La convergence de la gestion traditionnelle et de la gestion alternative, d"une part,
l'émergence de la gestion quantitative, d'autre part, reflètent la profonde mutation de la gestion d'actifs.
Ce livre propose d'aborder ces différents thèmes, tous basés sur le contrôle risque et les modèles d'allocation d'actifs.
Cet ouvrage offre un panorama des différentes modalités de la gestion quantitative, allant de
la gestion indicielle à la gestion hedge funds en passant par les gestions structurée, diversifiée,
profilée ou de performance absolue. L'ouvrage présente également les différentes stratégies quantitatives,
que sont les stratégies de réplication, d'allocation, d'options, de volatilité, d'arbitrage ou encore les
stratégies de suivi de tendance et de retour à la moyenne. Il montre en particulier comment l'optimisation de portefeuille,
l'économétrie financière et les stratégies de gestion s'emboitent pour former une stratégie quantitative.
Ce livre contient de nombreuses illustrations et exemples portant sur les différentes classes
d'actifs (actions, taux d'intéret, change et matières premières).
Ce livre s'adresse aux étudiants de master, qui veulent devenir des quants et travailler dans la finance quantitative, et
aux professionnels qui cherchent à mieux comprendre les modèles mathématiques et statistiques
utilisés dans la gestion d'actifs.
Editions Economica, Collection Finance, 680 pages
Télécharger la table des matières,
les extraits du livre,
l'annexe sur les exercices,
la correction des exercices,
(voir aussi les programmes Gauss correspondants) et
les applications numériques du livre
La Gestion des Risques Financiers (deuxième édition)
Auteur
T. Roncalli
Date
Octobre 2009
Résumé
Cette nouvelle édition a été l'occasion de revoir entièrement le texte, de supprimer un certain nombre de développement
qui ne sont plus d'actualité et d'apporter un éclairage nouveau par rapport à la crise actuelle. Elle contient aussi de
nouvelles illustrations et de nouvelles applications afin de mieux préciser certains concepts qui peuvent apparaïtre complexes.
Plusieurs sujets ont fait l'objet de nouveaux développements comme par exemple le risque de liquidité, les produits exotiques,
le risque de contrepartie sur opération de marché, les produits structurés, la gestion du risque de marché dans la gestion d'actifs,
la dépendance dans les dérives de crédit et la contribution en risque. Enfin, cette deuxième édition est accompagnée d'exercices
permettant de vérifier ses connaissances.
- Editions Economica, Collection Finance, 560 pages
- Télécharger les programmes Gauss,
les errata du livre,
la table des matières et
la correction des exercices du livre
- La Gestion des Risques Financiers
Auteur
T. Roncalli
Date
Aoüt 2004
Résumé
La gestion des risques financiers est en pleine évolution sous la
pression de la réglementation prudentielle et du développement des outils
pour mieux les maïtriser. Le Comité de Bâle a publié le Nouvel Accord
sur le ratio international de solvabilité (Bäle II) le 26 juin 2004,
et la Commission Européenne a déjà adopté les différentes propositions
de cet accord. Cet accord a été accueilli favorablement par la profession
bancaire et les établissements financiers ont maintenant deux ans et demi
pour mener à bien cette réforme afin d'en bénéficier pleinement.
Les banques n'ont cependant pas attendu le Nouvel Accord pour
moderniser leur gestion des risques. Depuis dix ans, on assiste en
effet à un développement technique du risk management et les modèles pour
mesurer les risques sont de plus en plus sophistiqués. Le Nouvel Accord
participe d'ailleurs à cette évolution, puisqu'il vise à définir un capital
réglementaire plus proche du capital économique obtenu avec les modèles internes.
Le présent ouvrage s'inscrit dans ces deux lignes directrices : réglementation du
risque et modélisation du risque. Il s'adresse aussi bien à des étudiants de
troisième cycle, qui désirent acquérir une culture financière du risque et
de sa gestion, qu'à des professionnels qui cherchent à mieux comprendre
les fondements de la modélisation mathématique du risque.
- Editions Economica, Collection Gestion, 455 pages
- Télécharger les programmes Gauss et les applications numériques du livre
- TSM (Time Series and Wavelets for Finance)
Author
T. Roncalli
Date
1996
Summary
TSM is a GAUSS library for time series modeling in both time domain and frequency domain.
It is primarily designed for the analysis and estimation of ARMA, VARX processes, state space models, fractional processes and structural models.
To study these models, special tools have been developed like procedures for simulation, spectral analysis, Hankel matrices, etc.
Estimation is based on the Maximum Likelihood principle or Gnereralized Method of Moments and linear restrictions may be easily imposed.
It also contains several filtering methods (Kalman Filter, FLS and GFLS) and several procedures for Time-Frequency analysis of 1-D signal
(wavelet analysis and wavelet packet analysis).
- Source code: 300 Ko, Examples code: 390 Ko, Manual: 230 pages.
- TSM description at Gauss Aptech Systems webpage
- Download TSM examples
- Introduction à la programmation sous Gauss
Auteur
T. Roncalli
Date
1995
- Global Design, 660 pages
Top
- Portfolio Construction with Climate Risk Measures, T. Le Guenedal and T. Roncalli,
Chapter 3 of the book Climate Investing:
New Strategies and Implementation Challenges, edited by Emmanuel Jurczenko, Wiley, December 2022 (pages 49-86)
- The Market Measure of Carbon Risk and its Impact on the Minimum Variance Portfolio, T. Roncalli, T. Le Guenedal, F. Lepetit, T. Roncalli and T. Sekine,
Journal of Portfolio Management, 47(9), 2021
- Machine Learning Optimization Algorithms & Portfolio Allocation, S. Perrin and T. Roncalli,
Chapter 8 of the book Machine Learning
for Asset Management: New Developments and Financial Applications, edited by Emmanuel Jurczenko, Wiley, June 2020 (pages 261-328)
- Factor Investing in Currency Markets: Does it Make Sense?, E. Baku, R. Fortes, K. Hervé, E. Lezmi, H. Malongo, T. Roncalli and J. Xu,
Journal of Portfolio Management, 46(2), 2019.
