis period
  3. The resulting normalized values represent relative performance:
  4. Values above 100 indicate outperformance relative to the GAU basket
  5. Values below 100 indicate underperformance relative to the GAU basket

For short-term analyses (less than 60 days), a scaling factor may be applied to make small changes more visible, while preserving the direction of movement.

Technical Implementation

Data Processing Pipeline

  1. Fetch historical price data from Yahoo Finance
  2. Calculate weights based on the selected weighting method
  3. Compute the GAU using the weighted geometric mean formula
  4. Normalize asset prices against the GAU
  5. Generate visualizations and data exports

Data Storage

Daily GAU values and component weights are stored in: - Individual daily files (gau_value_YYYYMMDD.csv, gau_weights_YYYYMMDD.csv) - Consolidated historical records (gau_values_historical.csv, gau_weights_historical.csv) - Rebalancing records (rebalancing_YYYYMMDD.csv, rebalancing_history.csv)

A data cleanup mechanism prevents excessive storage usage by maintaining a reasonable number of historical files.

Future Enhancements (Phase 2)

  • Integration of total-return indices instead of price indices
  • Implementation of Friday 16:00 ET timestamp synchronization
  • Enhanced API endpoints for programmatic access
  • Interactive visualization capabilities
  • Time-synchronized price data for 24/7 markets

Usage Guidelines

Interpretation

  • GAU is a unitless index, normalized to 100 at the beginning of any analysis period
  • Values above 100 indicate outperformance relative to the GAU basket
  • Values below 100 indicate underperformance relative to the GAU basket

Applications

  • Comparing diverse assets without currency bias
  • Measuring "real" returns across different asset classes
  • Identifying relative strength between assets
  • Hedging against currency devaluation

Phase 3 Roadmap

  • Risk-parity weighting implementation
  • Advanced analytics and reporting
  • Automated rebalancing alerts
  • Tokenized GAU tracker prototype
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