\sigma_{\text{anual}} = \sigma_{\text{diaria}} \cdot \sqrt{365}
Historically $$\sigma \approx 60%-100%$$ Decreasing trend with: * institutional adoption * greater liquidity * deeper derivatives markets *** ### 3.2. Correlations Bitcoin exhibits **non-fixed correlations**: | Asset | Short-term correlation | Long-term | | ------ | ---------------------- | --------- | | Nasdaq | 0.2 – 0.6 | ↓ | | Gold | 0.0 – 0.3 | ↑ | | DXY | negative | mixed | | Bonds | almost 0 | almost 0 | Bitcoin is an emerging asset → variable correlation. *** ### 3.3. Sharpe Ratio (historical)Sharpe = \frac{R - R_f}{\sigma}
Bitcoin historically: * Sharpe > 1.0 (one of the highest among global assets) * Gold ≈ 0.4 * Nasdaq ≈ 0.7 *** ## 4. Market cycles and halvings Bitcoin follows cycles tied to its **monetary policy**:\text{Halving cada 210,000 bloques} \approx 4 \text{ años}
Financial effects: 1. supply shock 2. upward pressure 3. asset repricing 4. excess euphoria 5. corrective fall 6. accumulation 7. new cycle *** ## 5. Quantitative models to analyze Bitcoin ### 5.1. Stock-to-Flow (S2F) ModelS2F = \frac{Stock}{Flujo\ anual}
Bitcoin will increase its S2F indefinitely, due to the halving. PlanB’s classic model:\log(\text{Precio}) = a + b \cdot \log(S2F)
Limitations: * ignores demand * ignores regulatory shocks * simplifies adoption * useful as a framework, not a perfect predictor *** ### 5.2. Metcalfe Model (network value) Metcalfe's law:Valor \propto N^2
For Bitcoin:Precio \sim k \cdot (\text{direcciones activas})^2
On-chain metrics for N: * active addresses * on-chain volume * UTXO age bands * dormancy * active entities Compatible with the idea of Bitcoin as a monetary network. *** ## 6. On-chain metrics (unique to Bitcoin) Bitcoin is the only asset whose complete accounting state is: * public * verifiable * mathematically auditable This enables metrics that DO NOT exist for traditional assets. *** ### 6.1. MVRV (Market Value / Realized Value)MVRV = \frac{Valor\ de\ mercado}{Valor\ realizado}
Interpretation: * 3: euphoria → risk * \~1: fair zone * < 1: undervalued *** ### 6.2. Realized Cap Based on the price at which each UTXO last moved. It is an indicator of the market's “aggregate cost.” *** ### 6.3. Coin Days Destroyed (CDD) Measures spending of old coins:CDD = \sum (\text{Monedas gastadas} \cdot \text{días acumulados})
Indicates long-term holders' behavior. *** ### 6.4. Supply LivelinessL = \frac{\sum CDD}{\text{Edad total de monedas}}
Indicates whether HODLers are selling or accumulating. *** ## 7. Adoption-dynamics-based models Bitcoin follows logistic adoption curves similar to: * The Internet * smartphones * electricity * communication technologies Logistic model:Adopción(t) = \frac{K}{1 + e^{-r(t-t_0)}}
Bitcoin is in an accelerated growth phase. *** ## 8. Bitcoin in traditional portfolios Studies show that: * optimal portfolio weight = 1%–10% * reduces total risk due to **uncorrelated diversification** * increases expected return * improves Sharpe *** ## 9. Simple quantitative simulation (pseudocode) Monte Carlo simulation: ```python import numpy as np N = 10000 days = 365*4 mu = 0.1 # expected annual return 10% sigma = 0.7 # annual volatility results = [] for i in range(N): daily_returns = np.random.normal(mu/365, sigma/np.sqrt(365), days) price = 1 * np.exp(np.cumsum(daily_returns)) results.append(price[-1]) print("Expected price:", np.mean(results)) print("Deviation:", np.std(results)) ``` *** ## 10. Bitcoin as collateral Bitcoin is one of the best financial collaterals because: * it is fungible * it is globally transferable * it does not depend on intermediaries * it cannot be frozen at the consensus layer * it has a fixed supply * growing liquidity This enables: * loans against BTC * decentralized collateral systems * multi-signature contracts * financial infrastructures without custodians ## 11. Financial risks Risks to consider: 1. **Short-term volatility** Mitigation: horizon ≥ 4–10 years. 2. **Regulatory risk** Mitigation: node sovereignty + global distribution. 3. **Liquidity risk** Declining with institutional volume. 4. **Risk** technological Extremely low after 15 years without critical failures. 5. **Macro risk** Bitcoin behaves like a global macro asset (sensitivity to global liquidity). *** ## 12. Bitcoin and derivatives markets The ecosystem includes: * perpetual futures * options (call/put) * institutional forwards * spot ETFs (high impact) * OTC swaps It implies: * greater price efficiency * lower structural volatility * global price discovery *** ## 13. Chapter conclusion Bitcoin is not just a digital asset; it is a macroeconomic financial asset, with unprecedented properties: * perfectly known supply * incorruptible monetary policy * cross-cutting on-chain metrics * adoption with logistic behavior * energy security * growing monetary utility **Bitcoin is the purest, the most transparent, the most scarce, the most verifiable and the most resilient asset that has existed in financial history**. *** > Bitcoin is not a technological bet. **It is a bet against inflation, monetary manipulation and the collapse of institutional trust.** *** --- # Agent Instructions This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com. ## Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter: ``` GET https://www.notbank.com/learn/academy/en/bitcoin/bitcoin-as-an-asset.md?ask=