Quantitative Trading Fundamentals
📌 Quant trading involves creating a statistical edge using models (often ML) and executing it to achieve risk-adjusted returns.
⚙️ Execution is considered equally important as developing the predictive model/edge itself.
📊 Models can be regression (predicting real numbers like price delta or return %) or classification (predicting categories like price up/down with a probability).
🧠 Univariate models (one input feature) are recommended initially for simplicity and to minimize the risk of overfitting to noise.

Core Skills for Quant Trading
📚 Econometrics provides a foundational vocabulary for time series analysis, covering concepts like autocorrelation and non-stationarity.
💻 Machine Learning is the primary focus for creating the edge, offering scalability to high-frequency data and flexibility without explicit formula programming.
🛠️ Strong programming skills are crucial for building reliable, latency-sensitive, and scalable research APIs for testing and deployment.
➕ Necessary mathematics includes linear algebra, multivariable calculus, and strong probability and statistics.

Quantifying the Edge and Risk
💰 The statistical edge is quantified by Expected Value (EV), representing the average net profit/loss per trade, where a positive EV dictates playing the game.
📉 Do not focus only on win rate; a strategy with a 30% win rate can profit if winners are large, and a 70% win rate can lose if losses are too big.
📈 Risk-adjusted return is commonly measured by the Sharpe Ratio (Expected Returns / Standard Deviation of Returns), which indicates return per unit of risk.
🎯 Higher Sharpe Ratios allow for safer, increased leverage and result in smoother equity curves, resembling a straight line at very high values.

Data Preprocessing and Time Series
📉 Log returns ($\ln(P_t / P_{t-1})$) are preferred over simple returns because they are time-additive and symmetric, which better suits ML models.
⏳ Time series data can be regular (evenly spaced intervals, fixed $\Delta t$) or irregular (common in high-frequency data where $\Delta t$ is inconsistent, predicting the next "tick").
⬅️ Autoregression involves using past values (lags) to predict future values, similar to how models like ChatGPT predict the next word.

Modeling Approaches (AR1 Model Example)
🤖 A simple Linear Regression (AR1 model) uses the last known value ($x$) to predict the future value ($\hat{y}$) with parameters: Weight ($w$) and Bias ($b$).
🔁 Mean Reversion is modeled when the optimized weight ($w$) is negative, causing the model to pull predictions back towards the mean (like a rubber band).
🚀 Momentum is modeled when the weight ($w$) is positive, reinforcing the existing direction of the previous return.

Parameter Optimization Methods
🔢 Closed-form solution (Ordinary Least Squares - OLS) provides an exact analytical answer but is inefficient for large, terabyte-scale datasets.
🔄 Gradient Descent is an iterative approach essential for big data, where parameters are updated incrementally using batches of data based on the partial gradient (derivative of the chosen loss function).
🧠 When loss functions are non-convex, the goal of gradient descent is to land in a good local minimum rather than finding the single global minimum.

Market Microstructure & Execution Strategies
📝 Quant strategies are broadly categorized into Making (adding liquidity via limit orders, often rewarded with rebates) and Taking (removing liquidity via market orders, incurring higher fees).
📊 The Order Book reflects supply/demand, showing Bids (buys) and Asks (sells). The Spread is the difference between the Best Ask and Best Bid.
⚖️ The Mid Price (average of Best Bid/Ask) is preferred over the last trade price for modeling because it avoids the noise introduced by the bid-ask bounce.
💥 A large market order that eats through multiple price levels results in slippage, where parts of the order fill at worse prices, causing the mid price to shift.

Taking Strategy Details (Longer Horizon)
⏱️ Taking strategies are typically deployed over longer horizons (hours to days) due to transaction costs. Key decisions are Timing and Sizing.
📅 Time-based timing executes trades at fixed intervals, aligning well with regular time series models.
🎯 Predicate-based timing filters predictions, only acting when a strong condition (e.g., predicted return $\geq 0.01$) is met to boost EV.
📏 Trade Sizing must control risk; common methods include Constant sizing (baseline), Piecewise Linear (scaling size with prediction strength using hard tangent clipping), and Nonlinear (smoother scaling using $\tanh$).

Making Strategy Details (Liquidity Provision)
💸 Making strategies revolve around setting a Spread (profit captured per trade) and a Bias/Skew (adjusting quotes relative to the mid price).
🛑 A wide spread risks not getting filled, while a narrow spread risks adverse selection (taking positions in the wrong direction).
⬆️ Biasing means systematically shifting the bid/ask quotes toward the predicted direction (upward or downward) to skew order fills in the direction of the model's mid-price prediction.

Key Points & Insights
➡️ Focus on Expected Value (EV) over win rate when evaluating a strategy's profitability over the long term.
➡️ For initial model development, prioritize univariate linear regression models due to their simplicity and robustness against noise (adhering to Occam's Razor).
➡️ When trading on high-frequency data, rely on log returns for symmetric time-additive properties, and use the Mid Price to eliminate bid-ask bounce noise.
➡️ For Taking strategies, bet small and bet often (Constant or scaled sizing) to exploit tiny edges without risking bankruptcy from large drawdowns.
➡️ For Making strategies, systematic biasing of quotes based on model predictions is where the primary alpha is often found.

📸 Video summarized with SummaryTube.com on Jan 15, 2026, 03:44 UTC