mathematics.md

Mathematical Analysis Documentation for Cryptocurrency Metrics

This document consolidates the mathematical equations and variables used for fundamental, technical, quantitative, and peer analysis of cryptocurrency metrics within the /src folder.

Table of Contents

1. Fundamental Analysis
2. Technical Analysis
3. Quantitative Analysis
4. Peer Analysis

Fundamental Analysis

1. NVT Ratio

• Equation: (P × S) / (V × P) (mean over period)
• Variables:
  • P: Close Price
  • S: Circulating Supply
  • V: Volume

2. Price/Volume Ratio

• Equation: P_current / (V × P)_mean
• Variables:
  • P_current: Current Close Price
  • (V × P)_mean: Average Quote Volume

3. Market Cap Growth Rate

• Equation: ((P_end × S) / (P_start × S))^(1 / t) - 1
• Variables:
  • P_end: End Price
  • P_start: Start Price
  • S: Circulating Supply
  • t: Time in Years (1)

4. Volume CAGR

• Equation: ((V_end × P_end) / (V_start × P_start))^(1 / t) - 1
• Variables:
  • V_end: End Volume
  • V_start: Start Volume
  • P_end: End Price
  • P_start: Start Price
  • t: Time in Years (1)

5. Liquidity Ratio

• Equation: (V × P)_mean / (P_current × S)
• Variables:
  • (V × P)_mean: Average Quote Volume
  • P_current: Current Price
  • S: Circulating Supply

6. Mayer Multiple

• Equation: P_current / SMA_200
• Variables:
  • P_current: Current Price
  • SMA_200: 200-day Simple Moving Average

7. Price Momentum

• Equation: (P_end - P_start) / P_start
• Variables:
  • P_end: End Price
  • P_start: Start Price

8. Volume Momentum

• Equation: ((V × P)_late - (V × P)_early) / (V × P)_early
• Variables:
  • (V × P)_late: Mean Quote Volume (second half)
  • (V × P)_early: Mean Quote Volume (first half)

9. Volatility-Adjusted Market Cap

• Equation: (P_current × S) / (1 + σ)
• Variables:
  • P_current: Current Price
  • S: Circulating Supply
  • σ: Annualized Volatility (std(P_pct_change) × √365)

10. Turnover Ratio

• Equation: Σ(V × P) / S
• Variables:
  • Σ(V × P): Total Quote Volume
  • S: Circulating Supply

11. Price Stability Ratio

• Equation: P_mean / σ
• Variables:
  • P_mean: Mean Price
  • σ: Annualized Volatility

12. Volume-to-Price Ratio

• Equation: (V × P)_mean / P_current
• Variables:
  • (V × P)_mean: Average Quote Volume
  • P_current: Current Price

13. Discounted Expected Utility Value (DEUV)

• Equation: (P_current × S) / Σ[(V × P)_current × (1 + g)^t / (1 + r)^t] (t = 1 to 5)
• Variables:
  • P_current: Current Price
  • S: Circulating Supply
  • (V × P)_current: Current Average Quote Volume
  • g: Growth Rate (0.08)
  • r: Discount Rate (0.12)

14. Price to Volatility Cost

• Equation: P_current / (P_current × σ)
• Variables:
  • P_current: Current Price
  • σ: Annualized Volatility

15. Regulatory Discount

• Equation: P_current × (1 - h)
• Variables:
  • P_current: Current Price
  • h: Haircut (0.20)

Technical Analysis

1. SMA 50-day

• Equation: Σ(P_i) / 50 (last 50 days)
• Variables:
  • P_i: Close Price at day i

2. EMA 20-day

• Equation: (P_current × k) + (EMA_prev × (1 - k)), k = 2 / (20 + 1)
• Variables:
  • P_current: Current Price
  • EMA_prev: Previous EMA
  • k: Smoothing Factor

3. RSI

• Equation: 100 - (100 / (1 + (Avg Gain / Avg Loss))) (14-day period)
• Variables:
  • Avg Gain: Mean of positive price changes
  • Avg Loss: Mean of negative price changes

4. MACD Histogram

• Equation: (EMA_12 - EMA_26) - Signal, Signal = EMA_9 of (EMA_12 - EMA_26)
• Variables:
  • EMA_12: 12-day EMA
  • EMA_26: 26-day EMA
  • Signal: 9-day EMA

