TFA Curriculum for Fixed-Income Investment and Risk Management (FIRM) Program
- Pankaj Maheshwari
- Mar 1
- 11 min read
Updated: Mar 23
Welcome to the Fixed-Income Investment and Risk Management Program!
A Transformation Journey in Fixed-Income Investment and Risk Management!
Dear Professional,
Welcome to the Fixed-Income Investment And Risk Management (FIRM) program, proudly offered by one of the most trusted and recognized platforms in financial education and training. You have taken a significant step toward building or advancing your career in fixed-income management.
The FIRM program is designed to provide structured learning and hands-on experience, combining rigorous theoretical foundations with real-world applications. Each module is carefully curated to build a deep, layered understanding—from core financial concepts to advanced fixed-income investment and risk management tactics—ensuring that you develop both the analytical precision and practical expertise required in today's financial markets.
We encourage you to fully immerse yourself—participate actively, ask questions, and be ready to apply your knowledge and expertise to tackle real-world challenges.
Basic Modules (1 to 2)
The foundational modules are designed to provide you with a strong foundational understanding of financial markets, financial products and derivative instruments, and essential data-handling techniques, ensuring a solid start and that you develop a comprehensive understanding of equities, interest rates, foreign exchange, commodities, financial derivatives, and market data automation.
Module 1: Equities, Interest Rates, and Monitoring Yield Spreads (10.5 hrs)
Equities form a core component of financial markets, and understanding their risks is fundamental for market risk management. This module introduces equity market data, return calculations, and risk modeling techniques, covering both systematic and unsystematic risk factors.
Market Data for Equities: Extract, process, and analyze historical equity time-series data, including price movements and returns.
Equity Returns and Shocks: Understand absolute, discrete, and continuous return calculation to quantify equity price movements.
Interest rates influence financial markets, corporate financing, and investment decisions. This module covers yield curves, interest rate shocks, and the impact of changing interest rates on market risk.
Fixed-Income Markets: Gain a structured understanding of US Treasury securities, bonds, and interest rate instruments.
Yield Curve Interpretation: Analyze the normal, inverted, and humped yield curves and their implications on macroeconomic conditions.
Interest Rate Shocks: Compute absolute and relative interest rate changes to measure their impact on portfolio valuation.
Market Monitoring and Reporting: Track and analyze US Treasury yield spread, particularly the 10Y-3M spread, as a key indicator of economic cycles.
Hands-On Application: Build automated market reports that monitor yield spread and SnP 500 equity market performance, using Python to extract, process, visualize, and generate reports.
Module 2: Market Data Management and Automation (7.8 hrs)
Efficient market risk management relies on high-quality market data across multiple asset classes. This module introduces financial data extraction, automation, and real-time monitoring techniques.
Multi-Asset Market Data: Learn to extract and manage data for equities, interest rates, currencies, and commodities, and derivatives.
Understanding Derivative Instruments: Explore futures, forwards, and options, including their price structures and risk profiles.
Python Automated for Market Data: Write Python scripts to automate data extraction, storage, and processing for financial instruments.
Crypto Market Data: Extract and analyze historical data for cryptocurrencies and understand their unique market characteristics.
Hands-On Application: Implement Python-based automation to streamline market data workflows, visualize price trends, and create dynamic dashboards for risk monitoring.
Interview Guide: Financial Instruments, Market Data Management, and Automation
To reinforce learning, participants will have access to a structured interview guide covering essential concepts on financial instruments, market data management, and automation.
Core Modules (3 to 7)
The core phase focuses on integrating your knowledge into advanced pricing, valuation, and risk management methodologies.
Module 3: Modeling Term-Structure of Interest Rates (10.4 hrs)
Understanding the term structure of interest rates is crucial for pricing fixed-income securities, managing interest rate risk, and constructing yield curves for scenario creation. This module introduces interpolation techniques used to construct smooth and continuous yield curves, regression models for yield curve estimation (including linear and polynomial regressions), and advanced factor-based models such as the Nelson-Seigel and Nelson-Seigel-Svensson models needed for accurate interest rate modeling and forecasting.
