Risk Management, Valuation, ESG

Measuring Returns in Private Markets: a Primer

Fundamentals of Risk Management and Valuation for Investment Funds

with the focus on Luxembourg-domiciled investment funds and investment fund managers

The book provides a structured walkthrough of the European investment fund landscape — from the regulatory and supervisory frameworks governing UCITS and AIFs to the specific ecosystem of Luxembourg investment vehicles such as SIFs, SICARs, RAIFs, and SCSps. It also covers the key functions carried out by investment fund managers, with emphasis on risk management and valuation.

Beyond the institutional context, the book dives into the technical foundations: asset classes and investment strategies (ranging from traditional securities to private capital, real assets, and crypto-assets), fundamental metrics for measuring return, risk, sensitivity, and performance, as well as a detailed treatment of derivatives and leverage calculation methods under both UCITS and AIFMD rules. The final major chapter on risk management fundamentals addresses market risk, credit risk, counterparty risk, liquidity risk, sustainability risk, and operational risk — each with dedicated mitigation strategies.

The book is released under a Creative Commons (CC BY-NC 4.0) licence, making it freely available for non-commercial use.

Portfolio Theory: an Introduction

This article is an introduction to the so-called modern portfolio theory. It assumes a basic knowledge of linear algebra and multivariable calculus. In the first section we show how to compute the variance and the expected value (mean) of portfolio returns. In the second section we deal with mean-variance constrained optimisation problems.

Option Pricing: an Introduction

This article is an introduction to option pricing theory. In the first section we deal with the discrete time binomial option pricing model for European options, giving some hints regarding its convergence to Black-Scholes as the continuous time limit. In the second section we show how to use the binomial model for pricing American options, while the last section contains the Python code used for computing the tables in the text.

Implementing the Black-Derman-Toy Model

The Black-Derman-Toy model is a simple no-arbitrage model of interest rates. The market term structure of long rates and their volatilities are used to construct a tree of possible future short rates. This tree can then be used to value interest rate-sensitive securities.

The R function below allows computing the Black-Derman-Toy short rate tree.