The Golden Constant: How 15-Year Horizons Transform Risk into Wealth

Executive Summary

This comprehensive analysis examines historical gold prices to determine if there were periods where gold was lower after 15 years of holding it. Additionally, it provides a detailed probability assessment of gold returns over 15-year periods, including Conditional Value at Risk (CVaR) analysis.

Key findings: – Based on available GLD ETF data (2004-2025), there were no instances where gold prices were lower after a 15-year holding period. – The probability of achieving at least a 5% return over 15 years is 100% based on historical data. – The probability of doubling your investment (100% return) over 15 years is approximately 94%. – Even in worst-case scenarios (as measured by CVaR), gold has demonstrated relatively contained losses compared to many other investment vehicles.

Data Sources and Methodology

Data Sources

Our analysis primarily used two data sources: 1. GLD ETF (SPDR Gold Shares): A widely recognized proxy for gold prices, with data available from December 2004 to May 2025. 2. Barrick Gold Corporation (GOLD): A major gold mining company, with data available from February 1985 to May 2025.

While we attempted to analyze the GOLD mining company data for a longer historical perspective, the irregular data intervals and gaps after resampling prevented reliable 15- year period analysis. Therefore, our primary conclusions are based on the more reliable GLD ETF data.

Methodology

Data Collection: Historical price data was collected and processed to ensure consistency and accuracy.
15-Year Return Analysis: We calculated returns for all possible 15-year holding periods in the dataset.
Probability Calculation: For each return threshold, we calculated the probability as the number of periods exceeding that threshold divided by the total number of periods.
CVaR Analysis: We calculated Value at Risk (VaR) and Conditional Value at Risk (CVaR) at various confidence levels to assess downside risk.

15-Year Holding Period Analysis

GLD ETF Analysis (2004-2025)

Our analysis of the GLD ETF data revealed: – Total 15-year periods analyzed: 67 – Periods with negative returns: 0 (0.00%) – Finding: There were no instances where gold prices were lower after 15 years of holding.

Best Performing 15-Year Periods:

July 2005 to July 2020: 333.05% return
August 2005 to August 2020: 325.88% return
May 2005 to May 2020: 291.14% return
June 2005 to June 2020: 285.29% return
October 2005 to October 2020: 279.74% return

Probability of Returns Exceeding Thresholds

The table below shows the probability of gold returns exceeding various thresholds over a 15-year holding period, based on GLD ETF data:

Return Threshold (%)	Probability (%)
5	100.00
10	100.00
15	100.00
20	100.00
25	100.00
30	100.00
40	100.00
50	100.00
75	100.00
100	94.03

This table demonstrates that based on historical data, gold has consistently provided positive returns over 15-year holding periods, with a very high probability (94.03%) of at least doubling in value.

Conditional Value at Risk (CVaR) Analysis

The table below presents the Value at Risk (VaR) and Conditional Value at Risk (CVaR) at different confidence levels for 15-year gold returns:

Confidence Level (%)	VaR (%)	CVaR (%)
75	122.38	104.89
80	113.18	102.04
85	108.27	98.42
90	103.69	95.39
95	97.87	90.27
99	87.54	76.52

Interpretation:

At a 95% confidence level, the VaR is 97.87%, meaning that with 95% confidence, the 15-year return will be at least 97.87%.
The corresponding CVaR of 90.27% indicates that in the worst 5% of scenarios, the average return would still be 90.27%.
Even at the 99% confidence level, the CVaR remains positive at 76.52%, suggesting extremely low downside risk over 15-year periods.

Structured Product Implementation: The GoldenX Note

Our analysis reveals a compelling opportunity to implement the GoldenX Strategy through a structured product approach. By leveraging the exceptional stability of gold over 15-year periods, we can design a financial instrument that offers both capital protection and participation in gold’s upside potential.

Structure and Key Features

The GoldenX Note is a 15-year structured product with the following key characteristics: (if it would be issued today with the market conditions we have).

Enhanced Capital Protection: Approximately 170% of the initial investment amount is protected at maturity, providing investors with both principal security and guaranteed returns.
Full Gold Performance Participation: 100% participation in gold price appreciation over the 15-year term, with no cap on potential returns.
Underlying Mechanism: The issuing bank obtains gold price exposure through rolling futures contracts, efficiently managing the long-term gold position while minimizing costs.

Expected Returns Based on CVaR Analysis

Our 95% CVaR analysis provides strong statistical support for the GoldenX Note’s value proposition:

At the 95% confidence level, the CVaR for 15-year gold returns is 90.27%.
This means that even in the worst 5% of scenarios, investors can expect:
The guaranteed 170% of initial capital at maturity Plus an additional 90.27% return from gold performance participation
Resulting in a total return of approximately 260% (or 2.6x the initial investment)

In more favorable scenarios (which represent 95% of historical outcomes), returns would be even higher, potentially reaching 3-4x the initial investment based on historical performance patterns.

