The Structural Hedge to Life’s Randomness - The Demand Side

Where chaos meets the serene apathy of a finite and non-productive asset—explained with unnecessarily complicated derivations

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Welcome to a series where first-principles thinking and just enough over-caffeination collide to demystify capital flows.

In the new section called The Quant Foundry, we’ll build models, test theories, and craft strategies to make sense of markets—and maybe even keep ourselves sane when they inevitably misbehave. This segment will focus on two key pillars: first, creating mathematical frameworks that can be empirically tested and used to develop real-time indicators, enabling us to explain the world economy and, ideally, spot trends before they hit Bloomberg or the FT. Second, we’ll aim to build parametric models that provide intuitive insights into the "why" behind market movements. As much of my time is dedicated to discretionary trading and investing, this trading journal is both a practical tool and a space to translate theory, modeling, and computation into trades that can be explained in plain language.

In this first iteration, we’ll explore the dynamics of capital flows into specific assets like gold and Bitcoin, chosen for their scarcity, durability, and independence, making them ideal foundations for our framework. We begin with gold—the elder statesman of safe havens, shaped by scarcity, inflation, and the occasional geopolitical drama. Its supply is constrained by physics and geology, while its demand thrives on its role as a hedge against uncertainty, creating a steady upward price bias that is far from random. Bitcoin, its rebellious digital counterpart, will have its turn in due course, but for now, gold takes center stage—earned through millennia of proving its value. The goal is to understand these assets such that when markets shift, we respond with clarity, not guesswork.

Right now we are trying to understand the relationship hinted at in the below chart. We will first focus on guessing a reasonable framework and then run some computing in later notes.

Wait, so bitcoin is not just magic internet money for degenerates to overpay for pizza on network fees but could be a logical addition to a global-macro portfolio? Full disclosure I have more exposure to bitcoin (via unlevered spot) than Gold (via derivatives on futures) but tactically allocate in and out of the two.

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Inflation and the Yield Curve

Understanding the relationship between inflation, currency debasement, and yields is foundational to discerning when it is optimal to own gold. These dynamics highlight the interplay of macroeconomic forces, investor psychology, and structural market factors, dictating the ebb and flow of gold’s appeal as an asset.

Market-Driven Inflation Modeling

Inflation, often modeled using economic indicators, can also be inferred directly from financial market data. Market-driven inflation measures leverage real-time information embedded in asset prices, offering a dynamic view of inflation expectations relative to observable market variables. This interpretability makes these models particularly valuable, allowing me to assess whether the market is underpricing or overpricing inflation compared to my economic inflation models. By incorporating these approaches, I can gauge how well market participants’ inflation expectations align with underlying economic realities and identify potential mispricings. Below are several key approaches to modeling inflation using market data, each capturing different facets of inflationary dynamics.

Linear Yield Curve Slope Model

The simplest approach ties inflation expectations to the slope of the yield curve, a well-established proxy for macroeconomic trends.

\(\pi(t) = \pi_0 + \gamma_y \cdot \left( y_{\text{long}}(t) - y_{\text{short}}(t) \right) \)

Where:

Intuition:

Exponential Yield Curve Model:

This nonlinear model accounts for disproportionate inflation responses to large yield curve movements.

\(\pi(t) = \pi_0 \cdot e^{\gamma_y \cdot \left( y_{\text{long}}(t) - y_{\text{short}}(t) \right)} \)

• Captures sharper inflation spikes during periods of steep curves.

• Suitable for volatile environments where inflation reacts more aggressively to yield changes.

Taylor Rule-Based Inflation Estimate

If monetary policy rates are included, use a Taylor Rule-style adjustment:

\(\pi(t) = \frac{r_{\text{policy}}(t) - r_{\text{neutral}}}{\gamma_r} + \gamma_y \cdot \left( y_{\text{long}}(t) - y_{\text{short}}(t) \right)\)

with:

Breakevens

The breakeven inflation rate, derived from the difference between nominal Treasury yields and TIPS yields, reflects market expectations for inflation over a specific horizon.

\(\pi(t) = \left( y_{\text{nominal}}^{10}(t) - y_{\text{real}}^{10}(t) \right) \)

Where:

• Breakeven inflation is directly derived from market prices and offers a forward-looking inflation measure.

• Independent of yield curve dynamics, focusing solely on inflation pricing in the bond market.

Hybrid Yield Curve and Breakeven Model

Combining yield curve steepness with breakeven inflation provides a more comprehensive view.

\(\pi(t) = \pi_{\text{breakeven}}(t) + \gamma_y \cdot \left( y_{\text{long}}(t) - y_{\text{short}}(t) \right) \)

Where:

\(\pi_{\text{breakeven}}(t) = \left( y_{\text{nominal}}^{10}(t) - y_{\text{real}}^{10}(t) \right) \)

• Balances macroeconomic signals (yield curve) with direct market pricing (breakeven rates).

• Useful in cases where either the breakeven rate or yield curve alone may be insufficient.

Yield Curve and Commodity Prices

Commodities, particularly energy and metals, are leading indicators of cost-push inflation. Adding commodity price changes enhances inflation modeling.

\(\pi(t) = \pi_0 + \gamma_y \cdot \left( y_{\text{long}}(t) - y_{\text{short}}(t) \right) + \gamma_c \cdot \Delta P_{\text{commodity}}(t) \)

Where:

• Rising commodity prices often precede inflation, particularly in energy-intensive economies.

• This approach incorporates both financial and real-world cost drivers of inflation.

Term Structure of Inflation Expectations

Build inflation expectations from a term structure model, akin to Nelson-Siegel for yields:

\(\pi(t, \tau) = \beta_0 + \beta_1 \cdot e^{-\tau / \lambda} + \beta_2 \cdot \left(\frac{\tau}{\lambda}\right) e^{-\tau / \lambda} \)

Here, τ is the time horizon, and the β coefficients describe the level, slope, and curvature of the inflation term structure. This allows inflation expectations to vary with time horizons.

Market-Derived Phillips Curve

Link inflation to unemployment rates and yield curve spreads (a proxy for growth expectations):

\(\pi(t) = \pi_0 + \gamma_y \cdot \left( y_{\text{long}}(t) - y_{\text{short}}(t) \right) - \gamma_u \cdot U(t) \)

with U(t) being the unemployment rate or a broader measure of labor slack. With its gamma being the sensitivity of inflation to changes in unemployment (inverse Phillips curve relationship)

I’ll elaborate on inflation models in a subsequent post in the Quant Foundry.

