Section 12 - Chapter 1 - Introduction to Quantitative Methods

Section 12 - Chapter 1 - Introduction to Quantitative Methods - Presented by Rohan Sharma - The CMT Coach - Chartered Market Technician CMT Level 1 Study Material - CMT Level 1 Chapter Wise Short Notes - CMT Level 1 Course Content - CMT Level 1 2025 Exam Syllabus Visit Site : www.learn.ptaindia.com and www.ptaindia.com

1. Chapter 1 - Introduction to Quantitative Methods Section 12 – Systems and Quantitative Methods Presented By : This Content is Copyright Reserved Rights Copyright 2025@PTAIndia

2. Agenda Introduction to Quantitative Analysis The Investment Process The Scientific Method and Its Application Preparing for Quantitative Analysis The Quantitative Process Quant for Discretionary Analysts The Importance of Context This Content is Copyright Reserved Rights Copyright 2025@PTAIndia

3. Investment Process Presented By : This Content is Copyright Reserved Rights Copyright 2025@PTAIndia

4. Investment Process Key Facts 1. Definition: Quantitative analysis in the investment process involves using mathematical models, statistical techniques, and computational methods to evaluate investment opportunities and risks. 2. Purpose: Helps in making objective, data-driven investment decisions by analyzing historical trends, correlations, and risk-return profiles . 3. Tools Used: o Statistical Models (e.g., Regression Analysis, Factor Models) o Machine Learning (Neural Networks, Random Forests) o Risk Metrics (Value at Risk, Sharpe Ratio, Beta) o Data Sources (Price Data, Financial Statements, Market Sentiment)

5. Investment Process Cheat Sheet Component Explanation Data Collection Gather historical price data, financial statements, macroeconomic indicators. Preprocessing Clean data, remove outliers, normalize variables. Factor Analysis Identify key drivers of asset performance (e.g., value, growth, momentum). Model Selection Choose regression, Monte Carlo simulations, machine learning, etc. Portfolio Optimization Use Modern Portfolio Theory (MPT) or Black- Litterman models to allocate assets. Risk Management Apply VaR , stress testing, and scenario analysis to evaluate risk exposure. Backtesting Test strategies using historical data to assess performance and refine models. Execution Implement algorithmic trading, automated rebalancing, and trade execution strategies.

6. Investment Process Comparison Interpretation: Quantitative vs. Qualitative Analysis Aspect Quantitative Analysis Qualitative Analysis Approach Data-driven, statistical models Subjective, based on judgment and experience Key Metrics Price trends, ratios, volatility, correlation Management quality, brand value, industry trends Tools Algorithms, backtesting, risk models Company reports, interviews, macroeconomic insights Risk Focus Measurable risks (VaR, Beta, drawdowns) Unmeasurable risks (regulatory changes, innovation impact) Bias Low (objective, data-driven) Higher (human judgment, emotions) Best Used For High-frequency trading, portfolio optimization Long-term investing, fundamental analysis

7. Basic Investment Decision Workflow Presented By : This Content is Copyright Reserved Rights Copyright 2025@PTAIndia

8. Investment Decision Workflow 1. Information (Data Gathering & Analysis) Objective: Collect and analyze relevant data to identify potential investment opportunities. 📌 Sources of Information: • Market Data: Stock prices, interest rates, inflation, economic indicators. • Company Reports: Financial statements, earnings reports, management discussions. • News & Events: Political developments, economic policies, global trends. • Quantitative & Technical Indicators: P/E ratios, moving averages, volatility measures. • Qualitative Insights: Industry trends, consumer behavior, competitive landscape. 🔍 Key Activities: • Perform fundamental and technical analysis. • Identify macroeconomic and sector-specific trends. • Assess risk factors and potential market inefficiencies.

9. Investment Decision Workflow 2. Idea (Develop Investment Hypothesis & Strategy) Objective: Formulate an actionable investment thesis based on the gathered information. 💡 Key Considerations: • Investment Rationale: Why is this asset attractive? (e.g., undervaluation, momentum, growth potential). • Risk-Reward Analysis: Expected return vs. potential downside. • Portfolio Fit: How does this investment align with existing holdings and diversification strategy? • Timing & Market Sentiment: Is this the right time to enter or exit the position? 🎯 Common Investment Strategies: • Value Investing (Buying undervalued assets). • Growth Investing (Investing in high-growth potential companies). • Momentum Trading (Capitalizing on short-term price trends). • Income Investing (Focusing on dividend-paying stocks or bonds).

