The EDHEC SciX platform assists institutional asset owners in understanding the risks of their portfolios. In this paper we present an implementation of the Instrumented Principal Component Analysis (IPCA) model [Kelly et al., 2019] for portfolios of equity portfolios, such as funds or mandates. We show that this model enable to decompose risk in many dimensions with high accuracy and stability. In contrast to current solutions, this model only requires widely available price data and extends easily to multi-region analysis. We present the model, address issues related to its calibration, and provide analytics that enable the decomposition of risks with a high level of historical and cross-sectional granularity. We also argue that the stability of this model makes its use possible not only in the context of risk analysis but also portfolio optimisation.

Introduction

The purpose of factor models is to identify and quantify how the value of a portfolio is exposed to the forces driving variations in asset prices. Their use in portfolio management is ubiquitous, from the identification of risks to their management via portfolio optimisation. In this paper, we propose an application of the Instrumented Principal Component Analysis (IPCA) model [Kelly et al., 2018] to the risk analysis of portfolio of equity funds. As we are going to show, the IPCA model has a number of striking features that make it particularly fit for analyzing the risks of these instruments.

Equity funds tend to be invested across many industrial sectors and geographies, and their management involves different styles of active risk taking. Consequently, the risks involved in funds are subject to a potentially large number of factors. For many investors who invest in portfolios of funds, the analysis of their risks is often problematic. Notably, the bottom-up approach that consists in using equity risk models to analyze the content of individual funds and then aggregate this information at the portfolio level, is difficult for a number of reasons.

First, detailed holding data at the fund level are often only precisely known to their managers. For asset owners relying on third parties to manage parts of their portfolios, a detailed knowledge of the positions held in each fund at all time is often not available. Many commercial equity models that require detailed holding data are therefore difficult to exploit. Second, the acquisition, maintenance and use of equity models is difficult. Expensive equity models need to be acquired for each region covered by the portfolio, and they are often not compatible between them, so that extra resources need to be expensed in order to combine their outputs. This creates a situation where the risk of each sub-portfolio is known, though the combined risks of the global portfolio are not well understood.

Against the backdrop, we have developed an implementation of the IPCA model that offers a solution to many of the key issues associated with the analysis of portfolios of funds. Importantly, it is designed to accommodate a great number of risk factors while also maintaining a high level of numerical stability. As we are going to explain, this combination of depth and stability is one of the key innovation of this new type of models compared to their predecessors. This makes them very efficient not only for the purpose of risk analysis, but also, as we will illustrate, for portfolio optimisation.

The IPCA model uses as key input the financial characteristics of instruments. However, it has inherited the flexbility of previous cross-sectional models with respect to the definition of what constitute a characteristic. In contrast to equities, for which the original implementation of the model was intended, the financial characteristics of funds are not always, and one could even say, not often, readily available. We will show that using the instruments exposures to risk factors as characteristics, we are able to build very efficient risk models. This approach, that only require the instrument prices, enables the consistent estimation of financial characteristics across a wide spectrum of risk factors.

The consistent estimation of characteristics for a wide range of risk factors enables the construction of risk models for portfolios exposed to many different styles and geographies. The ability to examine the risk of a global portfolio with a single model sharply reduces the possibility of unintended risk exposures resulting from the aggregation of individual strategies.
Also, the availability of a risk model that easily applies to any fund or mandate opens up many possibilities. For instance, it also allows a consistent analysis of many investments across a large number of dimensions. This is particularly useful when analyzing large portfolios or searching for new investments, in which cases the comparability and consistency of risk information is key. Also, a detailed understanding of the contributions to the risk of the portfolio with a high level of granularity provides crucial information for decision making.
This paper is divided into two parts. In the first part, we present the IPCA model from a contextual point of view and explain how it compares and extend existing models. Then we explain how to estimate funds characteristics, and how to use them to calibrate the model. Although the main originality of this paper is to extend the application of the IPCA model to a new asset class, we propose a number of techniques that complement the original methodology. Notably, the calibration of the model in the context of funds present
challenges that are not present for equities, for which we propose solutions. Also, we derive a number of original analytical formulas that enable the use of the model to decompose risk and returns into contributions that can be attributed to the different risk factors. We illustrate the use of these formulas on a universe of US mutual funds. We also provide discussions on the quantification of the model stability and why it lends itself well to portfolio optimisation tasks.

Authors

Matteo Bagnara, PhD
Quant Researcher,
Scientific Climate Indices ……………………………………….

Benoit Vaucher
Director of Research,
Scientific Climate Indices

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