Turning Market Noise into Meaning

12 year trendline for bitcoin price

anuj — Thu, 26 Feb 2026 21:11:02 +0000

Quantifying & Plotting the “Speed” of Bitcoin Price (12 Years)

Quantifying & Plotting the “Speed” of Bitcoin Price Over the Last 12 Years

A physics-style framing works well: treat price as a trajectory, then define position, velocity, speed (magnitude), and acceleration.
The key trick is to work in log price so movements are comparable across cycles.

1) Choose the Right “Position” Variable Use log price

Let price be $P(t)$. Define the position-like variable as:

\[
x(t) = \ln P(t)
\]

Returns become additive in time
Changes are scale-invariant (a move from \$1k→\$2k compares to \$30k→\$60k)
Plays nicely with diffusion-style market models

2) Define Velocity (Directional “Speed”) log-return

The discrete daily velocity is the daily log return:

\[
r_t = x_t – x_{t-1} = \ln P_t – \ln P_{t-1}
\]

A less noisy operational definition uses a rolling window $\Delta t$:

\[
v_t^{(\Delta t)} = \frac{x_t – x_{t-\Delta t}}{\Delta t}
\]

Units are “log-return per day.” Common choices: $\Delta t = 30,\; 90,\; 365$ days.

3) Define Speed (Magnitude Only) ignore direction

If you want true “speed” (how fast regardless of up/down), take the magnitude:

\[
\bigl|v_t^{(\Delta t)}\bigr|
\]

Spikes during blow-off tops and capitulation drops
Useful for detecting “eventfulness” independent of trend direction

4) Define Acceleration (Regime Change Detector) 2nd difference

Acceleration is the change in velocity. Daily version:

\[
a_t = r_t – r_{t-1}
\]

Equivalent second-difference form:

\[
a_t = x_t – 2x_{t-1} + x_{t-2}
\]

Highlights cycle tops, panic bottoms, and turning points
Pairs nicely with your “phase transition / halving” narrative

5) What to Plot (Practical Dashboard) 4 core plots

Recommended plots for the last 12 years:

Log Price $x(t)$
Velocity $v_t^{(365)}$ (trend strength)
Speed $\lvert v_t^{(365)} \rvert$ (movement magnitude)
Acceleration $a_t$ (regime changes)

Pro tip: add vertical halving lines and label major events. Velocity often expands
~6–12 months post-halving, while speed/acceleration spike near tops/bottoms.

6) “Market Kinetic Energy” (Optional, Physics-Consistent) energy proxy

If you want a single scalar “how intense is the motion?” measure:

\[
K_t = \frac{1}{2}\left(v_t^{(\Delta t)}\right)^2
\]

This pairs naturally with a volatility-as-temperature view ($\sigma^2$) and helps build a coherent analogy:
position → velocity → kinetic energy → temperature.

7) Python: Compute & Plot (12 Years) copy/paste

This script downloads BTC-USD, computes log-price, velocity, speed, acceleration, and plots them:

import yfinance as yf
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

# Download ~12+ years of daily BTC data
btc = yf.download("BTC-USD", start="2013-01-01", auto_adjust=True)

# Use Close (auto_adjust=True returns adjusted series where applicable)
btc["log_price"] = np.log(btc["Close"])

# Daily velocity (log return)
btc["velocity_daily"] = btc["log_price"].diff()

# Rolling velocities (trend speed over horizons)
btc["velocity_30d"]  = btc["log_price"].diff(30)  / 30
btc["velocity_90d"]  = btc["log_price"].diff(90)  / 90
btc["velocity_365d"] = btc["log_price"].diff(365) / 365

# Speed (magnitude)
btc["speed_365d"] = btc["velocity_365d"].abs()

# Acceleration (change in daily velocity)
btc["acceleration"] = btc["velocity_daily"].diff()

# --- Plot (no seaborn, no forced colors) ---
plt.figure(figsize=(14, 10))

plt.subplot(4, 1, 1)
plt.plot(btc.index, btc["log_price"])
plt.title("BTC: Log Price  ln(P)")

plt.subplot(4, 1, 2)
plt.plot(btc.index, btc["velocity_365d"])
plt.title("BTC: 365-Day Velocity  v^(365) = (ln P_t - ln P_{t-365}) / 365")

plt.subplot(4, 1, 3)
plt.plot(btc.index, btc["speed_365d"])
plt.title("BTC: 365-Day Speed  |v^(365)|")

plt.subplot(4, 1, 4)
plt.plot(btc.index, btc["acceleration"])
plt.title("BTC: Acceleration (Δ daily velocity)")

plt.tight_layout()
plt.show()

If you want the “speed” to be in percent per day instead of log-units,
multiply velocity by 100 (approximately valid for small returns), or work directly with simple returns.