- Keep Up The Momentum, T. Roncalli,
Journal of Asset Management, 19(5), 2018
- Alternative Risk Premia: What Do We Know?, T. Roncalli,
Chapter 10 of the book
Factor Investing: From Traditional to Alternative Risk Premia, edited by Emmanuel Jurczenko, Elsevier, October 2017
- Risk Parity Portfolios with Risk Factors, T. Roncalli and G. Weisang,
Quantitative Finance, 16(3), 2016
- Smart Beta: Managing Diversification of Minimum Variance Portfolios, J-C. Richard and T. Roncalli,
Chapter 2 of the book Risk-based and Factor Investing,
edited by Emmanuel Jurczenko, Elsevier, November 2015
- Introducing Expected Returns into Risk Parity Portfolios: A New Framework for Asset Allocation, T. Roncalli,
Bankers, Markets & Investors, 138, September 2015
- Measuring the Liquidity of ETFs: An Application to the European Market, T. Roncalli and B. Zheng,
Journal of Trading, 9(3), Summer 2014
- The Smart Indexing Puzzle, Z. Cazalet, P. Grison and T. Roncalli,
Journal of Index Investing, 5(1), Summer 2014
- Measuring Performance of Exchange-Traded Funds, M. Hassine and T. Roncalli,
Journal of Index Investing, 4(3), Winter 2013
- Multi-Asset Indices - An Idea Whose Time Has Come, P. Hereil, J. Laplante and T. Roncalli,
Journal of Indexes Europe, 4, January 2013
- Managing Sovereign Credit Risk - Risk Exposures in Bond Portfolios and Indices, B. Bruder, P. Hereil and T. Roncalli,
Journal of Indexes Europe, 4, November 2011
- Mesurer et gérer le risque de crédit souverain de la zone euro, B. Bruder, P. Hereil et T. Roncalli,
Revue Banque, 740, Octobre 2011
- Measuring the Risk Concentration of Investment Portfolios, P. Hereil and T. Roncalli,
Bloomberg Brief, Risk, July 2011
- Tracking Problems, Hedge Fund Replication, and Alternative Beta, T. Roncalli and G. Weisang,
Journal of Financial Transformation (Cass-Capco Institute Paper Series on Risk), 31, 2011
- The Properties of Equally Weighted Risk Contribution Portfolios, S. Maillard, T. Roncalli and J. Teiletche,
Journal of Portfolio Management, Summer 2010
- Risk Management Lessons from Madoff Fraud, P. Clauss, T. Roncalli and G. Weisang, Chapter 17 of the book
Credit, Currency or Derivatives Instruments of Global Financial Stability or Crisis?,
International Finance Review, 10, edited by Jay J. Choi and Michael Papaioannou, Emerald Group Publishing Limited, 2009
- An Alternative Approach to Alternative Beta, T. Roncalli and J. Teiletche, Journal of Financial Transformation,
Journal of Financial Transformation, 24, 2008
- Maximum Likelihood Estimate of Default Correlations, P. Demey, J-F. Jouanin, T. Roncalli and C. Roget,
Risk, November 2004
- Financial Applications of Copula Functions, J-F. Jouanin, G. Riboulet and T. Roncalli, Chapter 14 of the book
Risk Measures for the 21st Century,
edited by Giorgio Szego, John Wiley & Sons, 2004
- La prise en compte de la diversification des risques opérationnels, M. Pennequin, T. Roncalli et E. Salomon,
Banque Magazine, 660, Juillet 2004
- Correlation and diversification effects in operational risk modelling, A. Frachot, T. Roncalli and E. Salomon,
Operational Risk, May 2004
- Technical Note: Dependence and two-asset options pricing, G. Rapuch and T. Roncalli,
Journal of Computational Finance, 7/4, Spring 2004
- Loss Distribution Approach in Practice, A. Frachot, O. Moudoulaud and T. Roncalli,
Chapter 15 of the book The Basel Handbook: A Guide for Financial Practitioners,
edited by Michael Ong, Risk Books, December 2003
- How to avoid over-estimating capital charge for operational risk ?, N. Baud, A. Frachot and T. Roncalli,
Operational Risk, February 2003
- L'utilisation des données externes pour le risque opérationnel : comment économiser des fonds propres, N. Baud, A. Frachot et T. Roncalli,
Banque Magazine, 641, Novembre 2002
- La construction des modèles internes du risque opérationnel, A. Frachot et T. Roncalli,
Banque Magazine, 635, Avril 2002
- Analyse du plan épargne logement et évaluation de son option de conversion, N. Baud, P. Demey, D.Jacomy, G. Riboulet et T. Roncalli,
Bankers, Markets & Investors, 50, 2001
- Hopscotch methods for two state financial models, A. Kurpiel and T. Roncalli,
Journal of Computational Finance, 3/2, Spring 2000
- Retour à la moyenne dans les cours du change du méôcanisme de change européen : 1987-1995, J-S. Pentecôte et T. Roncalli,
Economie & Prévision, 124, Septembre 1996
Top
- The Economic Cost of the Carbon Tax
Authors
T. Roncalli and R. Semet
Date
March 2024
Abstract
The choice of the optimal environmental policy is an important question in the current climate change context.
While the carbon tax was the preferred policy of economists in the 1970s and 1980s, governments have implemented
both quantity-based policies, such as emissions trading schemes, and price-based policies, such as fossil fuel
taxes and renewable energy subsidies. The implementation of a general carbon tax on greenhouse gas emissions is
currently not very common, and a low carbon price is generally retained. However, with the development of the EU
Carbon Border Adjustment Mechanism, the Fit for 55 package and the need to achieve a low-carbon economy by 2050 if
we are to keep the temperature anomaly below 1.5°C, the issue of carbon taxes is back on the agenda and the old debate
of price vs. quantity regulation is reopened. In this article, we extend the input-output analysis by introducing
pass-through mechanisms to define a new cost-push price model that accounts for the cascading price effects of a
carbon tax through the supply chain. We can then calculate the government revenue from a carbon tax, the net
cost to the economy, and the impact on inflation. Implementing a global tax of $100/tCO2e generates revenue of 2.82% of
world GDP, but it also implies a net cost of 2.18% and inflation of 4.08% in terms of the producer price index (PPI) and
3.53% in terms of the consumer price index (CPI). In addition to these macroeconomic effects, we also analyze the
microeconomic effects of the carbon tax. In particular, we analyze the impact on issuers' earnings, distributive
implications, and social issues related to the carbon tax. We find that the implementation of a carbon tax is not
as efficient as economic theory tells us it should be, which justifies the reluctance of governments to
implement such a regulatory policy today.
Keywords
Climate change, carbon pricing, decarbonization policy instrument, carbon tax, emissions trading scheme,
net-zero emissions, negative externality, input-output analysis, social welfare
- Download the working paper
- Net Zero Investing
Author
T. Roncalli
Date
December 2023
Conference slides
- Download the PDF file
- Net Zero Investment Portfolios - Part 2. The Core-Satellite Approach
Authors
M. Ben Slimane, D. Lucius, T. Roncalli and J. Xu
Date
October 2023
Abstract
This article is the second part of a research project on net-zero investment. While the previous publication was
dedicated to the integrated approach, this one focuses on the core-satellite approach. As explained in the first part,
net-zero policies need to address two dimensions: decarbonizing the portfolio and financing the transition.
The integrated approach combines these two dimensions in an allocation process that considers both carbon intensity
for the decarbonisation dimension and green intensity for the financing dimension. However, we have found that
carbon intensity and green intensity are currently positively correlated. Therefore, we propose a second approach
to better identify the contribution of the two net-zero dimensions. In the core-satellite strategy, the decarbonization
dimension is managed within the core portfolio, while the objective of the satellite strategy is to finance the transition
to a low-carbon economy. The choice of the decarbonization policy is an important step in the design of the core portfolio.