Yield Curve Construction – Interpolation Methods: Learn basic interpolation techniques such as linear interpolation, polynomial fitting, and piecewise interpolation to estimate missing interest rate data.
Advanced Interpolation Methods:
Vandermonde Matrix: Used Understand how the Vandermonde matrix approach is used for higher-order polynomial fitting in yield curve estimation.
Newton Divided Difference: Explore Newton's divided difference technique, which improves curve fitting accuracy by considering successive rate differences.
Lagrange and Cubic Spline Interpolation: Compare Lagrange polynomial interpolation and cubic spline methods, which offer more flexible and smooth curve fitting for complex yield structures.
Modeling Yield Curve:
Linear Regression Model (Single Factor): Apply simple linear regression techniques to estimate interest rate relationships and predict yield curve movements.
Polynomial Regression Model (Single Factor): Extend the regression framework to quadratic and cubic polynomial models, capturing non-linear interest rate dynamics.
Nelson-Seigel (NS) and Nelson-Seigel-Svensonn (NSS) Models: Explore econometric models that describe interest rate curve movements using parameters for level, slope, and curvature.
Model Validation – NS and NSS Models: Evaluate model performance using error metrics such as RMSE, MSAR, and R², ensuring accuracy in interest rate curve fitting.
Hands-On Application: Implement yield curve modeling techniques, calibrate model parameters using real-world market data, and validate their predictive accuracy.
Module 4: Modeling Short-Rate and Interest Rate Factors (8.6 hrs)
Interest rates are fundamental drivers of financial portfolios, influencing bond pricing, derivatives valuation, and risk management strategies. This module introduces short-rate models and principal component analysis (PCA)—key techniques for modeling interest rate dynamics (level, slope, and curvature) and understanding market risk factors.
Vasicek Model: A mean-reverting stochastic process used for modeling interest rate movements. Learn how the model estimates yield curves, bond pricing, and risk factors under different market conditions.
Cox-Ingersoll-Ross (CIR) Model: An extension of the Vesicel model that ensures interest rates remain non-negative. This model is widely used for interest rate derivative pricing and risk modeling.
Hands-On Application: Implement and calibrate Vasicek and CIR models using historical interest rate data, simulate interest rate paths, and compare model accuracy in forecasting yield curve dynamics.
Introduction to PCA and Preliminaries: Learn the mathematical foundations of PCA, including variance-covariance matrices, eigenvalues, and eigenvectors, to identify key risk factors.
PCA for Interest Rate Risk Modeling: Decompose yield curve movements into primary components—level, slope, and curvature—to quantify how different maturities respond to interest rate shocks.
PCA – The Reduced Model in Perspective: Understand how PCA simplifies risk analysis by reducing dimensionality while preserving essential information about market dynamics.
Hands-On Application: Perform PCA on yield curve data, analyze historical interest rate movements, and use PCA-based shock modeling to simulate interest rate stress scenarios.
Module 5: Pricing and Valuation of Fixed-Income Securities (16.4 hrs)
Fixed-income securities are the most traded and concentrated in the financial markets. This module provides a comprehensive framework for pricing and valuing bonds and interest rate swaps, covering discounted cash flow (DCF) modeling, interest rate sensitivities, and scenario analysis techniques.
Full Valuation DCF Model for US Treasury Bills, Interest Rate Movements, and Mark-to-Market PnL: Learn to price short-term fixed-income securities using the DCF method, factoring in risk-free rates and discount yields. Analyze how changes in interest rates affect bond prices and track market-to-market profit and loss (PnL).
Interest Rate Scenario Analysis and Sensitivities – Duration, DV01, Convexity, and Residual: Compute bond price sensitivity (Delta) and dollar value of a basis point (DV01) to asses risk exposures. Extend risk analysis to include convexity adjustments, improving the accuracy in pricing fixed-income instruments.
Partial Revaluation Sensitivity-Based Model – First-Order, Higher-Order Approximation, and PnL Attribution: Implement duration and DV01-based approximations to estimate interest rate risk with greater efficiency. Implement second-order risk effects and PnL attribution methodologies to break down portfolio performance.