10. Investment Decision Workflow 3. Act (Execution, Monitoring & Adjustment) Objective: Execute trades, manage risk, and adjust strategy based on market changes. 📌 Execution Phase: • Choose trade type (market order, limit order, stop-loss). • Consider transaction costs and market liquidity. • Use automation for efficient execution (algorithmic trading, robo -advisors). 📊 Monitoring & Risk Management: • Track portfolio performance vs. benchmarks. • Adjust allocations through rebalancing strategies. • Implement hedging strategies (options, futures, diversification). 🔄 Continuous Improvement: • Learn from past trades to refine decision-making. • Adapt strategy based on market evolution and economic changes.

11. Investment Decision Workflow Steps of the Scientific Method in Quantitative Analysis Step Description 1. Observation & Research Identify a problem or phenomenon, review literature, and define the research question. 2. Formulating a Hypothesis Develop a testable, measurable prediction about the relationship between variables. 3. Designing the Experiment Define independent, dependent, and control variables; select a research method. 4. Data Collection Gather numerical data using experiments, surveys, or existing datasets. 5. Data Analysis Use statistical methods to interpret results (e.g., mean, regression, hypothesis testing). 6. Conclusion Accept or reject the hypothesis based on findings and discuss implications. 7. Reporting & Peer Review Publish results, validate findings, and allow replication by other researchers. Test Purpose T-test Compares means between two groups. ANOVA Compares means among multiple groups. Regression Analysis Determines relationships between variables. Chi-Square Test Tests relationships between categorical variables. Common Statistical Tests in Quantitative Analysis

12. Falsifiability and Deduction in the Investment Process 1. Falsifiability: The Key to a Testable Hypothesis 🔍 Definition: A hypothesis must be structured in a way that it can be proven false through evidence. This principle, introduced by Karl Popper, ensures that only testable and scientific theories are considered valid. Application to Investing: • A good investment hypothesis must be falsifiable, meaning it can be tested against real data and proven wrong if the data does not support it. • If a hypothesis cannot be disproven, it lacks predictive power and is not useful for making investment decisions .

13. Falsifiability and Deduction in the Investment Process 1. Falsifiability: The Key to a Testable Hypothesis 🔍 Example : ✅ Falsifiable Hypothesis: "Tech stocks will outperform value stocks in the next 5 years based on historical earnings growth and innovation trends." 🔎 Testability: This can be tested using historical returns, earnings growth data, and market performance over time. ❌ Non-Falsifiable Hypothesis: "Tech stocks are the best investment for the future." 🔎 Issue: This statement is too vague and subjective; it cannot be quantitatively tested or disproven.

14. Falsifiability and Deduction in the Investment Process 2. Deduction: Drawing Logical Investment Conclusions 💡 Definition: Deductive reasoning starts with a general principle and applies it to specific cases to draw conclusions. It moves from theory to observation. Application to Investing: • Deduction helps investors apply broad financial theories to specific investment decisions. • Investment strategies often follow if-then logic, where a general market principle leads to a specific action .

15. Falsifiability and Deduction in the Investment Process 2. Deduction: Drawing Logical Investment Conclusions 💡 Example of Deductive Reasoning in Investing: 1. Premise (General Principle): Rising interest rates negatively impact growth stocks. 2. Observation : The Federal Reserve is increasing interest rates. 3. Deductive Conclusion: Growth stocks (e.g., tech companies) will likely underperform, so I should reduce my exposure. ✅ Strength of Deduction: • Ensures logical consistency in investment decisions. • Helps formulate actionable strategies based on economic and financial principles.