5. Bollinger Bands Width

• Equation: (Upper - Lower) / SMA_20, Upper = SMA_20 + 2 × σ_20, Lower = SMA_20 - 2 × σ_20
• Variables:
  • SMA_20: 20-day SMA
  • σ_20: 20-day Standard Deviation

6. ATR

• Equation: Σ(TR_i) / 14 (last 14 days), TR_i = max(H - L, |H - C_prev|, |L - C_prev|)
• Variables:
  • H: High
  • L: Low
  • C_prev: Previous Close

7. OBV

• Equation: Σ(V × sign(C - C_prev))
• Variables:
  • V: Volume
  • sign(C - C_prev): 1 if C > C_prev, -1 if C < C_prev, 0 if equal

8. VWAP

• Equation: Σ((H + L + C) / 3 × V) / ΣV
• Variables:
  • H: High
  • L: Low
  • C: Close
  • V: Volume

9. Price ROC

• Equation: ((P_current - P_14) / P_14) × 100
• Variables:
  • P_current: Current Price
  • P_14: Price 14 days ago

10. Stochastic %K

• Equation: 100 × (C - L_14) / (H_14 - L_14)
• Variables:
  • C: Current Close
  • L_14: Lowest Low (14 days)
  • H_14: Highest High (14 days)

11. Williams %R

• Equation: -100 × (H_14 - C) / (H_14 - L_14)
• Variables:
  • H_14: Highest High (14 days)
  • L_14: Lowest Low (14 days)
  • C: Current Close

12. Momentum

• Equation: P_current - P_10
• Variables:
  • P_current: Current Price
  • P_10: Price 10 days ago

13. Volume Oscillator

• Equation: ((V_MA_5 - V_MA_20) / V_MA_20) × 100
• Variables:
  • V_MA_5: 5-day Volume MA
  • V_MA_20: 20-day Volume MA

14. Chande Momentum Oscillator (CMO)

• Equation: 100 × (ΣUp - ΣDown) / (ΣUp + ΣDown) (14-day period)
• Variables:
  • ΣUp: Sum of positive price changes
  • ΣDown: Sum of negative price changes

15. Price Channel Breakout

• Equation: 1 if P_current > H_20, -1 if P_current < L_20, else 0
• Variables:
  • P_current: Current Price
  • H_20: 20-day High
  • L_20: 20-day Low

Quantitative Analysis

1. NVT Ratio

• Equation: (P × S) / (V × P) (mean)
• Variables:
  • P: Close Price
  • S: Circulating Supply
  • V: Volume

2. Price/Volume Ratio

• Equation: P_current / (V × P)_mean
• Variables:
  • P_current: Current Price
  • (V × P)_mean: Average Quote Volume

3. Sharpe Ratio

• Equation: (R_mean + APY_d - Rf_d) / σ × √365
• Variables:
  • R_mean: Mean Daily Return
  • APY_d: Staking Yield / 365 (0.06 / 365)
  • Rf_d: Risk-Free Rate / 365 (0.025 / 365)
  • σ: Daily Return Std

4. Current Utility Value (CUV)

• Equation: (P_current × S) / (V × P)_mean
• Variables:
  • P_current: Current Price
  • S: Circulating Supply
  • (V × P)_mean: Average Quote Volume

5. Discounted Expected Utility Value (DEUV)

• Equation: (P_current × S) / Σ[(V × P)_current × (1 + g)^t / (1 + r)^t] (t = 1 to 5)
• Variables:
  • P_current: Current Price
  • S: Circulating Supply
  • (V × P)_current: Current Average Quote Volume
  • g: Growth Rate (0.08)
  • r: Discount Rate (0.12)

6. Volume CAGR

• Equation: ((V_end × P_end) / (V_start × P_start))^(1 / t) - 1
• Variables:
  • V_end: End Volume
  • V_start: Start Volume
  • P_end: End Price
  • P_start: Start Price
  • t: Time in Years (1)

7. Volume Composition (Buy)

• Equation: V_buy / (V × P)_total
• Variables:
  • V_buy: Taker Buy Quote Volume
  • (V × P)_total: Total Quote Volume