Full Valuation DCF Model – US Treasury Notes/Bonds – Mark-to-Market Adjustments: Understand pricing discrepancies between model estimates and market prices and analyze their implications.
Partial Revaluation Sensitivity-Based Model – Duration and Convexity (DC) Approach: Use duration and convexity measures to estimate bond price changes under different interest rate scenarios.
Taylor-Series Approximation: Simplify the modeling of non-linear risks by approximating changes using first and second-order derivatives.
Ladder-Based Interpolation: Use ladder structures to estimate intermediate values efficiently in risk modeling.
Bond Cash Flow Mapping Procedure – Nearest Tenor Matching and Variance Matching Approaches: Understand techniques for mapping bond cash flows to yield curve tenors, crucial for risk management and portfolio optimization.
Hands-On Application:
Valuation Report of US Treasury Securities and Mark-to-Market: Construct a comprehensive valuation report, summarizing bond pricing methodologies and market risk assessments—conduct interest rate risk assessments and prepare mark-to-market valuation reports using real market data.
Module 6: Sensitivity Analysis, Scenario Analysis, and Stress Testing (12.8 hrs)
Risk sensitivity analysis is a cornerstone of market risk management, allowing traders and risk managers to quantify portfolio risk exposure, optimize hedging strategies (as option positions are influenced by multiple risk factors, including price movements, volatility shifts, and time decay), and mitigate financial risks. This module focuses on fixed-income risk sensitivities (Duration, DV01, and Convexity), option greeks (Delta, Gamma, Vega, Theta, Rho, Vanna, and Volga), and advanced hedging techniques for equity, interest rate, and derivatives.
Interest Rate Sensitivities – Duration, DV01, and Convexity: Learn how modified duration, DV01, and convexity measure bond price sensitivity to interest rate changes.
Understanding DV01: A Key Measure in Fixed Income Risk Management: Explore DV01 (Dollar Value of a Basis Point) and its role in hedging interest rate risk.
DV01-Neutral Curve Spreads – Steepener and Flattener: Construct steepened and flattener trades by analyzing yield curve movements and DV01-neutral positioning.
Hands-On Applications: Compute duration, DV01, and convexity for bond portfolios, implement yield curve strategies, and construct hedged fixed-income positions.
Scenario analysis and stress testing are essential risk management techniques that evaluate a portfolio's resilience under extreme market conditions. This module focuses on designing market stress scenarios, asset prices, interest rates, exchange rate shifts, and regulatory stress test methodologies to assess the impact of adverse conditions on equity and fixed-income portfolios.
Introduction to Scenario Analysis and Portfolio Stress Testing: Understand the purpose of scenario analysis, its role in risk management, and how it helps quantify potential portfolio losses.
Market Interest Rate Scenarios
Parallel Shifts: Model parallel shifts in the yield curve, analyzing their effects on bond prices, swaps, and fixed-income portfolios.
Non-Parallel Shifts: Construct non-parallel shifts (bull and bear steepening and flattening, twist and turns) to assess risk exposures across different maturities.
FED Stress Test Scenarios: Understand the Federal Reserve’s stress testing framework, including adverse and severely adverse scenarios applied to financial institutions. Review of FED 2024 stress test scenarios by analyzing the latest regulatory stress test cases and their implications for market risk management and capital adequacy requirements.
Hands-On Applications: Build stress-testing models for equities and fixed income, simulate parallel and non-parallel yield curve shifts, and evaluate portfolio resilience using regulatory stress test cases.
This module expands on scenario-generation techniques and introduces advanced methodologies for stress-testing equity and fixed-income portfolios.
Scenario Creation for Identified Shocks: Design scenarios for Spot Shocks: Positive and Negative Shocks. Antithetic Scenarios for mirrored outcomes. Applied to asset classes: Rates and FX. Volatility Shocks: Normal/Local Volatility: Risk modeling for individual instruments. Log-Normal/ATM Implied Volatility: Comprehensive market impact analysis.