At least, three issues need to be considered: the magnitude of the decarbonization pathway, the sequence of decarbonization,
and the self-decarbonization property of the core portfolio. Moreover, a decarbonization pathway is not neutral if we refer
to a strategic asset allocation process. In fact, it is equivalent to changing the implied risk premia derived from the
Black-Litterman model. Building the satellite portfolio is certainly the most challenging part of the allocation process.
It requires a deeper understanding of how to achieve net-zero emissions by 2050, specifically how to transform the current
global value chain into a net-zero economy? As there is a gap in the current funding requirements, we need to prioritize
financial investments and narrow the definition of the eligible investment universe. As a result, the investment processes
of the core and satellite portfolios are very different. The core portfolio is more of a top-down allocation process and
exclusion strategy, where the central climate risk metric is carbon intensity. The satellite portfolio is more of a
bottom-up allocation process and asset selection strategy, where the central climate risk metric is green intensity.
Finally, the risk assessment of the global core-satellite portfolio must be addressed.
Keywords
Net zero emissions, core-satellite strategy, decarbonization, transition, greenness, carbon intensity, green intensity,
equity allocation, bond allocation, tracking error
- Download the working paper
- From Climate Stress Testing to Climate Value-at-Risk: A Stochastic Approach
Authors
B. Desnos, T. Le Guenedal, P. Morais and T. Roncalli
Date
June 2023
Abstract
This paper proposes a comprehensive climate stress testing approach to measure the impact of transition risk on investment portfolios.
Unlike most climate stress testing models, which are designed for the banking industry and follow a top-down approach,
our framework considers a bottom-up approach and is mainly relevant for the asset management industry.
In this paper, we model the distribution function of the carbon tax, provide an explicit specification of
indirect carbon emissions in the supply chain, introduce pass-through mechanisms of carbon prices, and
compute the probability distribution of potential (economic and financial) impacts in a Monte Carlo setting.
Rather than using a single or limited set of scenarios, we use a probabilistic approach to generate thousands of
simulated pathways. We can then examine the impact of transition risk at the economic level and analyse inflation,
growth and earnings risks at the sector and country level. By combining value-at-risk and stress-testing approaches,
we also define appropriate risk measures to manage climate risk in investment portfolios and asset allocation.
Keywords
Climate change, stress testing, value-at-risk, carbon tax, input-output analysis, pass-through, indirect emissions, inflation risk,
risk contribution, substochastic matrix, Neumann series, directed graph, copula, Monte Carlo simulations
- Download the working paper
- Green vs. Social Bond Premium
Authors
M. Ben Slimane, T. Roncalli and R. Semet
Date
May 2023
Abstract
While responsible investors consider that the environmental and social pillars are highly interconnected when implementing ESG and climate strategies,
our research shows that the green and social bond markets are not integrated. Indeed, we notice that the social bond premium is
not positively correlated with the greenium. On the contrary, we found a negative long-term relationship between the two premia.
If we consider a dynamic analysis, we observe that the premia are highly time-varying. On average, the greenium is about
-3 bps while the social bond premium is not significant and close to zero. These results indicate a behavioral difference
between the primary and secondary markets. This is particularly true for social bonds that had a positive premium last year.
More generally, the level of these two premia (especially the social bond premium) are a long way from reflecting the major concerns
about a just transition to a low-carbon economy, and the financing dimension of net zero policies.
In this research, we also highlight the differences between green and social preferences in terms of bond pricing. First, there is a difference
between green and social projects when they are financed in euros or other currencies. Clearly, non-euro projects are subject to a
higher premium. We also observe that the level of the greenium is related to the credibility of the green project. In line with other
academic studies, we confirm that certification, external review and the SDG dimension impact the greenium as expected by the signal theory.
On the contrary, it is more difficult to understand the pricing in the social bond market since empirical relationships between the social
bond premium and extra-financial factors are missing or seem counter intuitive. Therefore, we can assume that investors
consider social bonds to be more conventional instruments than green bonds.
Keywords
Sustainability, green bond, social bond, ESG, climate risk, risk premium, greenium, preferences
- Download the working paper
- Net Zero Investment Portfolios - Part 1. The Comprehensive Integrated Approach
Authors
I. Barahhou, M. Ben Slimane, N. Oulid Azouz and T. Roncalli
Date
October 2022
Abstract
The emergence of net zero emissions policies is currently one of the most important topics among asset owners and managers.
It considerably changes portfolio allocation and the investment framework of both passive and active investors.
The academic literature generally concludes that implementing net zero portfolios and sustainable investing is not costly.
Moreover, some investors have chosen to implement highly dynamic decarbonization pathways with a continuous reference
to business-as-usual benchmarks. The goal of this paper is to participate in the debate on climate investing by showing
that it is not a free lunch. Net zero investment portfolios may involve some substantial costs in terms of tracking,
diversification, and liquidity risks.
The decarbonization pathway requires the net zero emissions scenario to be defined. Transforming this absolute scenario into
an intensity-based scenario is not straightforward because it involves a carbon budget. Once the scenario is established,
it is important to assess the metrics that capture the different dimensions of a net zero emissions policy,
particularly the self-decarbonization and the green intensity of issuers. Then we can combine these different
figures to define the objective function involved in optimizing net zero portfolios by considering the asset class.
For instance, bond portfolios and equity portfolios are not constructed in the same way. The objective of this
comprehensive integrated approach is to deal with the multi-faceted dimensions of net zero investing.
Another method establishes a core-satellite portfolio, where decarbonization and transition dimensions are segregated.
If we focus on the comprehensive integrated approach, our results show that net zero investing goes beyond the simple exercise of dynamic decarbonization.
Compared to a business-as-usual benchmark, the tracking error cost may be relatively high, especially for equity portfolios. Moreover,
the diversification risk is critical for equities and bonds because we see significant deformation of investment universes.
Of course, these results depend on the parameter values we use. Nevertheless, they clearly indicate that climate investing is
not just a tilt of traditional investing. In this context, the reference to business-as-usual benchmarks is not always relevant.
Of course, this situation is transitory until the world is on the right track to becoming a net zero economy, but at that time,
we will again observe a convergence between business-as-usual and climate investing, and a growing correlation between the market and net zero portfolios.
Keywords
Climate change, net zero emissions scenario, decarbonization, transition, greenness
- Download the working paper
- Capturing Risk: Finding the Right Measures and Metrics (and Data)
Author
T. Roncalli
Date
June 2022
Conference slides
- Download the PDF file
- Multi-Period Optimization Portfolio
Authors
E. Lezmi, T. Roncalli and J. Xu
Date
March 2022
Abstract
In this article, we consider a multi-period portfolio optimization problem, which is an extension of the
single-period mean-variance model. We discuss several formulations of the objective function,
constraints and coupling relationships. We then derive three numerical algorithms that can be used
to solve such problems: the alternating direction method of multipliers, the block coordinate descent
algorithm and the augmented quadratic programming method. We illustrate the differences between
single-period and multi-period solutions by considering three asset allocation problems: transition
management (Rattray, 2003), total variation regularized portfolio (Corsaro et al., 2020) and trading
trajectory modeling (Gârleanu and Pedersen, 2013). Finally, we solve the portfolio alignment problem of
Le Guenedal and Roncalli (2022) when the fund manager has to dynamically control the carbon footprint of
his investment portfolio by integrating a carbon reduction scenario. Comparing the single-period and
multi-period solutions shows that the active share between the two portfolios may be greater than 25%.
