Advanced Risk and Portfolio Management

Attilio Meucci


About the ARPM LabPIC

The ARPM Lab® (Advanced Risk and Portfolio Management Lab) is a constantly updated online platform for learning and teaching quantitative finance.

The ARPM Lab spans the entire spectrum of Quantitative Finance, across Asset Management, Banking, and Insurance, from the foundations to the most advanced developments:

The ARPM Lab is developed “bottom-up” to address the practitioners’ needs, but is organized and presented “top-down” in a structured, academic manner.

While most materials on quantitative finance focus on asset pricing and risk neutral valuation (“”), the ARPM Lab focuses on the much broader applications to real world probability (“”, more at Section 1).

The ARPM Lab, in one framework and in one consistent set of notations, facilitates connections across disparate topics, and covers

  • all major asset classes: equities (public/private), fixed-income, credit, currencies, alternatives, high-frequency, enterprise, etc.
  • the most advanced quantitative techniques: data science and machine learning, factor modeling, portfolio construction, algorithmic trading, investment risk measurement, liquidity modeling, enterprise risk management, etc.

Organization of the ARPM Lab

The ARPM Lab is organized into five parts, built around the three sequential steps of the business process: valuation, ex-ante risk/portfolio management (the “Checklist”), and ex-post performance analysis (Figure 1).


Figure 1: Organization of the ARPM Lab ®

Part I - the “Checklist”. This represents the core of the ARPM Lab and consists of 10 sequential steps to model, assess, and improve the performance of the portfolio/firm, refer to Figure 0.1.

The first 5 steps (Data Processing) prepare all the required econometric and analytical background. The next 3 steps (Risk Management) discuss how to measure the risk profile of the portfolio/firm. The last 2 steps (Portfolio Management) discuss how to optimize the risk profile of the portfolio/firm, which is the ultimate goal of financial practitioners across the industry (asset management, banking, insurance).

In addition to the core steps of the “Checklist”, other pieces are crucial to fully understand and implement Advanced Risk and Portfolio Management (Figure 1).

Part II - Factor models and learning. This provides a deep understanding of factor models, which are used across the ten steps of the “Checklist” (Part I), as well as Valuation (Part III) and Performance analysis (Part IV). Machine Learning with its numerous connections with factor models is also covered in Part II. This represents a deeper dive into the Data Processing portion of the “Checklist”.

Part III - Valuation. This is a “prequel” to the “Checklist”. Risk management and portfolio management aim to forecast, assess, and improve future (“ex-ante”) performance, which ultimately is the future change in value of our portfolio. But to improve the future value we need to first know, or compute, the current value. In this part we provide a holistic treatment of valuation across liquidity buckets (bid/ask or mark-to-market versus mark-to-model), and across models (risk-neutral models for derivative traders versus real-measure models for investment bankers and actuaries).

Part IV - Performance analysis. This is a “sequel” to the “Checklist”. We first delve into the various definitions of performance (linear/compounded return, absolute/excess return, drawdown, cash component versus appreciation, etc.). Then we discuss the attribution of realized (“ex-post”) performance to different decisions and stakeholders.

Part V - Quant toolbox. This is a set of quantitative techniques used throughout the ARPM Lab.

To summarize, the full body of the ARPM Lab is organized in the following way:

Part IThe Checklist
Part II: Factor models and learning
Part III: Valuation
Part IV: Performance analysis
Part V: Quant toolbox

Table 1: Fundamental blocks of Advanced Risk and Portfolio Management.

Learning the ARPM Lab by topic


Figure 2: Parts of the ARPM Lab ® versus modules of the ARPM Certificate ®

The exhaustive Body of Knowledge of the ARPM Lab (Data Processing, Risk Management, Portfolio Management, Factor Models, Machine Learning, Valuation, Performance Analysis, and Quantitative Tools) is best learned through four Learning Modules, as we do in the ARPM Bootcamp® and the ARPM Marathon®, refer to Figure 2:

The same four modules are tested in the exams for the ARPM Certificate®, which proves proficiency across all the parts of the ARPM Lab.

Learning the ARPM Lab by channel

Different people learn in different ways. To facilitate the different learning styles of disparate audiences, the ARPM Lab is accessible via 9 interconnected Learning Channels. The interconnections among the channels maximize the effectiveness of unstructured, “bottom-up” learning, which does not follow the recommended dependencies of the four Learning Modules. For instance, one may land on a piece of interactive code, and follow the code forward and backward across different topics; or switch to the theory on that topic to deepen understanding, or watch a video first, and then try an exercise.