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Components of Demand

The total demand for gold can be expressed as:

\(D_{\text{total}}(t) = D_{\text{perpetual}}(t) + D_{\text{active}}(t) + D_{\text{speculative}}(t)) \)

Where:

We will leave out looking at speculative demand for this analysis on gold and focus on it more when looking at Bitcoin. The reason for this is that as of today, the core forces driving demand for gold is the perpetual bid and active management, while the dominant demand forces for bitcoin are active management and speculative with limited perpetual bid (for now).

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Perpetual Demand

Gold enjoys a few consistent sources of perpetual demand: central banks, long-term institutional holders, and individual investors seeking a hedge against economic instability. Central banks, in particular, have significantly increased their gold reserves, responding to economic fragility, geopolitical uncertainty, and the pursuit of financial independence. In 2022, central banks added approximately 1,136 tonnes of gold to their stockpiles—the highest annual purchase since 1967. This momentum carried into 2023, with another 1,037 tonnes acquired, marking the second-largest annual total in history. Such levels of accumulation highlight gold’s enduring relevance in an era defined by global unpredictability.

As nations rise and fall, gold remains a constant—a timeless bulwark against monetary excesses and global instabilities. Its universal acceptance, finite supply, and immunity to external control have made it indispensable to central banks navigating a rapidly changing financial order. Understanding the motivations behind this renewed interest not only highlights gold’s unique attributes but also sheds light on the shifting strategies of countries in a volatile world.

Gold as a Strategic Asset

Hedge Against Inflation and Currency Debasement

Gold's inherent scarcity ensures its status as a hedge against inflation and monetary debasement. When fiat currencies falter—whether from persistent inflation or policy missteps—gold serves as a stable store of value, preserving purchasing power. This is particularly relevant in an era of aggressive monetary easing and rising sovereign debt levels, where traditional financial assets face heightened risks.

Geopolitical Independence

The dominance of the U.S. dollar in global trade grants the United States immense power to impose sanctions, often disrupting access to international markets. In response, nations like China, Russia, and Turkey have turned to gold to reduce reliance on the dollar. Gold’s physical nature and immunity to sanctions or asset freezes foster financial autonomy, enabling nations to maintain trade flexibility and safeguard reserves during geopolitical tensions.

Crisis Asset

In a world increasingly shaped by wars, trade disruptions, and financial shocks, gold’s counterparty-free nature makes it a dependable reserve asset when confidence in other systems falters. Its universal acceptance and historical role as a "safe haven" further solidify its value during periods of global instability.

The Historical Arc of Central Bank Gold Demand

The Era of Net Selling: 1990s–2000s

The 1990s and early 2000s were marked by historic gold sell-offs, particularly by European central banks. Several factors contributed to this trend:

1. Economic Optimism and Falling Prices
   The 1990s saw robust global growth and declining gold prices, which dropped from $850/oz in 1980 to under $300/oz by the late 1990s. These conditions eroded gold’s appeal as a safe haven, with many central banks prioritizing yield-generating assets.

2. Yield Focus
   Gold, which earns no yield unless lent out, became less attractive compared to interest-bearing instruments like U.S. Treasuries. Reserve managers, under pressure to maximize returns, saw little value in holding large gold reserves.

3. European Sales
   European central banks, burdened with historically large gold reserves, became the dominant sellers, coordinating their efforts under the Central Bank Gold Agreement (CBGA) to avoid disrupting markets.

   • Key Sales:

     • CBGA signatories sold over 400 tonnes annually between 1999 and 2007.

     • Switzerland reduced its holdings by 1,550 tonnes from 2000 to 2008.

     • The UK sold 395 tonnes between 1999 and 2002, reducing gold’s share of reserves from 17.8% in 1999 to 14.7% in 2009.

The broader sentiment was shaped by confidence in fiat currencies, stable financial markets, and a perception that gold’s disadvantages—no yield, high storage costs, and volatility—outweighed its benefits.

The Shift to Net Buying: Post-2008

The 2008 financial crisis transformed the narrative. Central banks became net buyers of gold for the first time in decades, driven by these key factors:

1. Global Financial Crisis and Renewed Safe-Haven Demand
   The crisis highlighted vulnerabilities in fiat currencies and financial systems. Gold’s counterparty-free nature and historical reputation as a "safe haven" asset made it a natural choice for central banks seeking stability during unprecedented economic turbulence.

2. Emerging Market Accumulation
   Rising foreign exchange reserves in countries like China, India, and Russia led to significant gold purchases for diversification and risk management.

   • India: Purchased 200 tonnes from the IMF in 2009, raising gold’s share of its reserves from ~4% to ~7%.

   • China: Increased its gold holdings by 454 tonnes between 2003 and 2009—a 76% rise.

   • Russia: Boosted gold’s share of reserves from 3% in 2007 to 5% by 2010, emphasizing its role as a crisis asset.

3. Geopolitical and Currency Risks
   Concerns over the U.S. dollar’s stability and eurozone debt crises further boosted gold’s appeal. From 2001 to 2009, the dollar lost 38% of its value against the euro, prompting central banks to hedge against depreciation and reduce reliance on fiat currencies.

4. Reserve Rebalancing
   Rapidly expanding foreign exchange reserves diluted gold’s share, prompting central banks to restore balance. For example, China’s gold reserves, which accounted for 2.2% of total reserves in 2002, fell below 1% before a 454-tonne addition in 2009.

By 2009, annual net sales had plummeted to just 44 tonnes, with emerging markets driving the shift to net buying. This renewed focus underscored gold’s enduring relevance in a volatile world.

Gold’s perpetual demand from central banks, institutions, and individuals is a testament to its enduring value. The 1990s and early 2000s saw significant selling as gold lost its luster in a stable global economy. Yet the financial crisis of 2008 marked a turning point, reigniting interest and driving record levels of accumulation in recent years.

Today, gold remains a cornerstone of central bank strategy. Whether as a hedge against inflation, a crisis asset, or a tool for geopolitical independence, its appeal is timeless. As nations navigate an era of economic uncertainty and shifting global power dynamics, gold continues to shine as a symbol of stability, resilience, and strategic foresight.

The Differential Equation of Demand:

To capture the dynamics of persistent demand, we model its evolution as a differential equation. This approach allows us to represent how demand responds to changing economic conditions continuously, while ensuring flexibility for future extensions or simulations.

This approach allows the following benefits:

• Dynamic Representation:

  • Instead of treating demand as static, the differential equation captures the gradual changes driven by real-world forces like inflation and yields.