8) Interpretation: What You’ll Typically See cycle structure

Velocity tracks regime drift (bull vs bear trend strength).
Speed spikes at manic tops and panic bottoms (event intensity).
Acceleration is a sharp turning-point detector (phase-transition-ish moments).
Peak speeds often decline over time as liquidity deepens (a “maturing market” signature).

The post 12 year trendline for bitcoin price appeared first on Turning Market Noise into Meaning.

ForEx Trading – Summary of book

anuj — Thu, 26 Feb 2026 14:41:49 +0000

The Little Book of Currency Trading – by Kathy Lien — Summary

A clear, executive-style overview of the book’s core ideas, practical lessons, and mental models.

The Big Idea

Forex markets are driven primarily by macroeconomics, interest rates, central bank policy, and global capital flows.
Successful traders think like economists and risk managers, using charts mainly for timing.

Core frame: You’re always trading one economy versus another. Every currency trade is a relative bet.

1) What the Forex Market Really Is

Largest financial market; trades 24/5 across global sessions.
Decentralized, highly liquid, dominated by institutions and central banks.
You trade pairs (one currency against another).

Example: Buying EUR/USD is a view that Europe strengthens relative to the U.S.

2) The Core Driver: Interest Rates

The book’s central thesis: interest rates are the gravitational force of currencies.
Capital tends to flow toward higher yields.

Carry Trade

Borrow in a low-rate currency and invest in a higher-yield currency.
Profits can come from both the rate differential and exchange-rate movement.
Works best in stable “risk-on” regimes; can unwind violently in crises.

3) Economic Fundamentals That Move Currencies

The book emphasizes monitoring macro indicators and policy shifts over purely technical signals.

Central Banks

Hawkish tone (tighter policy) often supports a stronger currency.
Dovish tone (easier policy) often pressures a currency lower.
Forward guidance and credibility matter as much as the rate decision itself.

Key Indicators

GDP growth
Inflation (CPI/PPI)
Employment (e.g., U.S. NFP)
Retail sales
Trade balance

Key lesson: Markets often move on expectations vs. reality—surprises matter more than raw numbers.

4) Market Psychology & Risk Sentiment

Environment	Typical Behavior
Risk-on	Investors seek yield; “risk currencies” tend to rise.
Risk-off	Safe havens strengthen; leveraged trades unwind.

Common safe-haven currencies include USD, JPY, and CHF, especially during global stress.

5) Technical Analysis (But With Limits)

Technical tools are presented primarily as timing mechanisms, not crystal balls.

Support & resistance
Moving averages
Fibonacci levels
Momentum indicators

Takeaway: Fundamentals often drive direction; technicals help with entry/exit discipline.

6) Trading Strategies Discussed

Trend trading: align with macro momentum.
Range trading: exploit consolidation between policy shifts.
Breakout trading: act on post-surprise moves.
News trading: opportunity around releases, with elevated risk.

7) Risk Management (The Real Edge)

A recurring theme: most traders fail due to risk mismanagement rather than analysis.

Use stop losses and predefined invalidation points.
Risk a small fraction of capital per trade.
Limit leverage; avoid emotional “revenge trading.”
Prioritize survival and consistency over big wins.

8) The Role of Leverage

Forex leverage can be extreme. The book warns that small moves can wipe out accounts.
Professionals typically use far less leverage than retail traders.

Key insight: Survival matters more than profit.

9) Understanding Currency Relationships

Commodity currencies can track resource cycles.
Cross-market relationships matter (rates, commodities, risk sentiment).
Crowded positioning can unwind quickly during regime shifts.