16. Universe Selection & Survivorship Bias in Quantitative Analysis 1. Universe Selection in Quantitative Investing 🌍 Universe selection is the process of choosing a set of assets (stocks, bonds, ETFs, etc.) for analysis and trading. A well-defined universe ensures that investment models are applied to relevant and consistent datasets. Key Factors in Universe Selection: ✅ Market Cap – Large-cap vs. mid-cap vs. small-cap stocks. ✅ Sector/Industry – Tech, healthcare, financials, etc. ✅ Geography – Domestic vs. international stocks. ✅ Liquidity – Excluding low-volume stocks to avoid trading execution issues. ✅ Fundamentals – Screening based on financial metrics (e.g., P/E ratio, ROE ).

17. Universe Selection & Survivorship Bias in Quantitative Analysis 1. Universe Selection in Quantitative Investing 🌍 Example : Universe Selection in a Value Investing Strategy • Criteria: S&P 500 stocks with P/E < 15, Debt/Equity < 1.0, and positive earnings growth. • Outcome: The model selects only stocks that fit value-investing principles, avoiding high-risk speculative stocks. 💡 Good universe selection ensures models apply to relevant assets and avoid bias.

18. Universe Selection & Survivorship Bias in Quantitative Analysis 2. Survivorship Bias: The Hidden Risk in Data Selection ❌ Definition: Survivorship bias occurs when a dataset excludes companies that have failed or been delisted, leading to overly optimistic historical performance results. Why It’s a Problem: Overstates Returns: If only successful companies are analyzed, backtests show unrealistically high returns. Ignores Risk: Investors may underestimate the probability of stock failures. Distorts Historical Trends: If bankrupt or underperforming stocks are removed, long-term trends appear stronger than they actually were.

19. Universe Selection & Survivorship Bias in Quantitative Analysis Universe Selection vs. Survivorship Bias: Key Differences Concept Definition Potential Bias Solution Universe Selection Choosing a relevant set of stocks/assets for analysis. Selection bias if criteria are too narrow. Define clear, objective rules for stock inclusion. Survivorship Bias Excluding delisted, failed, or bankrupt stocks from historical data. Overestimates strategy performance by ignoring past failures. Use survivorship-bias-free datasets. Conclusion 🔹 Universe selection ensures that investment models apply to the right stocks. 🔹 Survivorship bias can distort results, making a strategy appear stronger than it really is. 🔹 The best quantitative models account for both factors to create realistic, reliable investment strategies.

20. Building Blocks of Quantitative Analysis Presented By : This Content is Copyright Reserved Rights Copyright 2025@PTAIndia

21. Building Blocks of Quantitative Analysis 1 . Data Collection & Preprocessing 📊 A strong quantitative model starts with high-quality data. Types of Data Used: ✅ Market Data – Stock prices, volume, bid-ask spreads, volatility. ✅ Fundamental Data – Earnings, revenue, P/E ratio, balance sheet metrics. ✅ Macroeconomic Data – Interest rates, inflation, GDP growth, unemployment rates. ✅ Alternative Data – Social media sentiment, satellite imagery, credit card transactions. Preprocessing Steps: 🔹 Cleaning – Removing missing values, handling outliers. 🔹 Normalization – Scaling variables to avoid bias. 🔹 Survivorship Bias Adjustment – Including delisted stocks in datasets. 💡 Example: Before testing a momentum strategy, you need to ensure price data is adjusted for stock splits and dividends .

22. Building Blocks of Quantitative Analysis 2 . Statistical & Mathematical Models 📈 Quantitative analysis relies on models that identify patterns, measure relationships, and optimize portfolios. Common Models: 📌 Descriptive Statistics – Mean, variance, skewness, and kurtosis to analyze return distributions. 📌 Regression Analysis – Examines relationships between variables (e.g., how interest rates impact stock prices). 📌 Time-Series Models – Autoregressive models (ARIMA, GARCH) to predict stock price movements. 📌 Factor Models – Fama -French, CAPM, and multi-factor models for asset pricing. 💡 Example: A hedge fund may use mean-reversion models to identify stocks that temporarily deviate from their fair value.