• Continuous Adjustment:

  • Persistent demand doesn’t shift abruptly—it accumulates or declines based on sustained pressures, such as prolonged inflation or geopolitical shocks.

• Generalizable Structure:

  • Using a differential framework, we can integrate new factors (e.g., central bank behavior or currency-specific shocks) without breaking the core model.

The simplest form for the change in persistent demand is given by:

\(\frac{dD_{\text{perpetual}}(t)}{dt} = \delta \cdot \left( \alpha_\pi \cdot \pi(t) - \alpha_y \cdot y(t) + \alpha_{\text{geo}} \cdot \text{geo}(t) + \beta_p \cdot \dot{G}_p(t) \right) \)

Where:

Drivers of Persistent Demand:

Integrated Form:

To find the total persistent demand over time, we integrate the differential equation:

\(D_{\text{perpetual}}(t) = D_{\text{CB}}^0 + \int_0^t \delta \cdot \left( \alpha_\pi \cdot \pi(\tau) - \alpha_y \cdot y(\tau) + \alpha_{\text{geo}} \cdot \text{geo}(\tau) + \beta_p \cdot \frac{dG_p(\tau)}{d\tau} \right) d\tau \)

This formulation explicitly accounts for how macroeconomic conditions and price momentum shape the accumulation or reduction of persistent demand.

Intuitive Alignment with Historical Trends

Inflation and Monetary Debasement

• Historical Context:

  • Gold serves as a hedge against inflation and monetary debasement, particularly during periods of aggressive monetary easing (e.g., post-2008 financial crisis).

  • Central banks, especially in emerging markets, have increased gold reserves to counterbalance the risks of fiat currency erosion.

• Model Alignment:

  • In the model:

    \(\frac{dD_{\text{perpetual}}(t)}{dt} \propto \alpha_\pi \cdot \pi(t) \)

    inflation π(t) directly drives persistent demand. For example:

    • Post-2008 quantitative easing and rising inflation expectations would naturally increase perpetual demand, consistent with the shift to net buying after the financial crisis.

Geopolitical Risks and Financial Independence

• Historical Context:

  • Nations like China, Russia, and Turkey have sought to reduce dependence on the U.S. dollar and safeguard reserves amid geopolitical tensions.

  • Gold's immunity to sanctions and asset freezes has made it a key reserve asset for financial autonomy.

• Model Alignment:

  • Geopolitical instability geo(t) is a core driver:

    \(\frac{dD_{\text{perpetual}}(t)}{dt} \propto \alpha_{\text{geo}} \cdot \text{geo}(t) \)

    Rising geopolitical risk increases perpetual demand, reflecting gold’s role as a hedge during global uncertainty.

    • Events like Russia’s pivot to gold reserves align with this mechanism.

Opportunity Cost of Yields

• Historical Context:

  • In the 1990s and early 2000s, gold was less attractive due to falling inflation, robust economic growth, and rising yields. Central banks prioritized yield-generating assets.

  • For example, Switzerland and the UK significantly reduced gold holdings during this period.

• Model Alignment:

  • In the model:

    \(\frac{dD_{\text{perpetual}}(t)}{dt} \propto -\alpha_y \cdot y(t) \)

    where higher yields y(t) reduce demand by increasing the opportunity cost of holding a non-yielding asset like gold.

    • The decline in perpetual demand during the 1990s is captured by this term.

Price Momentum and Reserve Rebalancing

• Historical Context:

  • Persistent demand isn’t entirely price-insensitive. Rising gold prices often signal heightened economic instability, prompting central banks to rebalance reserves in favor of gold (you can always count on the government to buy high and sell low for the good of the people…).

  • Post-2008, price momentum and the need for diversification led to significant gold accumulation by countries like China and India.

• Model Alignment:

  • The price momentum term accounts for this dynamic:

    \(\frac{dD_{\text{perpetual}}(t)}{dt} \propto \beta_p \cdot \dot{G}_p(t) \)

    • Positive price trends attract more demand, while negative trends reduce accumulation or trigger selling.

Cyclical Nature of Gold Demand

• Historical Context:

  • Gold demand cycles between net selling and net buying, influenced by macroeconomic conditions. For example:

    • Net Selling (1990s-2000s): Strong growth, low inflation, and high yields.

    • Net Buying (Post-2008): Financial crisis, inflation fears, and geopolitical uncertainty.

• Model Alignment:

  • The differential equation inherently captures cyclical behavior by allowing demand to rise or fall dynamically based on macroeconomic inputs:

\(D_{\text{perpetual}}(t) = D_{\text{CB}}^0 + \int_0^t \delta \cdot \left( \alpha_\pi \cdot \pi(\tau) - \alpha_y \cdot y(\tau) + \alpha_{\text{geo}} \cdot \text{geo}(\tau) + \beta_p \cdot \frac{dG_p(\tau)}{d\tau} \right) d\tau \)

Alternate Formulations to the Differential Equation of Perpetual Demand

Saturation and Threshold’s

\(\frac{dD_{\text{perpetual}}(t)}{dt} = \delta \cdot \left( \alpha_\pi \cdot f(\pi(t)) - \alpha_y \cdot g(y(t)) + \alpha_{\text{geo}} \cdot h(\text{geo}(t)) + \beta_p \cdot \dot{G}_p(t) \right) \)

Momentum-Dependent Scaling

We can include a scaling factor that adjusts the sensitivity of all inputs based on recent momentum in demand or price:

\(\frac{dD_{\text{perpetual}}(t)}{dt} = \gamma(t) \cdot \delta \cdot \left( \alpha_\pi \cdot \pi(t) - \alpha_y \cdot y(t) + \alpha_{\text{geo}} \cdot \text{geo}(t) + \beta_p \cdot \dot{G}_p(t) \right) \)

Momentum effects amplify or dampen demand depending on recent dynamics:

Strong upward momentum increases the impact of inflation, yields, or geopolitical risks.

\(\frac{dD_{\text{perpetual}}}{dt} > 0\)

Reversals dampen sensitivity to these drivers.

Mean-Reverting Dynamics

Introduce mean-reverting behavior to capture long-term equilibrium tendencies:

\(\frac{dD_{\text{perpetual}}(t)}{dt} = -\theta \cdot \left(D_{\text{perpetual}}(t) - D_{\text{CB}}^{\text{eq}} \right) + \delta \cdot \left( \alpha_\pi \cdot \pi(t) - \alpha_y \cdot y(t) + \alpha_{\text{geo}} \cdot \text{geo}(t) \right) \)

Captures the tendency of central banks and long-term holders to maintain target allocations of gold (e.g., as a percentage of reserves).