This figure can also reach 40% if we include carbon trends and they are increasing.
Keywords
Multi-period optimization, portfolio allocation, ADMM, block coordinate descent,
quadratic programming, coupling variables, transition management, total variation regularization,
optimal trading trajectory problem, portfolio decarbonization, net zero alignment
- Download the working paper
- Net Zero Carbon Metrics
Authors
T. Le Guenedal, F. Lombard, T. Roncalli and T. Sekine
Date
February 2022
Abstract
This research project is both an update of the analysis on carbon emissions trajectories proposed by Le Guenedal et al. (2020)
and a companion study of the climate risk measures defined by Le Guenedal and Roncalli (2022). While Le Guenedal et al. (2020)
use carbon intensities, we extend the track-record projection approach by considering absolute carbon emissions.
In particular, we propose a carbon budget approach that incorporates novel metrics for measuring the carbon emissions
reduction targets and the relative positioning with respect to the net zero emissions (NZE) scenario. Indeed,
current carbon emissions data are not sufficient to build portfolio alignment. The purpose of this paper is then
to define net zero carbon metrics, which are necessary to enhance the disclosure and the debate on corporates'
emissions (Créhalet, 2021; Le Meaux et al., 2021). These carbon metrics can be divided into two families.
The static measures are NZE duration, NZE gap, NZE slope and NZE budget. They can be computed using a target
scenario or the linear trend model. The dynamic NZE measures incorporate the past trajectory and the future
scenarios of carbon emissions. For instance, we break down the carbon budget by error and revision time contributions.
We also propose a velocity measure of the carbon emissions trend and two main dynamic NZE measures that are necessary
to assess the performance of an issuer compared to the NZE scenario: the zero-velocity scenario and the burnout scenario.
These different measures can then be used to define the PAC framework, that analyzes the participation, ambition and
credibility of issuers' NZE policies. Finally, we apply this framework to the CDP database. Empirical results show that
net zero carbon emissions are challenging for many issuers for two reasons. The first is that some issuers have a lack of
ambition concerning their NZE scenario. The second is that some targets are not compatible with past trends.
Keywords
Climate change, net zero emissions, reduction scenario, carbon budget, carbon trend, carbon reduction target,
participation, ambition, credibility, portfolio alignment, decarbonization.
- Download the working paper
- Portfolio Construction with Climate Risk Measures
Authors
T. Le Guenedal and T. Roncalli
Date
January 2022
Abstract
Because of the 2015 Paris Agreement, the development of ESG investing and the emergence of net zero emission policies,
climate risk is certainly the most important topic and challenge for asset owners and managers now and will remain so
over the next five years. It considerably changes portfolio allocation and the investment framework of both passive
and active investors. The goal of this paper is to conduct a survey of the various climate risk measures that are available
in the asset management industry and the practices of portfolio construction that use these metrics. Therefore, the first
part of this paper lists the different climate risk metrics -- e.g., carbon footprint, carbon transition pathway,
carbon transition and physical risks. The second part is dedicated to portfolio optimization, in particular portfolio
decarbonization and portfolio alignment (Paris-based benchmarks and net zero carbon objective). Among the different
findings, two are of great importance for investors. First, portfolio decarbonization is more difficult when we
include scope 3 carbon emissions. Indeed, optimizing using the sum of scopes 1, 2 and 3 emissions leads to a portfolio
with more tracking error risk than using direct plus first tier indirect carbon emissions. Second, portfolio alignment
is more complex than portfolio decarbonization. Since aligning portfolios with scope 3 is becoming the standard approach
to climate portfolio construction, the impact on portfolio management may be substantial, and the divergence between
carbon investing and traditional investing will increase.
Keywords
Climate change, risk measure, carbon emissions, reduction scenario, carbon trajectory, net zero emission,
optimized portfolio, decarbonization, portfolio alignment, index portfolio.
- Download the working paper
- Liquidity Stress Testing in Asset Management (Comprehensive Report)
Author
T. Roncalli et al.
Date
December 2021
Keywords
Asset-liability management, liquidity, stress testing, asset risk, funding risk, redemption rate, transaction cost, market impact, redemption coverage ratio, liquidity management tool.
- Download the comprehensive report
- Liquidity Stress Testing in Asset Management
Authors
T. Roncalli and A. Cherief
Date
December 2021
Conference slides
- Download the PDF file
- Liquidity Stress Testing in Asset Management - Part 4. A Step-by-step Practical Guide
Authors
T. Roncalli and A. Cherief
Date
November 2021
Abstract
This article is part of a comprehensive research project on liquidity risk
in asset management, which can be divided into three dimensions. The first
dimension covers liability liquidity risk (or funding
liquidity) modeling, the second dimension focuses on asset
liquidity risk (or market liquidity) modeling, and the third dimension
considers the asset-liability management of the liquidity gap risk (or
asset-liability matching). The purpose of this research is to propose a methodological
and practical framework in order to perform liquidity stress testing
programs, which comply with regulatory guidelines (ESMA, 2019,
2020) and are useful for fund managers. The review of the academic
literature and professional research studies shows that there is a lack of
standardized and analytical models. The aim of this research project is
then to fill the gap with the goal of developing mathematical and statistical
approaches, and providing appropriate answers.
The three dimensions have been developed in
the published working papers:
(1) modeling the liability liquidity risk,
(2) modeling the asset liquidity risk and
(3) managing the asset-liability liquidity risk.
This fourth working paper provides three examples
and the comprehensive details to compute the redemption coverage ratio,
implement reverse stress testing and
estimate the liquidation cost of the redemption portfolio. The portfolios
have been chosen in order to cover the main asset classes:
large-cap stocks, small-cap stocks, sovereign bonds and corporate bonds.
Since we provide the data in the appendix, these basic examples are easily reproducible
and may help quantitative analysts to understand the different steps to implement
liquidity stress testing in asset management.
Keywords
Liquidity risk, stress testing, asset-liability management, redemption coverage ratio,
reverse stress testing, transaction cost, reproducible research, knowledge transfer.
- Download the working paper
- ESG and Sovereign Risk: What is Priced in by the Bond Market and Credit Rating Agencies?
Authors
R. Semet, T. Roncalli and L. Stagnol
Date
October 2021
Abstract
In this paper, we examine the materiality of ESG on country creditworthiness from a
credit risk and fundamental analysis viewpoint. To address this, we consider a granular
set of 269 indicators within the three ESG pillars to determine what the sovereign bond
market is pricing in. From this set of ESG metrics covering the 2015-2020 period and
67 countries, we first determine the ESG indicators that are most relevant when it comes
to explaining the sovereign bond yield, after controlling the effects of traditional
fundamental variables such as economic strength and credit rating. We also emphasize
the major themes that are directly useful for investors when assessing the country risk
premium. At the global level, we notice that these themes mainly belong to the E and G pillars.