The 9 Learning Channels to access the exhaustive body of knowledge of the ARPM Lab are described below (the statistics below refer to the most recent update).

1. Theory (1,654 pages)
Theory is the pillar of the ARPM Lab. Explanations with formulas are self-contained, and laid out with grueling attention to a consistent set of notations, which facilitates connections across disparate topics. Geometrical arguments support intuition, and heuristics are favored over mathematical rigor.

2. Case studies (313)
Case studies use real data, large simulations, or large-scale analytical results. The user can replicate the case studies with the code, also provided. Case studies are wrapped in bordered gray boxes, and signaled by the image of a cog PIC .

3. Toy examples (823)
The many Toy examples provided illustrate the theory in low dimensions, in order to solidify the intuition and the comprehension of abstract theoretical concepts. Toy examples are wrapped in gray boxes with no border, and signaled by the image of a bulb PIC .

4. Data animations (205)
Data animations, generated from data using code, explain complex models visually. To access an animation, users can click on the “play” icon PIC on the right of the figure, which is one frame extracted from the animation.

5. Code (118,827 lines)
The Code allows the user to absorb hands-on the contents of the ARPM Lab, understanding all the practical implications behind the theory. The Code is editable and executable interactively from any browser, without any software installation. The Code is available in Python and MATLAB®/GNU Octave. To access the Code, the user can click on the code icon PIC , and then select the language of choice.

6. Documentation (851 pages)
Documentation in language-neutral pseudo-code provides all the details about the code, as well as cross references to Code and to Theory. To access the Documentation, the user can click on the documentation icon PIC .

7. Exercises (1,070)
Exercises support the learning and help the user to master the analytical aspects of the Theory. To access Exercises, the user can click on the exercise icon PIC .

8. Slides (2,416) 
Multi-media Slides summarize all the materials. To access the Slides, the user can click on the slide icon PIC at the top of each page.

9. Video lectures (134) 
Video lectures are video clips, one per section, featuring an ARPM Instructor who walks the reader across the ARPM Lab. The Video lectures can be viewed one at a time, by clicking on the video lecture icon PIC at the top of each page; they can also be viewed in sequence, clicking on the “previous”/“next” arrows on top of each video.

The Video lectures are available in two formats: Bootcamp and Marathon. The Bootcamp Video lectures provide a faster overview of the ARPM Lab, for a total of 30 hours of recording, and cover the program of the ARPM Bootcamp; the Marathon Video lectures provide an in-depth overview of the ARPM Lab, for a total of 150 hours of recording, and cover the program of the ARPM Marathon.

Audience and prerequisites

Access to the ARPM experience through different, interconnected channels ( Section 1) enables a diverse audience to benefit from it.

A solid quantitative background from an undergraduate program in the hard sciences allows for full absorption of the materials. No finance or coding knowledge are necessary, as both are developed during the ARPM experience.

Professional and academic backgrounds

The following categories represent the ideal audience for the ARPM experience.

  • Risk managers and portfolio managers with an undergraduate degree in the hard sciences, who wish to learn the principles behind the recipes that they implement every day, and wish to access a comprehensive reference for the most advanced techniques in their field.
  • Computer/data scientists, who want to learn the financial applications of their skills.
  • Derivative quants and quantitative actuaries, who wish to quickly switch from their field to a new one, leveraging the mathematical knowledge they already possess.
  • Students (advanced undergraduates and master level) in quantitative finance and hard sciences.
  • Academics in the hard sciences, who wish to learn and/or teach data science for finance, risk management, and portfolio management in the concise, rigorous language to which they are accustomed.

Mathematical proficiency

Throughout the ARPM experience, intuition is supported by visualizations. Heuristic arguments are favored over mathematical rigor. The mathematical formalism is used up to, and not beyond, the point where it eases the comprehension of the subject.

However, users extract the most value from the ARPM experience if they have a hard science undergraduate degree, or working knowledge of the following:

  • Linear algebra: matrix/vector notation and manipulations, trace, determinant, eigenvectors, eigenvalues.
  • Multivariate calculus: derivatives, integrals, and Taylor expansions.
  • Statistics: basic concepts of distributions, probability density function, and cumulative distribution function.

For users interested in brushing up their mathematics with a focus on applications, a Mathematics Refresher is available.

Programming proficiency

No coding experience is needed to fully benefit from the ARPM experience: coding skills can be, although need not be, acquired along the way, by working through the interactive code provided.

However, for users interested in learning to code or brushing up their coding skills, Coding Refreshers in the supported languages are available.

Finance proficiency

No knowledge of finance is necessary to benefit from the ARPM experience, although prior exposure to basic financial products would make the absorption of the materials faster.