finance-guide

1. Financial Data Standards

When processing market data for time-series analysis, the following conventions apply:

• Primary Pricing: The "Adjusted Close" price is the gold standard as it accounts for corporate actions (splits, dividends).
• Time Continuity: Data must be strictly chronological (ascending). Missing data points should be handled via "Forward Fill" (Last Observation Carried Forward) to preserve the integrity of technical indicators.
• Look-ahead Bias: Calculations at time $t$ must never access data from $t+1$. Any "future leakage" invalidates the simulation.

2. Discrete-Time Portfolio Model

The portfolio state at any time step $t$ is defined by:

• Cash Balance ($C_t$): Non-invested capital.
• Asset Holdings ($S_t$): Quantity of the security held.
• Portfolio Equity ($V_t$): $V_t = C_t + (S_t \times Price_t)$
• Order Execution: Orders generated by a signal at the close of $t$ are traditionally executed at the close of $t$ (theoretical) or the open of $t+1$ (realistic).

3. Performance & Risk Mathematics

Return Metrics

• Arithmetic Return: $R = \frac{V_{final} - V_{initial}}{V_{initial}}$
• Logarithmic Return: $r_t = \ln(Price_t / Price_{t-1})$
• Compound Annual Growth Rate (CAGR): $CAGR = \left( \frac{V_{final}}{V_{initial}} \right)^{\frac{1}{\text{years}}} - 1$

Risk Analytics

• Annualized Volatility ($\sigma$): $\sigma_{ann} = \text{std}(r_{daily}) \times \sqrt{252}$
• Sharpe Ratio: $S = \frac{\text{mean}(r_{daily})}{\text{std}(r_{daily})} \times \sqrt{252}$ (Assuming a risk-free rate of 0).
• Drawdown ($DD_t$): The percentage decline from the running peak: $DD_t = \frac{V_t - \text{Peak}_t}{\text{Peak}_t}$ where $\text{Peak}_t = \max(V_0 \dots V_t)$

4. Universal Strategy Logic Patterns

4.1 Passive Allocation (Buy & Hold)

• Logic: Full capital deployment at $t_0$. No rebalancing or exit signals.

4.2 Trend Following (Moving Average Crossover)

• Logic: Dual-window calculation.
• Signal: A "Golden Cross" (Short-term MA crosses above Long-term MA) triggers a Buy; a "Death Cross" (Short-term MA crosses below Long-term MA) triggers a Sell/Exit.

4.3 Systematic Accumulation (Dollar-Cost Averaging)

• Logic: Periodic capital injection ($C_{inject}$) at fixed intervals (weekly/monthly/quarterly) regardless of price.
• Share Acquisition: $S_{new} = S_{old} + \frac{C_{inject}}{Price_t}$

4.4 Momentum / Mean Reversion (RSI)

• Logic: Relative Strength Index calculation over $n$ periods.
• Signal: Buy when RSI < 30 (Oversold); Sell when RSI > 70 (Overbought).

4.5 Volatility Breakout (Bollinger Bands)

• Logic: Price relation to standard deviation bands $(\mu \pm 2\sigma)$.
• Signal: Buy/Sell triggered by price penetration of the upper or lower boundaries.

5. Trading Statistics & Quality Control

• Win Rate: Ratio of profitable trades to total closed trades.
• Profit Factor: Gross profits divided by gross losses.
• Time in Market: Percentage of the total duration where $S_t > 0$.
• Numerical Stability: Use 64-bit float precision; handle zero-volatility cases to avoid NaN results in Sharpe calculations.