Ensures that perpetual demand does not grow without bounds and reverts to an equilibrium absent strong macroeconomic drivers.

Coupled Dynamics with Active Demand

Model perpetual demand as partially influenced by active demand dynamics:

\(\frac{dD_{\text{perpetual}}(t)}{dt} = \delta \cdot \left( \alpha_\pi \cdot \pi(t) - \alpha_y \cdot y(t) + \alpha_{\text{geo}} \cdot \text{geo}(t) \right) + \eta \cdot D_{\text{active}}(t) \)

Volatility-Adjusted Demand

Incorporate market volatility as an additional driver:

\(\frac{dD_{\text{perpetual}}(t)}{dt} = \delta \cdot \left( \alpha_\pi \cdot \pi(t) - \alpha_y \cdot y(t) + \alpha_{\text{geo}} \cdot \text{geo}(t) + \alpha_\sigma \cdot \sigma_G(t) \right) \)

High price volatility may trigger risk-averse entities (e.g., central banks) to increase gold holdings as a hedge.

Conversely, persistent low volatility might signal reduced risk and lower the need for gold as a safe haven.

Additional Inputs to Consider

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Active Demand (This is where we allocate)

While perpetual demand for gold stems from structural, long-term drivers like currency debasement, geopolitical risks, and central bank reserve strategies, it remains relatively stable over time. Perpetual demand reflects gold’s role as a hedge against systemic risks rather than a response to transient economic signals. As such, the yield curve indirectly influences perpetual demand through its impact on inflation expectations and monetary debasement, but it does not directly dictate allocation decisions.

In contrast, active demand for gold arises from the strategic decisions of investors who dynamically adjust their exposure based on the macroeconomic environment. Unlike the steadiness of perpetual demand, active demand fluctuates in response to factors like yield curve dynamics, inflation risk, and monetary liquidity. Crucially, active demand can also turn negative, as investors sell gold when economic conditions favor alternative investments.

To model active demand, we begin by identifying three key drivers:

• Opportunity Cost of Yield (Short End of the Curve):

  • The short end of the yield curve (e.g., 2-year Treasury yield) reflects the immediate opportunity cost of holding a non-yielding asset like gold. Higher short-term yields make holding gold less attractive, while lower short-term yields reduce this opportunity cost.

• Inflation Risk (Long End of the Curve):

  • The long end of the yield curve (e.g., 10-year Treasury yield) captures the term premium, often reflecting inflation expectations and uncertainty. A steeper curve signals higher future inflation risk, increasing gold’s appeal as an inflation hedge.

• Monetary Liquidity (Money Supply):

  • An abundance of liquidity (e.g., increasing money supply) tends to drive active demand for gold, as excess money flows into alternative assets, including gold. Conversely, tightening monetary conditions reduce gold’s appeal.

• (Optional) Fiscal Environment:

  • Expansionary fiscal policies, such as deficit spending, may increase inflation risk and indirectly support demand for gold. However, this is often reflected in the yield curve, so fiscal dynamics can be treated as an implicit factor.

Yield Curve Regime Classification: A Bond Portfolio-Based Approach

First keep in mind that market implied means you contract away the work of figuring out what is the current state of the world to the market. The bond shorts we have put on were by contrasting the economic picture to the market implied picture and determining there was a mispricing and an opportunity to short bonds.

The yield curve is a powerful indicator macroeconomic conditions, but interpreting its movements—whether it is steepening, flattening, or shifting up or down—requires a structured framework. In this approach, we construct simple bond portfolios whose changes in value directly reflect the behavior of the yield curve. By carefully balancing the sensitivity of these portfolios to different parts of the curve, we can classify the yield curve into clear regimes: Bull/Bear and Steepener/Flattener.

This is a crucial framework to have in case the market moves faster than you at pricing a change in regime such that you can de-risk first and think later (but don’t put on risk first and think later).

Building the Bond Portfolios

To measure yield curve dynamics, we construct two bond portfolios:

1. Bear/Bull Portfolio: Measures whether yields are rising or falling across the curve.

2. Steepener/Flattener Portfolio: Measures changes in the slope of the yield curve.

Each portfolio combines long-duration bonds (e.g., 10-year Treasury bonds) and short-duration bonds (e.g., 2-year Treasury bonds). To ensure both ends of the curve contribute equally, the positions are duration-adjusted.

For every one long-duration bond in the portfolio we will need to scale the exposure to short-duration bonds by the ratio of the duration on long duration bonds to short duration bonds. We will denote the duration by kappa:

\( \kappa_{long} : \text{duration of tail end bonds ; } \kappa_{short} : \text{front end bond duration}\)

Bear/Bull Portfolio

The Bear/Bull Portfolio of being long both the long and short end of the yield curve captures directional movements of the yield curve:

\(\Delta P_{\text{BB}}(t) = -\kappa_{\text{long}} \cdot \Delta y_{\text{long}} - \kappa_{\text{short}} \cdot \frac{\kappa_{\text{long}}}{\kappa_{\text{short}}} \cdot \Delta y_{\text{short}} \)

Simplifying:

\(\Delta P_{\text{BB}}(t) = -\kappa_{\text{long}} \cdot \left( \Delta y_{\text{long}} + \Delta y_{\text{short}} \right) \)

Where we interpret:

Steepener/Flattener Portfolio

The Steepner/Flattener Portfolio of being long the long end and short the short end of the yield curve isolates changes in the slope of the yield curve.

\(\Delta P_{\text{SF}}(t) = -\kappa_{\text{long}} \cdot \Delta y_{\text{long}} + \kappa_{\text{short}} \cdot \frac{\kappa_{\text{long}}}{\kappa_{\text{short}}} \cdot \Delta y_{\text{short}} \)

Simplifying:

\(\Delta P_{\text{SF}}(t) = -\kappa_{\text{long}} \cdot \left( \Delta y_{\text{long}} - \Delta y_{\text{short}} \right) \)

Where we interpret:

Index Formulation

To classify regimes, we normalize the portfolio price changes into indices bounded between −1 and 1:

Bear/Bull Index:

\( I_{\text{BB}}(t) = \frac{\Delta P_{\text{BB}}(t)}{\left| \Delta P_{\text{BB}}(t) \right|} \)

Steepner/Flatner Index:

\( I_{\text{SF}}(t) = \frac{\Delta P_{\text{SF}}(t)}{\left| \Delta P_{\text{SF}}(t) \right|} \)

And we define the index vector:

\(\mathcal{I}(t) = \left( I_{\text{BB}}(t), I_{\text{SF}}(t) \right)\)

where:

• (+,+): Bull Steepener.

