Advanced Risk and Portfolio Management

Attilio Meucci


About this workPIC

The ARPM Lab® (short for “Advanced Risk and Portfolio Management Lab”) is a constantly updated online platform to learn and teach quantitative finance, from the foundations to the most advanced developments.

The topics of the ARPM Lab® span, in a unified framework, the whole spectrum of quantitative finance across

  • Financial services: asset management, banking and insurance.
  • Asset classes: credit, public/private equities, insurance, alternatives, high-frequency, business lines, etc.
  • Applications: portfolio construction, investment risk measurement, enterprise risk management, algo trading, etc.
  • Quantitative disciplines: machine learning, econometrics, optimization theory, pricing, decision theory, etc.

Whereas much material is already available on asset pricing and risk-neutral valuation, the ARPM Lab focuses on real-world randomness (the “” in ARPM)


Figure 1: Organization of the ARPM Lab ®

The ARPM Lab® is organized into five parts, built around the three sequential steps of the business process (Figure 1); and is best taught in four modules (Figure 2).

The ARPM Lab® is accessible from multiple interconnected channels: theory, simulations clips, examples, case studies, documented code, exercises, slides, and the video lectures of the ARPM Bootcamp® and the ARPM Marathon®.

Access to the same material through different, interconnected channels, has proved to optimize the learning experience for disparate audiences.

Here below we proceed to explain the above.

Parts: the business process

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

Part I - the “Checklist” - represents the core of our program: ten sequential steps to implement ex-ante risk management and ex-ante portfolio/firm management.

The Checklist consists of ten sequential steps to model, assess, and improve the performance of the portfolio/firm, refer to Figure 0.1. The first five steps (data processing) prepare all the required econometric and analytical background. The next three steps (risk management) discuss how to measure the risk profile of the portfolio/firm. The last two steps (portfolio management) discuss how to optimize the risk profile of the portfolio/firm, which is arguably the ultimate goal of financial practitioners across the industry (asset management, banking, insurance, and corporate/CFO office).

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 provides a deep understanding of factor models, which are used across the ten steps of the “Checklist” (Part I), as well as in valuation (Part III) and performance analysis (Part IV). Part II also covers machine learning, which has numerous connections with factor models. Machine learning represents a deeper dive into the data processing portion of the “Checklist” (Steps 1-5).

Part III is a “prequel” to the “Checklist”. Risk management and portfolio management aim at forecasting, assessing, and improving future (“ex-ante”) performance, which ultimately is the future change in value of our portfolio. 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 is a “sequel” to the “Checklist”: it addresses performance analysis. We first delve into the various definitions of performance (linear/compounded return, absolute/excess return, drawdown, cash component versus appreciation, etc.). Then we discuss how to attribute the realized (“ex-post”) performance to the different decisions and stakeholders.

Part V is a toolbox of quantitative techniques used throughout.

To summarize, the full body of the ARPM Lab is organized as follows

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.

Modules: the teaching process

The vast body of knowledge in the ARPM Lab® (data processing, risk management, portfolio management, factor models, machine learning, valuation, performance analysis, and quantitative tools) is best taught by organizing the different topics into four modules ( Figure 2), as we do in the ARPM Bootcamp® and the ARPM Marathon®.


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

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

Channels: the learning process

Different people learn in different ways. The ARPM Lab® is accessible from multiple interconnected channels ( Section 1): theory, simulations clips, examples, case studies, code, documentation, exercises, slides, and video lectures.

The interconnections among the channels maximize the effectiveness of unstructured, “bottom-up” learning, which does not follow the recommended dependencies of the teaching modules ( Section 1). 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.

Below we itemize the different channels of the ARPM Lab®; the statistics below refer to the most recent update.

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

Case studies (297) and toy examples (811)
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 .

Every case study is a component of one or more sequences of case studies, that together form large-scale analytics. To access and navigate across the different parts of the large-scale analytics, the user can click on the three-cog icon PIC to the side of the gray box.

Furthermore, a large number of “toy” examples illustrates the theory in low dimensions, 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 .

Simulation clips (204)
Video simulations, generated from data using code, explain complex models visually. To access a video, users can click on the “play” icon PIC on the right of the figure extracted from the video.

Code (117,003 lines) and documentation (659 pages)
The code allows the user to absorb hands-on the ARPM experience, understanding all the practical issues behind the theory. All 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 .

All the code is documented in language-neutral pseudo-code, and has plenty of cross references to the theory and links to directly access the code. To access the documentation, the user can click on the documentation icon PIC .

Exercises (1,063)
Exercises support the ARPM learning experience. To access the exercises, the user can click on the exercises icon PIC .

Slides (2,350) 
Multimedia slides summarize all the materials. To access the slides, the user can click on the slides icon PIC at the top of each page.

Video lectures (134) 
Video lectures walk the user through the materials. The video lectures are a collection of short clips, one per section, and follow the slides. They can be watched independently, by clicking on the video lecture icon PIC at the top of each page. They can also be watched in sequence, thereby covering the curriculum of parts or all of the ARPM Bootcamp® and ARPM Marathon®.

Q&A forum (5,816 members)
An online networking venue to exchange questions and answers on technical topics, the forum engages the large and growing community of like-minded individuals who learn and teach Advanced Risk and Portfolio Management. To access the forum, the user can click on the “?” sign.

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 desire to bridge 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.