10) The Professional Trader Mindset

Think probabilistically; accept uncertainty.
Focus on repeatable process and execution.
Avoid prediction ego; trade the plan.

Core Mental Models

Currency = Economy: you’re trading national performance.
Interest Rates = Gravity: capital chases yield.
Expectations Move Markets: surprises matter most.
Liquidity Drives Stability: crowded trades unwind violently.
Risk Management > Prediction: longevity beats brilliance.

The post ForEx Trading – Summary of book appeared first on Turning Market Noise into Meaning.

Global Liquidity and Bitcoin Price

anuj — Tue, 24 Feb 2026 00:43:33 +0000

Bitcoin Liquidity & Sentiment Signal Reference

Live app

1⃣ Signal

Values: -1, 0, 1

Signal	Interpretation
1	Short-term bullish / upside bias (final_score in top percentile)
0	Neutral (final_score in middle percentile range)
-1	Short-term bearish / downside bias (final_score in bottom percentile)

2⃣ Final Score

Formula: final_score = liq_weight * Liquidity_Z + fng_weight * FNG_Contrarian + mom_weight * Momentum_Signal

Typical range: ~ -2.5 → +2.5 (depends on weights and inputs)

Meaning: Positive = bullish bias, Negative = bearish bias, Near zero = neutral

3⃣ Fear & Greed Index (FNG)

Raw range: 0 → 100

Contrarian signal applied in code:

FNG Value	Market Sentiment	fng_signal
0–24	Extreme Fear	1 (Contrarian buy)
25–49	Fear	0 (Neutral)
50–74	Greed	0 (Neutral)
75–100	Extreme Greed	-1 (Contrarian sell)

4⃣ Momentum Signal

Values: -1, 1

Value	Interpretation
1	Short-term bullish momentum
-1	Short-term bearish momentum

5⃣ Liquidity Z-Score

Formula: liq_z = (liq_mom – rolling_mean_180d(liq_mom)) / rolling_std_180d(liq_mom)

Typical range: ~ -3 → +3 (under normal market conditions)

Z-Score	Interpretation
> 2	Strong liquidity expansion → bullish for risk assets
0–2	Moderate liquidity growth → neutral / mildly bullish
0	Average liquidity growth → neutral
-2–0	Moderate contraction → mildly bearish
< -2	Strong contraction → bearish for risk assets

Summary Table

Component	Range / Values	Meaning / Interpretation
Signal	-1, 0, 1	Downside / Neutral / Upside bias
Final Score	~ -2.5 → +2.5	Combined weighted score of liquidity, sentiment, momentum
Fear & Greed Index	0 → 100	0 = extreme fear, 100 = extreme greed (contrarian applied)
FNG Contrarian	-1, 0, 1	1 = buy, 0 = neutral, -1 = sell
Momentum Signal	-1, 1	1 = bullish, -1 = bearish
Liquidity Z-Score	~ -3 → +3	Standard deviations above/below 180-day mean liquidity growth

The post Global Liquidity and Bitcoin Price appeared first on Turning Market Noise into Meaning.

1980s vs 2026 Economic Comparison

anuj — Thu, 12 Feb 2026 20:57:08 +0000

1980s vs 2026 Economic Comparison

Comparison: Early 1980s vs 2025–2026 U.S. Economy

Economists sometimes draw broad parallels between the early 1980s and the 2025–26 U.S. economy.
While there are thematic similarities in inflation concerns and consumer sentiment, there are also
major differences in severity, causes, and policy responses.

1. Inflation & CPI

Early 1980s (Volcker Era)

Double-digit inflation (10%+)
Peak inflation reached the mid-teens
Part of the “Great Inflation” following 1970s oil shocks
Aggressive Federal Reserve tightening to control inflation

2025–2026

Inflation significantly lower than early 1980s
Generally moderate compared to double-digit era
Consumers still perceive inflation as elevated
Inflation expectations remain sensitive

Key Difference: The 1980s saw extreme inflation; today’s inflation is elevated relative to the past decade but not comparable in magnitude.