Interest Rate Sensitivity and Pre-Maturity Liquidity

A key advantage of the GoldenX Note is its sensitivity to interest rate movements:

Interest Rate Dynamics: If long-term interest rates decline during the instrument’s life, the market value of the note could appreciate significantly before maturity due to the present value effect on the guaranteed future payment.
Trading Flexibility: Despite the 15-year term, the GoldenX Note is designed to be fully tradable. Investors can sell the note back to the market at any time, with pricing adjusted to reflect:
1. Current gold prices
2. Prevailing interest rates
3. Remaining time to maturity
4. Market volatility conditions

This provides investors with both long-term security and short-term liquidity options, addressing one of the primary concerns with extended investment horizons.

Practical Example

Consider a $100,000 investment in the GoldenX Note:

At maturity (after 15 years), the investor is guaranteed to receive $170,000 (170% capital protection)
Based on our 95% CVaR analysis, the gold participation component would add at least $90,270 in the worst 5% of scenarios
Total expected minimum return (in 95% of scenarios): $260,270 (a 160.27% total return)
In the median case scenario, returns would likely exceed 300%

Note: If interest rates decline significantly during the term, an investor wishing to exit after 7-8 years might find the note trading at 130-140% of its initial value, even before the full maturity benefit is realized.

Understanding Probability and Odds

Basic Probability Formula

The probability of an event is calculated as:

P(Event) = Number of favorable outcomes / Total number of possible outcomes

For our gold price analysis:

P(Return ≥ X%) = Number of 15-year periods with returns ≥ X% / Total number of 15- year periods analyzed

Converting Between Probability and Odds

Odds represent the ratio of favorable outcomes to unfavorable outcomes:

Odds(Event) = Number of favorable outcomes / Number of unfavorable outcomes

For example, if the probability of gold prices increasing by at least 50% over 15 years is 0.8 (or 80%), the odds would be:

Odds(Return ≥ 50%) = 0.8 / 0.2 = 4:1

This means gold prices are 4 times more likely to increase by at least 50% than not.

Conversely, to convert odds to probability:

P(Event) = Odds / (1 + Odds)

Return Distribution Analysis

The distribution of 15-year gold returns shows a strong positive skew, with the majority of returns clustered in the high positive range. This visual representation reinforces gold’s historical performance as a reliable long-term investment vehicle.

Probability Thresholds Visualization

The probability of exceeding various return thresholds demonstrates gold’s consistent performance over 15-year periods. The visualization shows that the probability remains at 100% for most reasonable return thresholds, only dropping slightly for the most ambitious return targets.

CVaR Analysis Visualization

The CVaR analysis provides a visual representation of the downside risk at different confidence levels. Even at the highest confidence levels, both VaR and CVaR remain strongly positive, highlighting gold’s stability as a long-term investment.

Limitations and Considerations

Limited Data: The GLD ETF data only goes back to 2004, providing a limited number of complete 15-year periods for analysis.
Past Performance: Historical performance does not guarantee future results. Economic conditions, monetary policies, and market dynamics change over time.
Proxy Data: Using ETFs and mining companies as proxies for gold prices introduces some imprecision compared to direct gold price data. In a structured product like this rolling futures would be used to get the gold price exposure.
Inflation Adjustment: Our analysis uses nominal returns rather than inflation adjusted returns, which would provide a more accurate picture of real purchasing power.
Data Quality: Our analysis identified some data quality issues, including missing months and potential outliers, which could affect the precision of our results.
Structured Product Risks: The GoldenX Note depends on the creditworthiness of the issuing bank. While the capital protection feature is contractually guaranteed, it is subject to the issuer’s ability to meet its obligations at maturity.

The GoldenX Investment Strategy

Based on our comprehensive analysis, the GoldenX Strategy proposes a long-term gold investment approach with the following key principles:

15-Year Holding Period: Historical data strongly suggests that a holding period of 15 years virtually eliminates the risk of negative returns in gold investments.
Structured Product Implementation: The GoldenX Note provides an optimal vehicle for implementing this strategy, offering 170% capital protection plus full participation in gold’s performance.
Dollar-Cost Averaging: For investors not using the structured product approach, regular investments over time can help mitigate short-term volatility while maintaining the long-term benefits.
Portfolio Allocation: Gold should be considered as part of a diversified portfolio, with allocation percentages based on individual risk tolerance and investment goals.
Systematic Rebalancing Discipline: Periodic and systematic rebalancing to maintain target allocation percentages can help capture gains while maintaining the desired risk profile.

Conclusion

The GoldenX Strategy is built on robust historical evidence that gold has never shown negative returns over 15-year holding periods in our dataset. With a 100% probability of positive returns and a 94.03% probability of at least doubling in value over 15 years, gold represents a compelling long-term investment vehicle.

The CVaR analysis further supports gold’s reputation as a store of value, showing that even in worst-case scenarios, the expected returns remain strongly positive over 15-year horizons.

The GoldenX Note structured product offers an innovative way to leverage these statistical advantages, providing enhanced capital protection (170%) while maintaining full participation in gold’s upside potential. This combination of security and growth potential, along with interest rate sensitivity and trading flexibility, makes it an attractive option for both institutional and sophisticated individual investors.

While past performance does not guarantee future results, this historical analysis provides valuable context for understanding gold’s potential as a long-term investment vehicle and forms the foundation of the GoldenX Strategy.

Research prepared by Charles Villeneuve, Head Scientist May 20, 2025

Originally posted in Substack