• (+,−): Bull Flattener.

• (−,+): Bear Steepener.

• (−,−) Bear Flattener.

Here are some formulations which naturally follow to express this indicator:

General form:

\(I(t) = \frac{\Delta y_{\text{long}}(t) \pm \Delta y_{\text{short}}(t)}{|\Delta y_{\text{long}}(t)| + |\Delta y_{\text{short}}(t)|} \)

Integrated Changes:

Smooths short-term noise by aggregating rate changes over time, emphasizing trends. Suitable for identifying persistent yield curve shifts.

\(I(t) = \frac{\int_{t-T}^t \Delta y_{\text{long}}(\tau) \, d\tau \pm \int_{t-T}^t \Delta y_{\text{short}}(\tau) \, d\tau}{\left|\int_{t-T}^t \Delta y_{\text{long}}(\tau) \, d\tau\right| + \left|\int_{t-T}^t \Delta y_{\text{short}}(\tau) \, d\tau\right|} \)

Momentum-Based Changes:

Measures the acceleration (momentum) of yield changes, capturing inflection points or rapid movements. Useful for detecting shifts in market sentiment or policy.

\(I(t) = \frac{\frac{\partial^2 y_{\text{long}}(t)}{\partial t^2} \pm \frac{\partial^2 y_{\text{short}}(t)}{\partial t^2}}{\left|\frac{\partial^2 y_{\text{long}}(t)}{\partial t^2}\right| + \left|\frac{\partial^2 y_{\text{short}}(t)}{\partial t^2}\right|} \)

Exponential Sensitivity:

Amplifies significant movements while reducing sensitivity to small rate changes. Ideal for periods of high market volatility or stress.

\(I(t) = \frac{\exp(\Delta y_{\text{long}}(t)) \pm \exp(\Delta y_{\text{short}}(t))}{\exp(|\Delta y_{\text{long}}(t)|) + \exp(|\Delta y_{\text{short}}(t)|)} \)

Convexity Adjusted

While the above framework captures first-order effects via duration, large yield changes introduce second-order effects through convexity:

\(\Delta P \approx -\kappa \cdot \Delta y + \frac{1}{2} \cdot \xi \cdot (\Delta y)^2 \)

Where:

Convexity-Adjusted Bear/Bull Portfolio

\(\Delta P_{\text{BB}}(t) = -\kappa_{\text{long}} \cdot \left( \Delta y_{\text{long}} + \Delta y_{\text{short}} \right) + \frac{1}{2} \cdot \kappa_{\text{long}} \cdot \left( \xi_{\text{long}} \cdot (\Delta y_{\text{long}})^2 + \frac{\xi_{\text{short}}}{\kappa_{\text{short}}} \cdot (\Delta y_{\text{short}})^2 \right)\)

Convexity-Adjusted Steepener/Flattener Portfolio

\(\Delta P_{\text{SF}}(t) = -\kappa_{\text{long}} \cdot \left( \Delta y_{\text{long}} - \Delta y_{\text{short}} \right) + \frac{1}{2} \cdot \kappa_{\text{long}} \cdot \left( \xi_{\text{long}} \cdot (\Delta y_{\text{long}})^2 - \frac{\xi_{\text{short}}}{\kappa_{\text{short}}} \cdot (\Delta y_{\text{short}})^2 \right)\)

Where the index is normalized

Relative Gradient Approach

Instead of focusing solely on rate differences, use the gradient of the yield curve over multiple maturities to derive the dynamics.

\(I(t) = \frac{\nabla y_{\text{long-short}}(t) \pm \nabla^2 y_{\text{long-short}}(t)}{\left|\nabla y_{\text{long-short}}(t)\right| + \left|\nabla^2 y_{\text{long-short}}(t)\right|} \)

• First derivative ∇: Reflects the steepness of the curve.

• Second derivative ∇-squared: Captures how quickly the curve is changing, adding depth to the steepener/flattening dynamics.

Human Interpreted Interplay of the Yield Curve Dynamics on Gold Demand

• Bull Steepener (Falling Short-Term Rates, Steepening Curve):

  • Falling short-term rates reduce the opportunity cost of holding gold, making it more attractive.

  • The steepening curve reflects rising term premia and higher long-term inflation expectations, further boosting gold's appeal as an inflation hedge.

  • This regime typically signals accommodative monetary policy and economic uncertainty, both of which increase demand for gold.

• Bear Steepener (Rising Short-Term Rates, Steepening Curve):

  • Rising short-term rates increase the opportunity cost of holding gold, reducing its attractiveness.

  • However, the steepening curve reflects growing long-term inflation risk, which offsets some of the negative effect of higher opportunity costs.

  • In this regime, gold demand is moderate, as the inflation hedge appeal competes with the higher yield-driven opportunity cost.

• Bull Flattener (Falling Short-Term Rates, Flattening Curve):

  • Falling short-term rates reduce opportunity costs, which is favorable for gold demand.

  • A flattening curve, however, signals subdued long-term inflation expectations or economic tightening, diminishing the inflation-hedge appeal of gold.

  • Demand for gold in this regime depends on whether the opportunity cost benefit outweighs the lower inflation concerns.

• Bear Flattener (Rising Short-Term Rates, Flattening Curve):

  • Rising short-term rates sharply increase the opportunity cost of holding gold, strongly reducing its appeal.

  • The flattening curve reflects suppressed inflation expectations and potentially tighter monetary policy, further lowering gold’s attractiveness as an inflation hedge.

  • This regime is typically the least favorable for gold demand, as both opportunity cost and inflation risk work against its appeal.

Formulation of Active Demand

\(\frac{dD_{\text{active}}(t)}{dt} = F\left(C_{\text{opportunity cost}}(t), C_{\text{inflation}}(t), \mathcal{L}(t)\right) \)

Where:

Opportunity Cost

Gold, as a non-yielding asset, competes with interest-bearing instruments. When short-term yields rise, gold becomes less attractive due to the higher opportunity cost of holding an asset with no inherent return. Conversely, falling yields increase gold's relative appeal. To model this relationship, we anchor the formulation in two components:

\(C_{\text{opportunity cost}}(t) = -w_{\text{short}} \cdot y_{\text{short}}(t) + w_{\text{BB}} \cdot I_{\text{BB}}(t) \)

with:

We can express these relations with some alternative formulations:

Momentum-Based Opportunity Cost

\(C_{\text{opportunity cost}}(t) = -w_{\text{short}} \cdot \left( y_{\text{short}}(t) + \kappa \cdot \frac{d y_{\text{short}}(t)}{d t} \right) + w_{\text{BB}} \cdot I_{\text{BB}}(t) \)

• The static linear model ignores how quickly yields are moving, focusing only on their level. However, rapid changes in yields (positive or negative) often have an outsized psychological and economic impact on investors.