2. Jobs & Unemployment

Early 1980s

Sharp recession induced by high interest rates
Unemployment peaked around 10%+
Significant job losses across industries

2025–2026

Unemployment around the 4% range
Labor market relatively strong by historical standards
Job growth slowing but not collapsing
Consumers expressing concern about future job security

Key Difference: The early 1980s experienced severe unemployment; today’s labor market remains comparatively stable.

3. Consumer Confidence

Early 1980s

Confidence plunged amid recession and inflation
Tight credit conditions
High unemployment fears

2025–2026

Confidence has declined sharply
Concerns centered on inflation and future economic stability
Perception gap between macro data and consumer sentiment

Similarity: In both periods, inflation anxiety drove pessimism.

Difference: The 1980s pessimism reflected severe economic pain; today’s reflects anxiety despite relatively stable macro indicators.

4. Structural & Policy Differences

Monetary Policy

1980s: Deliberate recession engineered to crush inflation
2020s: More gradual tightening and balancing approach

Economic Structure

1980s economy more industrial
2020s economy more service-based and globally integrated
Modern economy influenced by global supply chains and digital markets

Summary Comparison Table

Indicator	Early 1980s	2025–2026	Broad Connection
Inflation	Very high (double-digit)	Moderate but notable	Inflation concerns present in both periods
Unemployment	High (~10%+)	Low (~4%)	Different labor market realities
CPI Growth	Rapid price increases	Moderate increases	Magnitude differs significantly
Consumer Confidence	Very low during recession	Declining despite stable labor data	Sentiment affected by inflation fears in both eras

Key Takeaways

There are thematic parallels, especially around inflation anxiety.
The early 1980s experienced extreme inflation and severe recession.
Today’s economy features moderate inflation and relatively low unemployment.
Consumer sentiment in both periods reflects concern about purchasing power and stability.
The scale and policy response differ substantially between the two eras.

The post 1980s vs 2026 Economic Comparison appeared first on Turning Market Noise into Meaning.

M1 Money Supply and Bitcoin

anuj — Wed, 11 Feb 2026 22:26:07 +0000

M1 Money Supply and Bitcoin

Current U.S. M1 Money Supply (December 2025)

The most recent data shows that the U.S. M1 money supply is approximately $19.1 trillion
(seasonally adjusted).

M1 includes the most liquid forms of money:

Physical currency in circulation
Demand (checking) deposits
Other highly liquid deposits

What M1 Means for Bitcoin

The relationship between M1 and Bitcoin is indirect but important from a macroeconomic perspective.

1. Liquidity and Asset Prices

An expanding M1 increases liquidity in the financial system. Greater liquidity can:

Encourage investment into risk assets
Support higher asset valuations
Increase capital flows into alternative assets like Bitcoin

2. Inflation Expectations

If M1 growth contributes to inflation concerns:

Investors may seek hedges against fiat currency debasement
Bitcoin is sometimes viewed as “digital gold”

3. Market Psychology

Traders sometimes compare Bitcoin’s market cap relative to money supply growth.
In periods of monetary expansion, bullish narratives around Bitcoin often strengthen.

4. Stablecoin Liquidity

Within crypto markets, stablecoin issuance can act as a form of dollar liquidity,
providing purchasing power that can flow into Bitcoin.

Key Takeaways

Current M1: ~$19.1 trillion
Higher liquidity can support Bitcoin demand
The relationship is indirect and influenced by broader macro conditions
Bitcoin price depends on multiple factors beyond money supply

The post M1 Money Supply and Bitcoin appeared first on Turning Market Noise into Meaning.

Black Scholes – and non Gaussian Price Distributions

anuj — Thu, 11 Dec 2025 03:08:03 +0000

Alternatives to Black–Scholes — HTML

Alternatives to Black–Scholes and What Happens When Gaussian Assumptions Fail

Below is a structured HTML version of the explanation covering: Black–Scholes assumptions, consequences of incorrect Gaussian assumptions, major alternative models, and a compact summary table.

1. Background: What Black–Scholes Assumes

Asset returns follow a log-normal distribution — equivalently, log-returns are Gaussian with constant volatility.
Price follows geometric Brownian motion:
Volatility is constant (not stochastic).

