Single AHR DCA (HM) — AHR Pane (customized quantile)

Customized note

• []The log-regression window LR length controls how long a long-term fair value path is estimated from historical data.
  []The AHR window AHR window length controls over which historical regime you measure whether the coin is “cheap / expensive”.
  
• When you choose a log-regression window of length L (years) and an AHR window of length A (years), you can intuitively read the indicator as:
  
  “Within the last A years of this regime, relative to the long-term trend estimated over the same A years, the current price is cheap / neutral / expensive.”
  []Guidelines:
  • []In general, set the AHR window equal to or slightly longer than the LR window:
    
    • []If the AHR window is much longer than LR, you mix different baselines (different LR regimes) into one distribution.
      []If the AHR window is much shorter than LR, quantiles mostly reflect a very local slice of history.
      
    []For BTC / ETH and other BTC-like assets, you can use relatively long horizons (e.g. LR ≈ 3–5 years, AHR window ≈ 3–8 years).
    []For major altcoins (BNB / SOL / XRP and similar high-beta assets), it is recommended to use equal or slightly shorter horizons, e.g. LR ≈ 2–3 years, AHR window ≈ 2–3 years.
    

1. Price series & windows

• []Working timeframe: daily (1D).
  []Let the daily close of the current symbol on day t be P_t.
  []Main length parameters:
  
  • []HM window: L_HM = maLen (default 200 days)
    []Log-regression window: L_LR = lrLen (default 1095 days ≈ 3 years)
    []AHR window (regime window): W = windowLen (default 1095 days ≈ 3 years)
    

2. Harmonic moving average (HM)

• On a window of length L_HM, define the harmonic mean:
  
  HM_t = [ (1 / L_HM) * sum_{i=0..L_HM-1} ( 1 / max(P_{t-i}, eps) ) ]^(-1)
  
  []Here eps = 1e-10 is used to avoid division by zero.
  []Intuition: HM is more sensitive to low prices – an extremely low price inside the window will drag HM down significantly.
  

3. Log-regression baseline (LR)

• []On a window of length L_LR, perform a linear regression on log price:
  []Over the last L_LR bars, build the series
  
  x_k = log( max(P_k, eps) ), for k = t-L_LR+1 ... t, and fit
  
  x_k ≈ a + b * k.
  The fitted value at the current index t is
  
  log_P_hat_t = a + b * t.
  Exponentiate to get the log-regression baseline:
  
  LR_t = exp( log_P_hat_t ).
  
• Interpretation: LR_t is the long-term trend / fair value path of the current regime over the past L_LR days.
  

4. HM-based AHR (valuation ratio)

• At each time t, build an HM-based AHR (valuation multiple):
  
  AHR_t = ( P_t / HM_t ) * ( P_t / LR_t )
  []Interpretation:
  
  • []P_t / HM_t : deviation of price from the mid-term HM (e.g. 200-day harmonic mean).
    []P_t / LR_t : deviation of price from the long-term log-regression trend.
    []Multiplying them means:
    
    • []if price is above both HM and LR, “expensiveness” is amplified;
      []if price is below both, “cheapness” is amplified.
      
  []Typical reading:
  
  • []AHR_t < 1 : price is below both mid-term mean and long-term trend → statistically cheaper.
    
  • AHR_t > 1 : price is above both mid-term mean and long-term trend → statistically more expensive.
    

5. Empirical quantile thresholds (Opp / Risk)

• On each new day, whenever AHR_t is valid, add it into a rolling array:
  
  A_t_window = { AHR_{t-W+1}, ..., AHR_t } (at most W = windowLen elements)
  []On this empirical distribution, define two quantiles:
  []Opportunity quantile: q_opp (default 15%)
  []Risk quantile: q_risk (default 65%)
  []Using standard percentile computation (order statistics + linear interpolation), we get:
  Opp threshold:
  
  theta_opp = Percentile( A_t_window, q_opp )
  Risk threshold:
  
  theta_risk = Percentile( A_t_window, q_risk )
  
• We also compute the percentile rank of the current AHR inside the same history:
  
  q_now = PercentileRank( A_t_window, AHR_t ) ∈ [0, 100]
  []This yields three valuation zones:
  []Opportunity zone: AHR_t <= theta_opp
  
  (corresponds to roughly the cheapest ~q_opp% of historical states in the last W days.)
  []Neutral zone: theta_opp < AHR_t < theta_risk
  []Risk zone: AHR_t >= theta_risk
  
  (corresponds to roughly the most expensive ~(100 - q_risk)% of historical states in the last W days.)
  
• All quantiles are purely empirical and symbol-specific: they are computed only from the current asset’s own history, without reusing BTC thresholds or assuming cross-asset similarity.
  

6. DCA simulation (lightweight, rolling window)

• []Given:
  []a daily budget B (input: budgetPerDay), and
  []a DCA simulation window H (input: dcaWindowLen, default 900 days ≈ 2.5 years),
  []The script applies the following rule on each new day t:
  []If thresholds are unavailable or AHR_t > theta_risk
  → classify as Risk zone → buy = 0
  []If AHR_t <= theta_opp
  → classify as Opportunity zone → buy = 2B (double size)
  []Otherwise (Neutral zone)
  → buy = B (normal DCA)
  []Daily invested cash:
  
  C_t ∈ {0, B, 2B}
  
• Daily bought quantity:
  
  DeltaQ_t = C_t / P_t
  []The script keeps rolling sums over the last H days:
  []Cumulative position:
  
  Q_H = sum_{k=t-H+1..t} DeltaQ_k
  Cumulative invested cash:
  
  C_H = sum_{k=t-H+1..t} C_k
  Current portfolio value:
  
  PortVal_t = Q_H * P_t
  Cumulative P&L:
  
  PnL_t = PortVal_t - C_H
  Active days:
  
  number of days in the last H with C_k > 0.
  
• These results are only used to visualize how this AHR-quantile-driven DCA rule would have behaved over the recent regime, and do not constitute financial advice.