• By including the rate of change (momentum) of short-term yields, this formulation captures how sudden yield movements affect gold demand:

  • Rapidly rising yields create urgency to shift away from gold due to rising opportunity costs.

  • Rapidly falling yields may amplify demand for gold as holding cash or bonds becomes less attractive.

Risk-Neutral Opportunity Cost (for those who hate themselves and my preferred way)

Using the Breeden-Litzenberger formula to derive a risk-neutral probability density function (PDF) from option prices provides a nuanced approach (although more computationally expensive) to calculate the opportunity cost of holding gold. By incorporating the market’s implied expectations for the distribution of future rates, this method can reflect not only the baseline yield levels but also the range and likelihood of possible rate outcomes.

When traders price options on short-term rates, they implicitly embed their expectations about future rate movements. These expectations are not limited to a single point estimate (e.g., the forward rate) but encompass the entire distribution of possible outcomes, including:

• Baseline expectations (mean rate level).

• Uncertainty (variance).

• Directional biases (skewness).

• Tail risks (kurtosis or fat tails).

Core Concept: Breeden-Litzenberger Formula

The Breeden-Litzenberger formula allows us to extract the risk-neutral PDF of an underlying rate r at a specific time T from the prices of European call options:

\(p(r,t) = \frac{\partial^2 C(r,t)}{\partial K^2}\)

Where:

This formula assumes a continuum of strike prices. In practice, discrete strikes are interpolated or smoothed to approximate the PDF.

The opportunity cost of holding gold, can be dynamically adjusted based on the full shape of the risk-neutral distribution. Let’s break this down:

With the PDF p(r) in hand, we can construct the opportunity cost of holding gold, by integrating over the full distribution. The formula takes the form:

\(C_{\text{opportunity cost}}(t) = -w_{\text{short}} \cdot \int_{-\infty}^\infty r \cdot \phi(r) \cdot p(r) \, dr + w_{\text{BB}} \cdot I_{\text{BB}}(t), \)

Where:

We can be as dull as one can imagine with the weight function of 1 where we find once again our old friend in its option implied form of:

\(C_{\text{opportunity cost}}(t) = -w_{\text{short}} \cdot \mathbb{E}[r_{\text{short}}] + w_{\text{BB}} \cdot I_{\text{BB}}(t) \)

the difference between this form and the first expression of opportunity cost in this section is that instead of looking at the current short term yield, we are looking at the option market implied short term yield at the time of our chosen option maturity.

We can amplify contributions from rate levels far from the mean, highlighting periods of high uncertainty with:

\(\phi(r) = e^{\kappa \cdot (r - \mathbb{E}[r_{\text{short}}])^2} \)

Capturing moments

Using the risk neutral distribution we can express our opportunity cost in term of its moments.

\(\mu_n = \int_{-\infty}^\infty r^n \cdot p(r) \, dr\)

Where:

We use this to rewrite the opportunity cost function:

\(C_{\text{opportunity cost}}(t) = -w_{\text{short}} \cdot \left( \phi_0 \cdot \mu_0 + \phi_1 \cdot \mu_1 + \phi_2 \cdot \mu_2 + \cdots \right) + w_{\text{BB}} \cdot I_{\text{BB}}(t), \)

where:

With the first few moments, we can capture significant behaviors of our risk-neutral distribution

Baseline Mean Adjustment

The baseline expectation for the short-term rate is given by the expected value of the risk-neutral distribution:

\(\mu_1 = \mathbb{E}[r_{\text{short}}] = \int_{-\infty}^\infty r \cdot p(r) \, dr\)

This reflects the central tendency of the market’s expectations for future rates.

We can also use the formulation for the Momentum-Based Opportunity Cost with this expression, which gives it some interpretability based on options market-implied expectations of rate drift.

\(C_{\text{opportunity cost}}(t) = -w_{\text{short}} \cdot \left( \mathbb{E}[r_{\text{short}}] + \kappa \cdot \frac{d\mathbb{E}[r_{\text{short}}]}{dt} \right) + w_{\text{BB}} \cdot I_{\text{BB}}(t) \)

where:

Variance Adjustment:

\(\sigma_r^2 = \mu_2 - \mu_1^2 = \int_{-\infty}^\infty (r - \mu_1)^2 \cdot p(r) \, dr \)

Variance in short-term rates, often interpreted as a measure of uncertainty, has a dual and context-dependent relationship with the opportunity cost of holding gold. On one hand, higher variance signals a wider distribution of potential rate outcomes, which might include scenarios where short-term rates significantly rise. This prospect increases the appeal of yield-bearing assets relative to gold, a non-yielding asset, thus raising the opportunity cost. On the other hand, if the variance reflects broader market instability or policy uncertainty, it can increase gold's attractiveness as a safe-haven asset. In this case, the opportunity cost of holding gold diminishes, as investors prioritize its stability over the speculative appeal of alternative investments. Therefore, the impact of variance depends critically on whether it reflects the potential for higher rates or systemic instability.

We can incorporate variance into the opportunity cost function in a flexible way, allowing it to either increase or decrease the opportunity cost depending on the prevailing market regime.

\(C_{\text{opportunity cost}}(t) = -w_{\text{short}} \cdot \mathbb{E}[r_{\text{short}}] + w_{\text{BB}} \cdot I_{\text{BB}}(t) + \phi_{\sigma} \cdot \sigma_r^2(t), \)

Where:

To make the expression dynamic, we can express the coefficient as follows:

\(\phi_{\sigma}(t) = \phi_0 + \phi_1 \cdot \text{Skew}(p(r)) + \phi_2 \cdot \text{Geo}(t) \)

Where:

• Skew(p(r)): Skewness of the risk-neutral PDF, capturing directional bias in rate uncertainty.

• Geo(t): Geopolitical or systemic instability measure, reflecting safe-haven demand.