Those results confirm that extra-financial criteria are integrated into bond pricing.
However, we also identify a clear difference between high-and middle-income countries.
Indeed, whereas the S pillar is lagging for the highest income countries, it is nearly
as important as the G pillar for the middle-income ones. Second, we determine which ESG
metrics are indirectly valuable for assessing a country's solvency. More precisely, we attempt
to infer credit rating solely from extra-financial criteria, that is the ESG indicators that
are priced in by credit rating agencies. We find that there is no overlap between the set of
indicators that predict credit ratings and those that directly explain sovereign bond yields.
The results also highlight the importance of the G and S pillars when predicting credit ratings.
The E pillar is lagging, suggesting that credit rating agencies are undermining the impact of
climate change and environmental topics on country creditworthiness. This is consistent with the
traditional view that social and governance issues are the main drivers of the sovereign risk,
because they are more specific and less global than environmental issues. Finally, taking these
different results together, this research shows that opposing extra-financial and fundamental
analysis does not make a lot of sense. On the contrary, it advocates for greater integration of
ESG analysis and credit analysis when assessing sovereign risk.
Keywords
ESG, Sovereign risk, debt, bond yield, credit spread.
- Download the working paper
- Liquidity Stress Testing in Asset Management - Part 3. Managing the Asset-Liability Liquidity Risk
Author
T. Roncalli
Date
October 2021
Abstract
This article is part of a comprehensive research project on liquidity risk
in asset management, which can be divided into three dimensions. The first
dimension covers the modeling of the liability liquidity risk (or funding
liquidity), the second dimension is dedicated to the modeling of the asset
liquidity risk (or market liquidity), whereas the third dimension considers
the management of the asset-liability liquidity risk (or asset-liability
matching). The purpose of this research is to propose a methodological
and practical framework in order to perform liquidity stress testing
programs, which comply with regulatory guidelines (ESMA, 2019, 2020)
and are useful for fund managers. The review of the academic
literature and professional research studies shows that there is a lack of
standardized and analytical models. The aim of this research project is
then to fill the gap with the goal of developing mathematical and statistical
approaches, and providing appropriate answers.
In this third and last research paper focused on managing the
asset-liability liquidity risk, we explore the ALM tools that can be put in
place to control the liquidity gap. These ALM tools can be split into
three categories: measurement tools, management tools and monitoring tools.
In terms of measurement tools, we focus on the computation of the
redemption coverage ratio (RCR), which is the central instrument of
liquidity stress testing programs. We also study the redemption liquidation
policy and the different implementation methodologies, and we show how
reverse stress testing can be developed. In terms of liquidity management
tools, we study the calibration of liquidity buffers, the pros and cons of
special arrangements (redemption suspensions, gates, side pockets and
in-kind redemptions) and the effectiveness of swing pricing. In terms of
liquidity monitoring tools, we compare the macro- and micro-approaches to
liquidity monitoring in order to identify the transmission channels of liquidity risk.
Keywords
Asset-liability management, liquidity risk, liquidity management tool (LMT), stress testing,
redemption coverage ratio, liquidity buffer, swing pricing.
- Download the working paper
- The Impact of ESG Investing on Asset Pricing,
Credit Rating, Financial Analysis and the Cost of the Debt
Authors
Amundi Quantitative Research
Date
October 2021
Conference slides
- Download the PDF file
- Liquidity Stress Testing in Asset Management - Part 2. Modeling the Asset Liquidity Risk
Authors
T. Roncalli, A. Cherief, F. Karray and M. Regnault
Date
May 2021
Abstract
This article is part of a comprehensive research project on liquidity risk in asset management,
which can be divided into three dimensions. The first dimension covers liability liquidity risk
(or funding liquidity) modeling, the second dimension focuses on asset liquidity risk
(or market liquidity) modeling, and the third dimension considers the asset-liability management
of the liquidity gap risk (or asset-liability matching). The purpose of this research is to
propose a methodological and practical framework in order to perform liquidity stress testing programs,
which comply with regulatory guidelines (ESMA, 2019, 2020) and are useful for fund managers.
The review of the academic literature and professional research studies shows that there is a
lack of standardized and analytical models.
The aim of this research project is then to fill the gap with the goal of developing mathematical
and statistical approaches, and providing appropriate answers.
In this second article focused on asset liquidity risk modeling, we propose a market impact model
to estimate transaction costs. After presenting a toy model that helps to understand the main
concepts of asset liquidity, we consider a two-regime model, which is based on the power-law
property of price impact. Then, we define several asset liquidity measures such as liquidity cost,
liquidation ratio and shortfall or time to liquidation in order to assess the different dimensions
of asset liquidity. Finally, we apply this asset liquidity framework to stocks and bonds and discuss
the issues of calibrating the transaction cost model.
Keywords
Asset liquidity, stress testing, bid-ask spread, market impact, transaction cost,
participation rate, power law, liquidation cost, liquidation ratio, liquidation shortfall, time to liquidation.
- Download the working paper
- Understanding the Performance of the Equity Value Factor
Authors
L. Stagnol, C. Lopez, T. Roncalli and B. Taillardat
Date
February 2021
Abstract
After decades of sound performance, doubts have been raised on the ability of the equity value
factor to continue to deliver a positive performance in the aftermath of the 2008 Global
Financial Crisis. Indeed, in a context dominated by low yields, sluggish growth and subdued
inflation combined with an accelerating digitalization of the economy, the performance of value
strategies struggled over the past decade. In this paper, we investigate potential drivers
behind this performance lag, such as macroeconomic and microeconomic determinants, ESG characteristics
or credit-borrowed components. Based on European and American data, we find that inflation and tightening
credit spread levels are the most supportive factors for value stocks. As far as interest rates are
concerned, their sustained low levels prevented the value stock universe from clearing its most distressed
issuers, also known as "deep value", and thus dampened value performance. As a matter of fact, we show that
value has not been systematically an investment strategy bearing a heightened default risk. Our ESG analysis
corroborates the "transatlantic divide", the historical gap between the U.S. and Europe on this front, and shows
that value and growth stocks are not necessarily all brown and green stocks. In addition, we demonstrate that the
small cap segment has not been the magical cure to value underperformance. Finally, we conclude that value is not
dead yet, and might even have bright days ahead considering the current improvements in market sentiment, especially
if inflation does materialize. Nevertheless, we also emphasize that the current value risk factor is probably different
in nature from the one we observed during the golden age of value investing at the beginning of the 2000s. Indeed, trading
facilities, ease of access to fundamental data for a large number of investors, ESG investing and the digitalization of the
economy may have changed the rules of the game.
Keywords
Value, risk factor, risk premium, factor investing, valuation, deep value, inflation, interest rates, ESG, carbon risk.