2. What Happens if the Gaussian Assumption Is Incorrect?

Real markets deviate from Gaussian assumptions in several important ways:

“`

Fat tails

Large moves (jumps, crashes) occur much more frequently than a Gaussian would predict. Effect: Black–Scholes tends to underprice deep out-of-the-money options (puts and sometimes calls).

Skew / Smile

Empirically implied volatilities vary with strike; if Black–Scholes held perfectly the implied-volatility surface would be flat. Markets show a smile or skew.

Volatility is not constant

Volatility varies with time (stochastic volatility), exhibits clustering, and is affected by market events. Black–Scholes underestimates convexity and time-value effects when volatility is not constant.

Returns may have memory

Autocorrelation, volatility clustering, and other dependencies break the independent-increments assumption of geometric Brownian motion.

In short: When Gaussian/log-normal assumptions fail, Black–Scholes produces systematic pricing biases and practitioners typically back out an implied volatility surface to force the model to match observed prices.

“`

3. Major Alternatives to Black–Scholes

Below are widely used model families that address various weaknesses of Black–Scholes.

“`

A. Stochastic Volatility Models

Heston model — volatility follows a mean-reverting square-root process:

Pros: produces skew/smile and stochastic volatility; widely used for equities and FX.
SABR — popular in interest-rate derivatives (produces analytic approximations for the smile).
GARCH family — volatility driven by past returns (volatility clustering), useful in econometric and risk settings.

B. Jump–Diffusion Models

Merton jump–diffusion — adds Poisson jumps to the diffusion:

Captures sudden large moves, produces fatter tails and helps explain the smile.
Kou double-exponential jump model — asymmetric jumps with heavier tails on one side; better fit for crash/rally asymmetry.

C. Lévy and Heavy-Tailed Models

Variance Gamma — replaces Brownian motion with a pure-jump process driven by a Gamma time-change.
CGMY / KoBoL — flexible infinite-activity Lévy models with tunable tail behavior.

These model families greatly increase tail mass and skew relative to Gaussian models.

D. Local Volatility Models

Dupire local volatility — volatility is a deterministic function of spot and time, , calibrated to match the entire implied-volatility surface exactly.
Pros: exact calibration to market prices; Cons: questionable realistic dynamics for forward evolution (may misrepresent pathwise behavior).

E. Machine Learning & Data-Driven Models

Neural networks to model implied volatility surfaces or directly price options.
Reinforcement-learning based hedging strategies that learn from historical data rather than relying on closed-form Greeks.
Nonparametric density estimation for risk and pricing.

These methods are increasingly used in practice where rich data and computational power are available.

“`

4. Practical Consequences (Pricing & Hedging)

Systematic mispricing: deep OTM options (especially puts) often become underpriced by Black–Scholes.
Hedging failures: Greeks computed under wrong assumptions cause under- or over-hedging, especially around jumps — P/L surprises often occur.
Implied volatility surface: traders use implied vol as a corrective plug-in; better models attempt to explain and predict that surface rather than merely fit it.

5. Summary Table

Model Type	Fixes Gaussian Weakness?	Captures Jumps?	Captures Stochastic Vol?	Common Use
Black–Scholes	No	No	No	Baseline / pedagogical
Heston	Yes	No	Yes	Equity, FX
SABR	Yes	No	Yes	Rates (swaptions, caps)
Merton Jump	Yes	Yes	No	Modeling crashes / large moves
Kou Jump	Yes	Yes	No	Asymmetric jump fits
Variance Gamma / CGMY	Yes	Yes	Implicit	Exotic options, fat tails
Dupire Local Vol	Yes	No	Implicit	Exact calibration to IV surface
ML / Data-driven	Yes	Yes	Yes	Quant shops, empirical pricing

6. Want More?

If you’d like, I can provide any of the following right away as HTML/attachments:

A visual comparison of Gaussian vs heavy-tailed distributions (plot).
Diagrams contrasting Black–Scholes, Heston, and Jump-Diffusion dynamics.
Concrete pricing code (Python) for Heston or Merton jump model with sample calibration.
An explainer on how implied-volatility surfaces are built and used in practice.

The post Black Scholes – and non Gaussian Price Distributions appeared first on Turning Market Noise into Meaning.