Interest Rate Scenario Generation and Expansion: Learn techniques for creating interest rate shock scenarios, including historical, hypothetical, and model-driven approaches.
Scenario Methodologies: Understand different scenario construction methodologies:
Ladder-Based: Gradual rate shifts for incremental stress testing.
Historical Scenarios: Using past market crises as stress test inputs.
Event-Specific Stress: Tailoring stress tests for specific financial shocks.
Hypothetical Scenarios: Designing custom stress environments based on macroeconomic conditions.
PCA Model Calibration and Scenario Generation – Interest Rate Curve: Apply Principal Component Analysis (PCA) to model yield curve shocks and simulate multi-factor interest rate movements.
Scenario Revaluation and PnL Attribution – Full Revaluation and Partial Revaluation Sensitivity-Based Model: Compare the effectiveness of full revaluation (rigorous scenario testing) versus sensitivity-based approximations for risk assessment.
Breaches and Exceptions in Scenario Limits: Flagging Exceptions: Identify breaches in predefined scenario limits, flags, or thresholds. Monitor deviations that may indicate significant risk exposures. Management Action: Provide actionable recommendations to mitigate identified risks. Develop contingency strategies for handling exceptions.
Market Scenario Risk Report for Fixed-Income Portfolios: Construct a consolidated market risk report, summarizing stress test results and scenario-driven profit and loss (PnL) attributions.
Hands-On Applications: Design custom market stress scenarios, implement PCA-based interest rate shocks, and generate scenario-driven PnL reports for risk assessment.
Module 7: Value-at-Risk (VaR), Stress Value-at-Risk (SVaR), and Expected Shortfall (ES) Methodologies and Advancements (21.6 hrs)
Value-at-Risk (VaR) is a fundamental risk measure used by financial institutions to quantify potential losses under adverse market conditions. This module provides a comprehensive exploration of VaR, stress VaR, Expected Shortfall (ES), and risk model validation techniques. Participants will gain hands-on experience in historical simulation, parametric VaR, Monte Carlo simulations, and PCA-based risk estimation for equities, bonds, futures, options, and swaps.
Introduction to Value-at-Risk (VaR) Measure: Learn the concept, assumptions, and limitations of VaR as a risk quantification tool.
Value-at-Risk Explained: A Practical Guide for Risk Professionals: A step-by-step breakdown of VaR models and their practical applications in risk management.
Historical Simulation VaR Method for Interest Rate Bonds: Apply historical VaR techniques to fixed-income securities, capturing yield curve movements and rate shocks.
Full vs. Partial Revaluation for VaR Estimation: Compare full vs. partial revaluation VaR estimates, assess their impact on risk assessment efficiency, and optimize risk reporting strategies.
Hands-On Applications: Market Value-at-Risk Report for Fixed-Income Securities and Portfolio: Generate a structured risk report summarizing VaR-based risk assessments for bond portfolios.
Historical Simulation VaR Method for Interest Rate Swaps: Extend historical VaR techniques to derivatives, incorporating leverage and option-specific risks.
Parametric VaR Method for Fixed-Income Securities: Implement variance-covariance (parametric) VaR models, assuming a normal distribution of returns.
Monte Carlo Simulation VaR Method Bonds, and Interest Rate Options: Simulate thousands of possible market scenarios to estimate VaR under stochastic conditions.
PCA Model Calibration and VaR – Interest Rate Bonds: Apply Principal Component Analysis (PCA) to interest rate risk, extracting key risk factors affecting yield curves.
Other Risk Methodologies – Conditional VaR (CVaR), Incremental VaR (IVaR), and Marginal VaR (MVaR): Understand advanced risk measures that extend VaR’s capabilities by assessing tail risks and risk contributions.
Hands-On Applications: Compute VaR across asset classes, calibrate PCA models for fixed-income risk, and analyze incremental and marginal VaR for portfolio optimization.
Expected Shortfall (ES) provides a more accurate measure of tail risk, capturing average losses beyond VaR estimates.
Expected Shortfall for Interest Rate Bonds: Apply Expected Shortfall methods to fixed-income portfolios, analyzing credit risk and interest rate fluctuations.