23. Building Blocks of Quantitative Analysis 3. Hypothesis Testing & Falsifiability A hypothesis must be testable and capable of being rejected if the data does not support it. Steps in Hypothesis Testing: 1. Define a Null Hypothesis (H₀): Example – "There is no correlation between earnings growth and stock returns." 2. Select a Statistical Test: Example – Pearson correlation, t-test, or ANOVA. 3. Test the Hypothesis: Apply the test to historical data. 4. Interpret the Results: Reject or fail to reject H₀ based on statistical significance (p-value < 0.05). 💡 Example: A quantitative analyst tests whether a "January Effect" (stocks rising in January) is statistically significant over 50 years.

24. Building Blocks of Quantitative Analysis 4. Back testing & Performance Metrics Back testing is used to evaluate a strategy’s performance using historical data. Key Performance Metrics: ✅ Sharpe Ratio – Risk-adjusted return measurement. ✅ Sortino Ratio – Similar to Sharpe but penalizes only downside risk. ✅ Alpha & Beta – Measures excess returns vs. market risk. ✅ Drawdown – Measures the largest peak-to-trough decline. 💡 Example: A quant trader back tests a momentum strategy on S&P 500 stocks and finds a Sharpe ratio of 1.5 (indicating strong risk-adjusted returns).

25. Building Blocks of Quantitative Analysis 5. Risk Management & Optimization Every quantitative model must balance return potential vs. risk exposure. Risk Management Techniques: 📌 Value at Risk ( VaR ): Estimates the maximum potential loss in a given timeframe. 📌 Monte Carlo Simulations: Runs thousands of possible market scenarios to model risk. 📌 Portfolio Optimization: Uses Markowitz Modern Portfolio Theory (MPT) to maximize return for a given level of risk. 💡 Example: A quant portfolio manager adjusts allocations using the Black- Litterman Model, which optimizes portfolios based on investor views and historical data.

26. Building Blocks of Quantitative Analysis 6. Execution & Algorithmic Trading Once a model is validated, it can be deployed using automated trading systems. Trading Strategies Based on Quantitative Models: ✅ Mean Reversion: Buying undervalued stocks and selling overvalued ones. ✅ Momentum Trading: Buying stocks that have performed well in the past. ✅ Statistical Arbitrage: Exploiting temporary mispricings between related assets. ✅ High-Frequency Trading (HFT): Executing trades in milliseconds based on microstructure signals. 💡 Example: A hedge fund uses machine learning models to analyze order book data and execute high-frequency trades.

27. Trading Signals: When Rules Are Triggered 1. What Are Trading Signals? A trading signal is a trigger generated by a predefined rule in an automated trading system. Signals indicate when to buy, sell, hold, or exit a position based on quantitative criteria. 📌 Signals occur when trading rules are met. 📌 Signals drive automated execution, reducing human intervention. 💡 Example: • Buy Signal → When a stock’s 50-day moving average crosses above its 200-day moving average. • Sell Signal → When RSI crosses above 70, indicating overbought conditions.

28. Trading Signals: When Rules Are Triggered 2. Types of Trading Signals 🔹 Entry Signals – Indicate when to open a position (buy/sell short). 🔹 Exit Signals – Indicate when to close a position (take profit or cut losses). 🔹 Confirmation Signals – Validate entry/exit conditions with additional indicators. 🔹 Risk Management Signals – Trigger stop-losses or adjust position sizes . 3. Signal Confirmation (Avoiding False Positives) To reduce false signals, traders often require confirmation from multiple indicators: ✅ Example of Confirming a Buy Signal: 🔹 Rule: Buy when 50-day MA crosses above 200-day MA 🔹 Confirmation: RSI < 60 (ensures stock isn’t already overbought )

29. Trading Signals: When Rules Are Triggered 4. Example: Momentum Strategy Signals 📌 Trading Idea: Buy stocks when their price increases by 5% in 10 days and sell when they fall 3% from peak. 📌 Trading Rules & Signals: ✅ Buy Signal: 🔹 If price change 10d > 5% → BUY ✅ Sell Signal: 🔹 If price drop from peak > 3% → SELL ✅ Stop-Loss Signal: 🔹 If price drop from entry > 7% → SELL IMMEDIATELY

30. Trading Signals: When Rules Are Triggered 5. Key Takeaways 🚀 Signals occur when trading rules are met. 🔹 Entry signals trigger trade execution. 🔹 Exit signals prevent excessive losses or lock in profits. 🔹 Risk management signals ensure controlled losses. 🔹 Confirmation signals help reduce false trades.

