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    <title>Week 6: Lasso and Ridge Regression in Finance</title>
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        <h2>Week 6: Lasso and Ridge Regression for Financial Analysis</h2>

        <section>
            <h3>Learning Objectives:</h3>
            <ul>
                <li>Understand overfitting and the need for regularization in finance</li>
                <li>Master the fundamentals of Lasso (L1) and Ridge (L2) regularization</li>
                <li>Implement regularized regression for financial applications</li>
                <li>Optimize model parameters using cross-validation</li>
                <li>Interpret and utilize feature selection from Lasso</li>
            </ul>
        </section>

        <section>
            <h3>Core Resources:</h3>

            <h4>1. Theoretical Foundations</h4>
            <ul>
                <li><a href="https://www.jstor.org/stable/2346178">Original Ridge Regression Paper - Hoerl & Kennard (1970)</a></li>
                <li><a href="https://www.jstor.org/stable/2335738">The Lasso Method - Tibshirani (1996)</a></li>

            </ul>

            <h4>2. Technical Implementation</h4>
            <ul>
                <li><a href="https://scikit-learn.org/stable/modules/linear_model.html">Scikit-learn Linear Models Documentation</a></li>
                <li><a href="https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.Lasso.html">Lasso Implementation Guide</a></li>
                <li><a href="https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.Ridge.html">Ridge Implementation Guide</a></li>
                <li><a href="https://scikit-learn.org/stable/modules/cross_validation.html">Cross-Validation Methods</a></li>
            </ul>

            <h4>3. Financial Applications</h4>
            <ul>
                <li><b>Data Sources and Tools:</b>
                    <ul>
                        <li><a href="https://wrds-www.wharton.upenn.edu/">WRDS Platform</a>
                            <ul>
                                <li><a href="https://wrds-www.wharton.upenn.edu/pages/support/data-analytics/">Analytics Tools</a></li>
                                <li><a href="https://wrds-www.wharton.upenn.edu/pages/support/applications/python-programming/">Python Integration</a></li>
                            </ul>
                        </li>
                        <li><a href="https://glassnode.com/">Glassnode</a>
                            <ul>
                                <li><a href="https://docs.glassnode.com/">Documentation</a></li>
                                <li><a href="https://docs.glassnode.com/basic-api/api-guides">Implementation Guides</a></li>
                            </ul>
                        </li>
                    </ul>
                </li>
                <li><b>Research Papers and Repositories:</b>
                    <ul>
                        <li><a href="https://www.sciencedirect.com/science/article/abs/pii/S0304405X19300595">Machine Learning in Asset Pricing - Gu, Kelly, Xiu (2020)</a></li>
                        <li><a href="https://github.com/mk0417/open-asset-pricing-download">Open Asset Pricing</a></li>
                    </ul>
                </li>
            </ul>
        </section>

        <section>
            <h2>Weekly Assignment</h2>
            <div class="alert alert-info">
                <strong>Due:</strong> End of Week 6
            </div>

            <h3>Option 1: Predicting Stock Returns with Regularization</h3>
            <ol>
                <li>Data Preparation
                    <ul>
                        <li>Use WRDS to obtain monthly stock returns and firm characteristics</li>
                        <li>Include standard factors: Size, Book-to-Market, Momentum</li>
                        <li>Add accounting ratios: ROE, Leverage, Asset Growth</li>
                        <li>Prepare a panel dataset spanning at least 10 years</li>
                    </ul>
                </li>
                <li>Model Implementation
                    <ul>
                        <li>Implement both Lasso and Ridge for return prediction</li>
                        <li>Use expanding window cross-validation (to respect time series nature)</li>
                        <li>Compare with standard OLS using out-of-sample R²</li>
                        <li>Document the impact of different λ values</li>
                    </ul>
                </li>
                <li>Analysis
                    <ul>
                        <li>Which features survive Lasso's variable selection?</li>
                        <li>How do Ridge coefficients differ from OLS?</li>
                        <li>Does prediction improve in high volatility periods?</li>
                    </ul>
                </li>
            </ol>

            <h3>Option 2: Research-Based Application</h3>
            <p>Design your own application of regularization in finance. Some suggestions:</p>
            <ul>

                <li>Risk Factor Selection
                    <ul>
                        <li>Start with a large set of potential risk factors</li>
                        <li>Use Lasso to identify the most important ones</li>
                        <li>Compare with Fama-French factors</li>
                    </ul>
                </li>
                <li>Credit Risk Assessment
                    <ul>
                        <li>Predict corporate defaults using accounting ratios</li>
                        <li>Compare Lasso/Ridge with traditional models</li>
                        <li>Evaluate prediction accuracy</li>
                    </ul>
                </li>
            </ul>

            <div class="alert alert-warning">
                <strong>Submission Requirements:</strong>
                <ul>
                    <li>Code with clear documentation</li>
                    <li>Brief report  including:
                        <ul>
                            <li>Problem motivation and relevance</li>
                            <li>Methodology and implementation details</li>
                            <li>Results and interpretation</li>
                            <li>Challenges encountered and solutions</li>
                        </ul>
                    </li>
                    <li>If choosing Option 2, include references to papers of similar applications</li>
                </ul>
            </div>
        </section>

        <section>
            <h3>Implementation Tips:</h3>
            <div class="alert alert-info">
                <strong>Key Considerations:</strong>
                <ul>
                    <li>Scale features before applying regularization</li>
                    <li>Use TimeSeriesSplit for financial data</li>
                    <li>Consider the trade-off between bias and variance</li>
                    <li>Document parameter selection process</li>
                    <li>Be mindful of look-ahead bias in financial applications</li>
                    <li>Consider computational efficiency for large datasets</li>
                </ul>
            </div>
        </section>

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