- Download the working paper
- The Market Measure of Carbon Risk and its Impact on the Minimum Variance Portfolio
Authors
T. Roncalli, T. Le Guenedal, F. Lepetit, T. Roncalli and T. Sekine
Date
January 2021
Abstract
Like ESG investing, climate change is an important concern for asset managers and owners, and a new challenge for portfolio construction.
Until now, investors have mainly measured carbon risk using fundamental approaches, such as with carbon intensity metrics.
Nevertheless, it has not been proven that asset prices are directly impacted by these fundamental-based measures. In this paper, we
focus on another approach, which consists in measuring the sensitivity of stock prices with respect to a carbon risk factor.
In our opinion, carbon betas are market-based measures that are complementary to carbon intensities or fundamental-based measures
when managing investment portfolios, because carbon betas may be viewed as an extension or forward-looking measure of the
current carbon footprint. In particular, we show how this new metric can be used to build minimum variance strategies
and how they impact their portfolio construction.
Keywords
Carbon, climate change, risk factor, carbon beta, carbon intensity, minimum variance portfolio.
- Download the working paper
- Liquidity Stress Testing in Asset Management - Part 1. Modeling the Liability Liquidity Risk
Authors
T. Roncalli, F. Karray, F. Pan and M. Regnault
Date
December 2020
Abstract
This article is part of a comprehensive research project on liquidity risk in
asset management, which can be divided into three dimensions. The first
dimension covers liability liquidity risk (or funding
liquidity) modeling, the second dimension focuses on asset
liquidity risk (or market liquidity) modeling, and the third dimension considers
asset-liability liquidity risk management (or asset-liability
matching). The purpose of this research is to propose a methodological and
practical framework in order to perform liquidity stress testing programs,
which comply with regulatory guidelines \citep{ESMA-2019} and are useful
for fund managers. The review of the academic literature and professional
research studies shows that there is a lack of standardized and analytical
models. The aim of this research project is then to fill the gap with the
goal to develop mathematical and statistical approaches, and provide
appropriate answers.
In this first part that focuses on liability liquidity risk modeling,
we propose several statistical models for estimating redemption shocks. The
historical approach must be complemented by an analytical approach based on
zero-inflated models if we want to understand the true parameters that
influence the redemption shocks. Moreover, we must also distinguish aggregate
population models and individual-based models if we want to develop
behavioral approaches. Once these different statistical models are
calibrated, the second big issue is the risk measure to assess normal and
stressed redemption shocks. Finally, the last issue is to develop a factor
model that can translate stress scenarios on market risk factors into stress
scenarios on fund liabilities.
Keywords
Liquidity, stress testing, liability, redemption rate, redemption frequency, redemption severity, zero-inflated beta model, copula.
- Download the working paper
- Measuring and Managing Carbon Risk in Investment Portfolios
Authors
T. Roncalli, T. Le Guenedal, F. Lepetit, T. Roncalli and T. Sekine
Date
August 2020
Abstract
This article studies the impact of carbon risk on stock pricing. To address this, we consider the seminal approach of Görgen et al. (2019), who proposed
estimating the carbon financial risk of equities by their carbon beta. To achieve this, the primary task is to develop a brown-minus-green (or
BMG) risk factor, similar to Fama and French (1992). Secondly, we must estimate the carbon beta using a multi-factor model. While Görgen et al. (2019)
considered that the carbon beta is constant, we propose a time-varying estimation model to assess the dynamics of the carbon risk. Moreover, we test
several specifications of the BMG factor to understand which climate change-related dimensions are priced in by the stock market. In the second
part of the article, we focus on the carbon risk management of investment portfolios. First, we analyze how carbon risk impacts the construction of a
minimum variance portfolio. As the goal of this portfolio is to reduce unrewarded financial risks of an investment, incorporating the carbon risk
into this approach fulfils this objective. Second, we propose a new framework for building enhanced index portfolios with a lower exposure to carbon risk
than capitalization-weighted stock indices. Finally, we explore how carbon sensitivities can improve the robustness of factor investing portfolios.
Keywords
Carbon, climate change, risk factor, Kalman filter, minimum variance portfolio, enhanced index portfolio, factor investing.
- Download the working paper
- Improving the Robustness of Trading Strategy
Backtesting with Boltzmann Machines and Generative Adversarial Networks
Authors
E. Lezmi, J. Roche, T. Roncalli and J. Xu
Date
June 2020
Abstract
In this article, we explore generative models in order to build a market generator. The underlying idea is to simulate artificial multi-dimensional
financial time series, whose statistical properties are the same as those observed in the financial markets. In particular, these synthetic data must
preserve the first four statistical moments (mean, standard deviation, skewness and kurtosis), the stochastic dependence between the different
dimensions (copula structure) and across time (autocorrelation function). The first part of the article reviews the more relevant generative
models, which are restricted Boltzmann machines, generative adversarial networks, and convolutional Wasserstein models. The second part of the
article is dedicated to financial applications by considering the simulation of multi-dimensional times series and estimating the probability distribution
of backtest statistics. The final objective is to develop a framework for improving the risk management of quantitative investment strategies.
Keywords
Machine learning, generative approach, discriminative approach, restricted Boltzmann machine, generative adversarial network, Wasserstein distance,
market generator, quantitative asset management, backtesting, trading strategy.
- Download the working paper
- ESG Investing in Fixed Income: It's Time to Cross the Rubicon
- ESG Investing in Corporate Bonds: Mind the Gap
Authors
M. Ben Slimane, T. Le Guenedal, T. Roncalli and T. Sekine
Date
January 2020
Abstract
This research is the companion study of three previous research projects conducted at Amundi that address the issue of socially responsible investing (SRI) in the stock
market (Berg et al., 2014; Bennani et al., 2018a; Drei et al., 2019). The underlying idea of this new study is to explore the impact of ESG investing on asset pricing in the
corporate bond market. For that, we apply the methodologies that have been used by Bennani et al. (2018a) for testing ESG screening in active and passive management.
n particular, we consider the sorted portfolio approach of Fama and French (1992), and the index optimization method that consists in minimizing the tracking risk with
respect to the benchmark while controlling for the ESG excess score. Moreover, we test how ESG has impacted the cost of corporate debt. Three investment universes are
analyzed: euro-denominated investment grade bonds, dollar-denominated investment grade bonds, and high-yield bonds. Results differ from one universe to another. In
particular, we observe that ESG has had a more positive impact on EUR IG bonds in recent years than on the USD IG and HY investment universes. Nevertheless, we observe
a common trend that ESG is increasingly integrated into the pricing of corporate bonds and is a concern when building an investment portfolio. Moreover, we also show
that ESG does not only affect the demand side, but is also a significant factor when it comes to understanding the supply side.
Keywords
SRI, ESG investing, environmental, social, governance, asset pricing, active management, bond picking, passive management, credit rating, yield spread, cost of debt.