31. Trading Strategy: The Complete Framework A trading strategy is a structured set of rules that guides automated or manual trading. It combines entry and exit rules, capital allocation, position sizing, and risk management to achieve consistent results . 1. Components of a Trading Strategy 1. Entry Rules (When to Enter a Trade) Defines conditions for opening a position. ✅ Example: Buy when the 50-day MA crosses above the 200-day MA (Golden Cross). 2. Exit Rules (When to Close a Trade) Determines when to take profits or cut losses. ✅ Example: Sell when the price falls 3% from peak or crosses below a moving average. 3. Starting Capital (Initial Investment Amount) Defines how much money is available for trading. ✅ Example: A trader starts with $10,000 in capital .

32. Trading Strategy: The Complete Framework 1 . Components of a Trading Strategy 4. Position Sizing (How Much to Invest per Trade) Controls how much capital is allocated to each trade to manage risk. ✅ Example: Risk 2% of total capital per trade, meaning a $10,000 portfolio risks $200 per trade. 5. Stop-Loss & Risk Management (Predefined Loss Limits) Protects against major losses by setting automatic exit points. ✅ Example: Set a 5% stop-loss on each trade, meaning if a stock falls 5% below entry, it is automatically sold.

33. Trading Strategy: The Complete Framework 2. Example: A Momentum Trading Strategy 🚀 Rules: ✅ Entry Rule: Buy when price is 5% higher than 10 days ago. ✅ Exit Rule: Sell when price drops 3% from peak. ✅ Starting Capital: $10,000 ✅ Position Size: 5% of capital per trade ($500 per trade). ✅ Stop-Loss: 7% below entry price . Key Takeaways 📌 A strategy is a structured combination of: ✅ Entry & exit rules → Define when to buy and sell. ✅ Starting capital → Sets the initial portfolio size. ✅ Position sizing → Manages risk per trade. ✅ Stops → Prevent excessive losses .

34. The Role of Backtesting What is Backtesting ? Backtesting is the process of testing a trading strategy using historical data to evaluate its performance before deploying it in real markets. It helps assess whether a strategy would have been profitable and robust in the past. 📌 Purpose of Backtesting : ✅ Validates a strategy’s effectiveness. ✅ Identifies strengths and weaknesses. ✅ Helps refine parameters to improve results. ✅ Reduces the risk of implementing a flawed model. 💡 Example: A moving average crossover strategy is backtested using 10 years of S&P 500 data to check its historical profitability.

35. The Role of Backtesting Steps in the Back testing Process 1. Define Strategy Rules: • Entry rules (e.g., Buy when 50-day MA crosses above 200-day MA). • Exit rules (e.g., Sell when 50-day MA crosses below 200-day MA). • Position sizing & stop-loss settings. 2. Collect Historical Data: • Stock prices, volume, fundamental factors, macroeconomic indicators. 3. Simulate Trades: • Apply trading rules to historical data. • Record each trade's entry, exit, profit/loss.

36. The Role of Backtesting Steps in the Back testing Process 4. Evaluate Performance Metrics: • Sharpe Ratio: Risk-adjusted return. • Max Drawdown: Largest peak-to-trough decline. • Win Rate: Percentage of profitable trades. 5. Optimize and Improve: • Adjust parameters based on results (e.g., test different moving average lengths). • Avoid overfitting (making the strategy too tailored to past data )

37. The Role of Backtesting 3. Example: Backtesting a Simple Moving Average Strategy Strategy: • Buy Signal: 50-day MA crosses above 200-day MA. • Sell Signal: 50-day MA crosses below 200-day MA. • Stop-Loss: 5% below entry price . 4. Common Pitfalls in Backtesting ❌ Look-Ahead Bias: Using future data that wouldn’t be available at the time. ❌ Survivorship Bias: Ignoring delisted stocks, which makes the dataset overly optimistic. ❌ Overfitting: Over-optimizing a strategy for past data, reducing real-world effectiveness. ❌ Ignoring Transaction Costs: Failing to include spreads, slippage, and commissions.

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