8. Volume Composition (Sell)

• Equation: V_sell / (V × P)_total
• Variables:
  • V_sell: Total Quote Volume - V_buy
  • (V × P)_total: Total Quote Volume

9. Volatility Reduction

• Equation: (σ_early - σ_late) / σ_early (if > 0, else 0)
• Variables:
  • σ_early: Std of Returns (first half) × √365
  • σ_late: Std of Returns (second half) × √365

10. Price Momentum

• Equation: (P_end - P_start) / P_start
• Variables:
  • P_end: End Price
  • P_start: Start Price

11. Risk-Adjusted Volume Discount

• Equation: (V × P)_mean / (1 + (Rf + β × MRP) × σ) / (V × P)_mean
• Variables:
  • (V × P)_mean: Average Quote Volume
  • Rf: Risk-Free Rate (0.025)
  • β: Beta (1.4)
  • MRP: Market Risk Premium (0.06)
  • σ: Annualized Volatility

12. Trading Volume

• Equation: (V × P)_mean
• Variables:
  • (V × P)_mean: Average Quote Volume

13. Volume Volatility

• Equation: σ_v / (V × P)_mean
• Variables:
  • σ_v: Std of Quote Volume
  • (V × P)_mean: Average Quote Volume

14. Volume-to-Price Ratio

• Equation: (V × P)_mean / P_current
• Variables:
  • (V × P)_mean: Average Quote Volume
  • P_current: Current Price

15. Price Correlation

• Equation: corr(P_pct_change, P_pct_change) (self-correlation = 1)
• Variables:
  • P_pct_change: Daily Price Returns

16. Mayer Multiple

• Equation: P_current / SMA_200
• Variables:
  • P_current: Current Price
  • SMA_200: 200-day SMA

17. Price DCF Intrinsic Value

• Equation: Σ[P_current × (1 + g)^t / (1 + r)^t] (t = 1 to 5)
• Variables:
  • P_current: Current Price
  • g: Growth Rate (0.10)
  • r: Discount Rate (0.15)

18. Price DCF Valuation Ratio

• Equation: DCF_Intrinsic / P_current
• Variables:
  • DCF_Intrinsic: Price DCF Intrinsic Value
  • P_current: Current Price

19. Price to Volatility Cost

• Equation: P_current / (P_current × σ)
• Variables:
  • P_current: Current Price
  • σ: Annualized Volatility

20. Regulatory Discount

• Equation: P_current × (1 - h)
• Variables:
  • P_current: Current Price
  • h: Haircut (0.20)

21. Price/Volume Ratio (Alt)

• Equation: P_current / (V × P)_30day_mean
• Variables:
  • P_current: Current Price
  • (V × P)_30day_mean: 30-day Average Quote Volume

Peer Analysis

1. NVT Ratio

• Equation: (P × S) / (V × P) (mean)
• Variables:
  • P: Close Price
  • S: Circulating Supply
  • V: Volume

2. Sharpe Ratio

• Equation: (R_mean + APY_d - Rf_d) / σ × √365
• Variables:
  • R_mean: Mean Daily Return
  • APY_d: Staking Yield / 365 (0.05 / 365)
  • Rf_d: Risk-Free Rate / 365 (0.025 / 365)
  • σ: Daily Return Std

3. Price/Volume Ratio

• Equation: P_current / (V × P)_mean
• Variables:
  • P_current: Current Price
  • (V × P)_mean: Average Quote Volume

4. Mayer Multiple

• Equation: P_current / SMA_200
• Variables:
  • P_current: Current Price
  • SMA_200: 200-day SMA

5. Speculative Signal

• Equation: 1 if NVT > 50 or Mayer > 2.4, else 0
• Variables:
  • NVT: NVT Ratio
  • Mayer: Mayer Multiple

6. RSI

• Equation: 100 - (100 / (1 + (Avg Gain / Avg Loss))) (14-day period)
• Variables:
  • Avg Gain: Mean of positive price changes
  • Avg Loss: Mean of negative price changes

7. MACD Histogram

• Equation: (EMA_12 - EMA_26) - Signal, Signal = EMA_9 of (EMA_12 - EMA_26)
• Variables:
  • EMA_12: 12-day EMA
  • EMA_26: 26-day EMA
  • Signal: 9-day EMA

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