- Download the working paper
- Download the discussion paper
- Download the report at Amundi Research Center
- ESG Investing in Recent Years: New Insights from Old Challenges
Authors
A. Drei, T. Le Guenedal, F. Lepetit, V. Mortier, T. Roncalli and T. Sekine
Date
December 2019
Abstract
This research is an update of the study that we published last year (Bennani et al., 2018)
and that explored the impact of ESG investing on asset pricing in the stock market.
It extends the original period 2010-2017 by adding eighteen months from January 2018 to June 2019.
These new results confirm the previous results as we reach the same essential conclusions once again.
ESG investing tended to penalize both passive and active ESG investors between 2010 and 2013.
Contrastingly, ESG investing was a source of outperformance from 2014 to 2019 in Europe and North America.
Moreover, ESG can be considered as a risk factor in the Eurozone, while it continues to be an alpha strategy in North America.
However, the last 18 months exhibit new interesting patterns. First, we observe a transatlantic divide
since the results for North America and the Eurozone are different for the recent period.
Second, we document a partial ordering between ESG ratings and performance that can be explained by a
shift from a static to a dynamic approach to ESG investing. Third, we note some
discrepancies between active and passive management.
Fourth, the social pillar seems to have gained traction these last years, and is no longer the laggard pillar.
Fifth, factor investing and ESG investing are more and more connected.
In what follows, we develop and explain these five key findings.
Keywords
ESG, environmental, social, governance, asset pricing, active management, passive management, factor investing.
- Download the PDF file
- Download the discussion paper at Amundi Research Center
- A Note on Portfolio Optimization with Quadratic Transaction Costs
Authors
P. Chen, E. Lezmi, T. Roncalli and J. Xu
Date
November 2019
Abstract
In this short note, we consider mean-variance optimized portfolios with
transaction costs. We show that introducing quadratic transaction costs makes
the optimization problem more difficult than using linear transaction costs.
The reason lies in the specification of the budget constraint, which is no
longer linear. We provide numerical algorithms for solving this issue and
illustrate how transaction costs may considerably impact the expected returns of
optimized portfolios.
Keywords
Portfolio allocation, mean-variance optimization, transaction cost, quadratic programming, alternating direction method of multipliers.
- Download the PDF file
- Machine Learning Optimization Algorithms & Portfolio Allocation
Authors
S. Perrin and T. Roncalli
Date
July 2019
Abstract
Portfolio optimization emerged with the seminal paper of Markowitz (1952).
The original mean-variance framework is appealing because it is very
efficient from a computational point of view. However, it also has one
well-established failing since it can lead to portfolios that are not optimal
from a financial point of view (Michaud, 1989). Nevertheless, very few models
have succeeded in providing a real alternative solution to the Markowitz model.
The main reason lies in the fact that most academic portfolio optimization
models are intractable in real life although they present solid
theoretical properties. By intractable we mean that they can be implemented
for an investment universe with a small number of assets using a lot of
computational resources and skills, but they are unable to manage a universe
with dozens or hundreds of assets. However, the emergence and the
rapid development of robo-advisors means that we need to rethink portfolio optimization
and go beyond the traditional mean-variance optimization approach.
Another industry and branch of science has faced similar issues concerning
large-scale optimization problems. Machine learning and applied statistics
have long been associated with linear and logistic regression models. Again,
the reason was the inability of optimization algorithms to solve
high-dimensional industrial problems. Nevertheless, the end of the 1990s
marked an important turning point with the development and the rediscovery of
several methods that have since produced impressive results. The goal of this
paper is to show how portfolio allocation can benefit from the development of
these large-scale optimization algorithms. Not all of these algorithms are
useful in our case, but four of them are essential when solving complex
portfolio optimization problems. These four algorithms are the coordinate
descent, the alternating direction method of multipliers, the proximal
gradient method and the Dykstra's algorithm. This paper reviews them and
shows how they can be implemented in portfolio allocation.
Keywords
Portfolio allocation, mean-variance optimization, risk budgeting optimization, quadratic programming,
coordinate descent, alternating direction method of multipliers, proximal gradient method, Dykstra's algorithm.
- Download the PDF file
- Factor Investing in Currency Markets: Does it Make Sense?
Authors
E. Baku, R. Fortes, K. Hervé, E. Lezmi, H. Malongo, T. Roncalli and J. Xu
Date
June 2019
Abstract
The concept of factor investing emerged at the end of the 2000s and has
completely changed the landscape of equity investing. Today, institutional
investors structure their strategic asset allocation around five risk
factors: size, value, low beta, momentum and quality. This approach has been
extended to multi-asset portfolios and is known as the alternative risk
premia model. This framework recognizes that the construction of diversified
portfolios cannot only be reduced to the allocation policy between asset
classes, such as stocks and bonds. Indeed, diversification is multifaceted
and must also consider alternative risk factors. More recently, factor
investing has gained popularity in the fixed income universe, even though the
use of risk factors is an old topic for modeling the yield curve and pricing
interest rate contingent claims. Factor investing is now implemented for
managing portfolios of corporate bonds or emerging bonds.
In this paper, we focus on currency markets. The dynamics of foreign exchange
rates are generally explained by several theoretical economic models that are
commonly presented as competing approaches. In our opinion, they are more
complementary and they can be the backbone of a Fama-French-Carhart risk
factor model for currencies. In particular, we show that these risk factors
may explain a significant part of time-series and cross-section returns in
foreign exchange markets. Therefore, this result helps us to better
understand the management of forex portfolios. To illustrate this point, we
provide some applications concerning basket hedging, overlay management and
the construction of alpha strategies.
Keywords
Foreign exchange rates, factor investing, carry, value, momentum, reversal, interest rate parity,
purchasing power parity, BEER, FEER, NATREX, cross-section analysis, time-series analysis, risk premium,
basket hedging, overlay management, risk aggregation, alpha strategy.
- Download the PDF file
- The Alpha and Beta of ESG Investing
Author
T. Roncalli
Date
April 2019
Conference slides
- World Bank Group, Treasury IBRD & IDA, May 28, 2019 (Washington)
- RIA Conference 2019, April 24 & 25, 2019 (Montréal) — Summary here
- Third Workshop, ESSEC-Amundi Research Chair, May 21, 2019 (Paris)
- 12th Financial Risks International Forum, Institut Louis Bachelier, March 18 & 19, 2019 (Paris)
- Download the PDF file
- How Machine Learning Can Improve Portfolio Allocation of Robo-Advisors
Author
T. Roncalli
Date
May 2019 (new version of the WBG slides)
Conference slides
- Download the PDF file
- Financial Applications of Gaussian Processes and Bayesian Optimization
Authors
J. Gonzalvez, E. Lezmi, T. Roncalli and J. Xu
Date
February 2019
Abstract
In the last five years, the financial industry has been impacted by the emergence of digitalization and
machine learning. In this article, we explore two methods that have undergone rapid development in
recent years: Gaussian processes and Bayesian optimization. Gaussian processes can be seen as a
generalization of Gaussian random vectors and are associated with the development of kernel methods.
Bayesian optimization is an approach for performing derivative-free global optimization in a
small dimension, and uses Gaussian processes to locate the global maximum of a black-box function.