Skew Adjustment

\(\gamma_1 = \frac{\int_{-\infty}^\infty (r - \mu_1)^3 \cdot p(r) \, dr}{\sigma_r^3}\)

The skew reflects asymmetry in the rate distribution where a positive skew (long tail on the right) increases opportunity cost, signaling potential for higher rates.

Kurtosis Adjustment

\(\gamma_2 = \frac{\int_{-\infty}^\infty (r - \mu_1)^4 \cdot p(r) \, dr}{\sigma_r^4} \)

Measures the "tailedness" of the distribution where a high kurtosis indicates greater tail risk, which can influence the perceived opportunity cost. We can also adjust the coefficient for skew to dynamically represent the market regime we are in regarding the variance.

Inflation Risk

Inflation is a dynamic force in the financial system, shaping how investors perceive risk and allocate assets. For active gold demand, inflation interacts with broader market conditions, such as the yield curve, to influence short-term investment decisions. The inflation cost function captures these effects by responding to both the momentum of inflation expectations and macroeconomic signals embedded in the yield curve.

Revisiting our Yield Curve Indicator

Now that we have provided some intuition and initial formulations on the risk-neutral framework; let’s use this to provide an option market implied forward view to our yield curve indicator. We derive our risk-neutral distribution for short and long rates respectively:

\(p_{\text{short}}(r) = \frac{\partial^2 P_{\text{short}}(r)}{\partial r^2}, \quad p_{\text{long}}(r) = \frac{\partial^2 P_{\text{long}}(r)}{\partial r^2}\)

Where:

The mean and momentum of rates for short- and long-duration rates are computed as:

\(\mathbb{E}[r_{\text{short}}] = \int_{-\infty}^\infty r \cdot p_{\text{short}}(r) \, dr, \quad \mathbb{E}[r_{\text{long}}] = \int_{-\infty}^\infty r \cdot p_{\text{long}}(r) \, dr\)

\(\Delta \mathbb{E}[r_{\text{short}}] = \frac{\partial}{\partial t} \int_{-\infty}^\infty r \cdot p_{\text{short}}(r) \, dr, \quad \Delta \mathbb{E}[r_{\text{long}}] = \frac{\partial}{\partial t} \int_{-\infty}^\infty r \cdot p_{\text{long}}(r) \, dr\)

which allows us to write our index as:

\(I(t) = \frac{\Delta \mathbb{E}[r_{\text{long}}](t) \pm \Delta \mathbb{E}[r_{\text{short}}](t)}{|\Delta \mathbb{E}[r_{\text{long}}](t)| + |\Delta \mathbb{E}[r_{\text{short}}](t)|}\)

This allows us to look beyond realized changes in the spot rates curve and glimpse into the option market implied changes to the yield curve. But always remember that this formulation offloads the work of estimating yield curve changes based on economic data to the market. Market-implied indicators have the great advantage of being live compared to economy-implied indicators, which require now-casting.

We could conceptually also extend our earlier market implied inflation estimation using this framework at no additional computational cost once we already did the work of calculating the yield curve change index with the above method.

The Inflation Cost Function

The inflation cost function, is designed to reflect the nuanced relationship between inflation and gold demand. It combines inflation momentum with yield curve dynamics to offer a comprehensive view of how inflation-related risks shape active demand for gold.

\(C_{\text{inflation}}(t) = \phi \cdot \frac{d\pi(t)}{dt} + \eta_{\text{BB}} \cdot I_{\text{BB}}(t) + \eta_{\text{SF}} \cdot I_{\text{SF}}(t), \)

Where:

The first term captures inflation momentum, which measures the rate of change in inflation expectations over time. This term highlights the dynamic nature of investor behavior: positive inflation momentum indicates accelerating inflation expectations, prompting a stronger demand for gold as a hedge against eroding purchasing power. Conversely, negative momentum reflects decelerating or falling inflation expectations, reducing the urgency to hold gold. This component aligns with short-term investor strategies, emphasizing how rapidly evolving macroeconomic signals influence gold allocations.

The second term incorporates the steepener/flattening dynamics of the yield curve. This captures the relative movements between short- and long-term rates. A steepening yield curve suggests rising long-term inflation expectations or easing monetary policy, both of which enhance gold’s appeal as a hedge. A flattening curve, on the other hand, signals subdued inflation expectations or tightening monetary policy, reducing gold demand. This term focuses on the relative adjustments across the yield curve, providing insights into how investors perceive inflation risks and their impact on term premia.

By combining inflation momentum and yield curve slope dynamics we balance short-term and regime-specific signals. Inflation momentum ensures sensitivity to immediate changes in inflation expectations, while the Steepener/Flattener index reflects broader macroeconomic conditions that influence demand. Together, these components create a robust, dynamic measure of inflation's impact on active gold demand.

Money Liquidity Index: A Combined Market-Economic Hybrid

The monetary liquidity component captures the relationship between the availability of money in the financial system and its influence on the active demand for gold. Unlike perpetual demand, which responds to structural monetary trends over long horizons, active demand is highly sensitive to short-term changes in liquidity conditions. In an environment of expanding liquidity, excess money tends to flow into alternative assets like gold, increasing demand. Conversely, when liquidity tightens, gold demand typically declines as investors prioritize higher-yielding or more liquid instruments.

Here is a possible formulation of the liquidity index. This is a portion of my research where I am doing significant active work. How to model/represent monetary liquidity conditions?

\(\mathcal{L}(t) = \alpha \cdot \frac{\Delta M(t)}{M(t-1)} + \gamma \cdot \frac{D(t)}{\text{GDP}(t)} + \zeta \cdot \frac{\Delta C(t)}{C(t-1)} + \nu \cdot \frac{\Delta \text{Reserves}(t)}{\text{Reserves}(t-1)}, \)

Where:

Change in Money Supply
The money supply reflects the total liquidity injected into the economy by central banks, captured through aggregates like M1 or M2. An expanding money supply signals that central banks are easing monetary policy, creating excess liquidity that often flows into alternative assets like gold. For example, during periods of quantitative easing, central banks flood the system with money, making gold more attractive as a store of value. Conversely, when the money supply contracts due to tightening policies, liquidity dries up, reducing the appeal of holding gold.

Debt-to-GDP Ratio
This measures a country's fiscal sustainability and its long-term risk of monetary instability. A rising debt-to-GDP ratio reflects increasing fiscal pressure, often leading to inflation fears or concerns about the government’s ability to meet obligations. As such, gold demand typically rises during periods of fiscal stress. For instance, during debt crises in developed economies, gold often serves as a hedge against currency depreciation. On the other hand, a declining ratio indicates fiscal stability, making gold less necessary as a protective asset.