Hands-On Applications: Compute CVaR for multi-asset portfolios, compare VaR vs. Expected Shortfall performance, and analyze tail risk distributions.
Stressed VaR measures risk under extreme historical market conditions, helping financial institutions prepare for black swan events and crisis scenarios.
Stressed Period Selection Model for Fixed-Income Portfolios: Identify historical crisis periods to simulate realistic stress test scenarios. Apply historical stressed periods to fixed-income instruments, modeling interest rate shocks and liquidity crises.
Historical Simulation Stressed VaR Method for Fixed-Income Portfolio: Implement stressed VaR techniques for equity markets, simulating extreme downside risk scenarios. Quantify worst-case losses for bond portfolios, incorporating yield curve dislocations and credit risk factors.
Hands-On Applications: Construct stressed VaR models, analyze historical crisis periods, and simulate black swan events for portfolio risk assessments.
Model Development and Validation
Model validation is crucial for ensuring accuracy, robustness, and compliance in risk management frameworks. This module also covers backtesting, stress testing, and model verification techniques.
Model Development: VaR and Expected Shortfall Models – Equities and Interest Rate Bonds: Build and refine VaR and ES models, incorporating historical market data and Monte Carlo techniques.
Model Validation:
Backtesting VaR Models for Fixed-Income Portfolios: Compare VaR predictions to actual market losses, ensuring model accuracy and reliability.
Stress Testing VaR Models for Equity Portfolio: Conduct stress tests to assess portfolio risk exposure under hypothetical crisis scenarios.
Exceptions and Breaches: Learn how to flag, monitor, and address breaches in VaR limits or risk thresholds.
Traffic Light Approach for VaR Model Validation: A regulatory framework for evaluating VaR model accuracy based on exception frequency. Classifies models into green (acceptable), yellow (moderate risk), or red (unacceptable) categories based on deviation from predicted risk levels.
Model Validation: Backtesting and Stress Testing Expected Shortfall for Fixed-Income Portfolios: Validate Expected Shortfall calculations, ensuring tail risk measures align with historical performance.
Basel III Compliance: Understand how VaR and ES influence capital allocation, stress testing, and market risk capital calculations.
Hands-On Applications: Market Risk Validation Report: Backtesting and Stress Testing Risk Methodologies – Investment Portfolio: Generate a comprehensive model validation report, summarizing key risk methodologies, backtesting results, and stress testing outcomes.
Getting Started!
Your journey begins with setting up your development environment—a critical first step in ensuring a seamless and productive experience throughout the program. You’ll establish your tools, gain familiarity with essential platforms, and integrate Python with Excel for a powerful analytics workflow.
What You’ll Learn
How to use Anaconda Navigator as your central hub for performing automated tasks.
Introduction to Jupyter Notebook, an interactive platform for coding, data visualization, and presenting Python-based projects.
Seamless integration of Python with Microsoft Excel for enhanced data handling and visualization capabilities.
Installation Guide: Getting Started with Anaconda Navigator: Installation Guide
To begin, download and install Anaconda Navigator, a comprehensive platform for managing Python libraries, packages, and environments.
Watch: Anaconda Navigator Application
In this session, You’ll explore everything you need to get started with Anaconda Navigator:
Installation Process: From download to setup on your machine.
Understanding the differences between an Integrated Development Environment (IDE), Code Editor, and Compiler.
Managing Python Libraries and Packages for efficient workflows.
Recommended tools and configurations for this course.
Watch: Jupyter Notebook
In this session, You’ll explore the Jupyter Notebook, a powerful and versatile platform for interactive computing.
Launching Jupyter Notebook from Anaconda Navigator.
Navigating the interface: Default directories, creating new notebooks, and managing files.
Understanding the Menu Options, Toolbar, and commonly used Keyboard Shortcuts.
Using Code Cells for writing and executing Python code.
To complete your setup, ensure you have Microsoft Excel installed: Microsoft's official site
How to Download: Visit Microsoft’s official site to download Excel. Note that a valid license or subscription may be required for full access.
Comments