Change in Private-Sector Credit
Private-sector credit measures the flow of borrowing by businesses and households. Rapid credit growth often signals optimism and confidence in economic conditions, reducing demand for defensive assets like gold. For instance, when private credit is expanding, investors tend to allocate more to higher-yielding investments. Conversely, a contraction in credit reflects tightening financial conditions or economic stress, making gold more attractive as a safe haven during these periods. A good example of this dynamic is during financial crises when banks pull back lending, and investors turn to gold.

Change in Central Bank Reserves
Central bank reserves reflect the amount of liquidity held by commercial banks with central banks. When these reserves rise, it often indicates that central banks are injecting liquidity into the financial system, boosting confidence and supporting gold demand. During crises, central banks increase reserves to stabilize markets, indirectly supporting gold demand. However, falling reserves reflect tightening liquidity conditions, where gold demand may decline as the system prioritizes liquidity for immediate needs.

Additional Considerations

To enhance the liquidity indicator, we can integrate other components that reflect broader monetary, fiscal, and financial market dynamics. These additions would complement the existing focus on money supply, debt-to-GDP, private-sector credit, and central bank reserves.

Velocity of Money

• What It Measures: The rate at which money circulates in the economy, calculated as the ratio of nominal GDP to the money supply (e.g., M2).

• Why It Matters: A declining velocity of money suggests hoarding or reduced economic activity, often increasing demand for gold as a safe-haven asset. Conversely, rising velocity reflects a more dynamic economy, reducing gold demand.

• Example: During economic contractions, the velocity of money often declines, coinciding with increased gold demand.

Cross-Border Capital Flows

• What It Measures: Net inflows or outflows of capital across borders, reflecting global liquidity conditions and risk sentiment.

• Why It Matters: Large outflows from emerging markets often drive demand for gold as investors seek to hedge against currency depreciation or financial instability.

• Example: During times of global financial stress, capital flows into safe-haven currencies and assets, including gold.

Gold Lease Rates (GLR)

• What It Measures: The cost of borrowing gold in the interbank market, typically reflecting gold’s availability relative to demand.

• Why It Matters: Rising lease rates indicate tighter liquidity in the gold market itself, often coinciding with increased demand for physical gold. Falling rates reflect easier liquidity conditions, reducing gold’s appeal.

• Example: During the 2008 financial crisis, gold lease rates spiked as demand for gold surged.

Central Bank Balance Sheet Growth

• What It Measures: The growth or contraction of central bank balance sheets as a measure of monetary stimulus or tightening.

• Why It Matters: An expanding balance sheet signals monetary easing, increasing gold demand. Conversely, a shrinking balance sheet reflects tightening liquidity conditions, often reducing demand.

• Example: The Federal Reserve’s balance sheet expansions during quantitative easing programs significantly supported gold prices.

Global Trade Volumes

• What It Measures: Changes in global trade activity, often reflecting economic health and liquidity conditions.

• Why It Matters: Declining trade volumes signal slowing economic activity and reduced liquidity, increasing gold demand. Rising trade volumes reflect economic dynamism, reducing gold’s appeal.

• Example: Trade slowdowns during geopolitical crises or recessions often align with higher gold demand.

Shadow Banking Indicators

• What It Measures: Metrics like total assets under management in shadow banking institutions, including money market funds and securitization vehicles.

• Why It Matters: A contraction in shadow banking liquidity signals stress in the broader financial system, driving demand for gold. Growth reflects ample liquidity, reducing demand.

• Example: Shadow banking contractions during the 2008 financial crisis significantly drove gold demand as traditional liquidity mechanisms failed.

Real Effective Exchange Rate (REER)

• What It Measures: A country’s currency value adjusted for inflation relative to a basket of other currencies.

• Why It Matters: A declining REER indicates weakening currency competitiveness, often driving gold demand as a hedge against currency devaluation.

• Example: Declining REER values for the U.S. dollar during periods of aggressive monetary easing have historically aligned with rising gold prices.

Financial Stress Index

• What It Measures: A composite index that combines credit spreads, equity market volatility, and funding market stress.

• Why It Matters: Rising financial stress often aligns with tighter liquidity and increased gold demand as a safe-haven asset.

• Example: Financial stress indices spiked during the 2008 crisis, coinciding with a surge in gold prices.

Sovereign CDS Spreads

• What It Measures: Credit default swap (CDS) spreads for sovereign debt, reflecting market-perceived risk of sovereign default.

• Why It Matters: Widening CDS spreads indicate growing concerns over fiscal sustainability, often boosting demand for gold.

• Example: During the eurozone debt crisis, widening CDS spreads for countries like Greece drove up gold demand.

To put everything together, we can reference back to the work we did on perpetual demand to express different ways to join the dynamics of opportunity cost to holding gold, inflation risk and monetary liquidity into one active demand formula differential equation which will allow us to estimate changes in demand sensitive to market changes from today.

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Conclusion and Future Directions

This analysis synthesizes existing frameworks and market phenomena to build practical models that inform investment strategies. The interplay of inflation, yield dynamics, and monetary liquidity offers well-trodden paths to understanding asset demand, particularly for gold and Bitcoin. By documenting these relationships, the goal is not to reinvent the wheel but to operationalize established concepts for tactical allocation and portfolio management.

Gold, with its unique combination of scarcity, historical reliability, and utility as a hedge, provides fertile ground for applying these models. The focus on demand drivers, from inflation to opportunity costs, translates directly into actionable insights for trading decisions. Incorporating live market data—such as yield curve regimes, breakeven inflation, and risk-neutral metrics—serves as a way to refine execution timing and identify mispricing opportunities.

Looking forward, the work naturally extends into two critical areas:

1. Supply-Side Dynamics: Building on the demand-side focus, integrating supply constraints into the framework—such as mining output for gold or algorithmic issuance for Bitcoin—will add depth to the models. This will provide a more comprehensive basis for anticipating price moves based on shifts in supply-demand balance.

2. Asset Pricing Models: The ultimate objective is to translate these insights into robust pricing strategies. By leveraging the interplay of supply and demand with market data, the goal is to identify relative value opportunities across asset classes and monetize misalignments efficiently.

Rather than uncovering new truths, this process is about systematically applying known principles to better navigate market volatility and capture returns. The exercise here is one of disciplined implementation, turning abstract relationships into concrete, profit-driven investment strategies.

Cheers!