The first part of the article reviews these two tools and shows how they are connected.
In particular, we focus on the Gaussian process regression, which is the core of Bayesian
machine learning, and the issue of hyperparameter selection. The second part is
dedicated to two financial applications. We first consider the modeling of the term
structure of interest rates. More precisely, we test the fitting method and compare the GP
prediction and the random walk model. The second application is the construction of trend-following
strategies, in particular the online estimation of trend and covariance windows.
Keywords
Gaussian process, Bayesian optimization, machine learning, kernel function, hyperparameter selection,
regularization, time-series prediction, asset allocation, portfolio optimization, trend-following strategy,
moving-average estimator, ADMM, Cholesky trick.
- Download the PDF file
- Portfolio Allocation: From Quadratic Programming to Machine Learning Optimization Algorithms
Author
T. Roncalli
Date
February 2019
Abstract
In this presentation, we show how the development of the portfolio optimization has been related
to the development of quadratic programming (QP) algorithms.
We make a parallel between portfolio allocation problems and some statistical modeling
problems (least squares, lasso and svm). Since the nineties, the emergence of machine learning has changed
the landscape of optimization. New algorithms have emerged, for example CCD or ADMM.
After a review of these techniques, we show how they can be used to solve new problems in asset allocation.
We first consider mean-variance optimized portfolios and illustrate how they can be regularized
when they are used in robo-advisors. Then, we apply CCD and ADMM algorithms to risk budgeting portfolios.
Keywords
Quadratic programming, least squares, lasso regression, support vector machines,
gradient descent, CCD, ADMM, MVO portfolios, risk budgeting.
- Download the PDF file
- Constrained Risk Budgeting Portfolios: Theory, Algorithms, Applications & Puzzles
Authors
J-C. Richard and T. Roncalli
Date
February 2019
Abstract
This article develops the theory of risk budgeting portfolios, when we would
like to impose weight constraints. It appears that the mathematical problem
is more complex than the traditional risk budgeting problem. The formulation
of the optimization program is notably critical to determine the right risk
budgeting portfolio. We also show that numerical solutions can be found using
methods that are used in large-scale machine learning problems. Indeed, we
develop an algorithm that mixes the method of cyclical coordinate descent
(CCD), alternating direction method of multipliers (ADMM), proximal operators
and Dykstra's algorithm. This theoretical body is then applied to some
investment problems. In particular, we show how to control dynamically the
turnover of a risk parity portfolio and how to build smart beta portfolios
based on the ERC approach by improving the liquidity of the portfolio or
reducing the small cap bias. Finally, we highlight the importance of the
homogeneity property of risk measures and discuss the related scaling puzzle.
Keywords
Risk budgeting, large-scale optimization, Lagrange function, cyclical coordinate descent (CCD),
alternating direction method of multipliers (ADMM), proximal operator, Dykstra's algorithm, turnover,
liquidity, risk parity, smart beta portfolio.
- Download the PDF file
- How ESG Investing Has Impacted the Asset Pricing in the Equity Market
Authors
L. Bennani, T. Le Guenedal, F. Lepetit, L. Ly, V. Mortier, T. Roncalli and T. Sekine
Date
November 2018
Abstract
ESG investing has gained considerable traction over the past few years and, alongside smart beta, factor investing and
alternative risk premia, is one of the current hot topics for the asset management industry. Nevertheless,
even though large institutions such as insurance companies, pension funds and sovereign wealth funds have
invested significantly in ESG strategies over recent years and we are observing a substantial and increasing
interest from other investors such as wealth management or retail investors, the question of performance
remains a controversial issue and a puzzle for the financial community. Indeed, academic findings have been
mixed and have revealed a U-shape pricing of stocks in the equity market, meaning that both best-in-class
and worst-in-class ESG stocks have been rewarded by the equity market in the past.
In this research, we analyze the relationship between ESG and performance in the recent years (2010 – 2017)
since ESG was more an anecdotal and explanatory investment idea before the Global Financial Crisis. For that,
we consider different regions (North America, Europe, Japan, World) and different investment styles (passive
management, active management and factor investing). We show that ESG investing has been rewarded since 2014,
but not before. Across the three ESG pillars, the Environment factor in North America and the Governance factor
in the Eurozone performed the strongest. Overall, the study reveals that ESG does not impact all stocks, but tends
to impact best-in-class and worst-in-class assets.
Contrary to common beliefs, we also observe that ESG had little impact on volatility and drawdown management
during the 2010-2017 period. In the case of passive management, implementing an ESG strategy helps to
improve the information ratio if the investor accepts to take a tracking error risk. Finally,
we show that ESG investing is related to factor investing. In particular, we conclude that ESG investing
remains an alpha strategy in North America, whereas it has become a beta strategy in the Eurozone.
Keywords
SRI, ESG investing, environmental, social, governance, asset pricing, active management, stock picking, passive
management, optimized benchmarking portfolio, factor investing, factor picking,impact investing.
- Download the PDF file
- Download the full working paper at Amundi Research Center
- Nonnegative Matrix Factorization and Financial Applications
Authors
Z. Cazalet and T. Roncalli
Date
May 2011 (made publicly available in November 2018)
Abstract
Nonnegative matrix factorization (NMF) is a recent tool to analyse multivariate
data. It can be compared to other decomposition methods like principal component
analysis (PCA) or independent component analysis (ICA). However, NMF differs from
them because it requires and imposes the nonnegativity of matrices. In this paper, we
use this special feature in order to identify patterns in stock market data. Indeed, we
may use NMF to estimate common factors from the dynamics of stock prices. In this
perspective, we compare NMF and clustering algorithms to identify endogenous equity
sectors.
Keywords
Nonnegative matrix factorization, principal component analysis, clustering, sparsity.
- Download the PDF file
- Robust Asset Allocation for Robo-Advisors
Authors
T. Bourgeron, E. Lezmi and T. Roncalli
Date
September 2018
Abstract
In the last few years, the financial advisory industry has been
impacted by the emergence of digitalization and robo-advisors. This
phenomenon affects major financial services, including wealth
management, employee savings plans, asset managers, private banks,
pension funds, banking services, etc. Since the robo-advisory model
is in its early stages, we estimate that robo-advisors will
help to manage around \$1 trillion of assets in 2020 (OECD, 2017).
And this trend is not going to stop with future generations, who
will live in a technology-driven and social media-based world.
In the investment industry, robo-advisors face different challenges:
client profiling, customization, asset pooling, liability
constraints, etc. In its primary sense, robo-advisory is a term for
defining automated portfolio management. This includes automated
trading and rebalancing, but also automated portfolio allocation.
And this last issue is certainly the most important challenge for
robo-advisory over the next five years. Today, in many robo-advisors,
asset allocation is rather human-based and very far from being
computer-based. The reason is that portfolio optimization is a very
difficult task, and can lead to optimized mathematical solutions
that are not optimal from a financial point of view (Michaud, 1989).
The big challenge for robo-advisors is therefore to be able to optimize
and rebalance hundreds of optimal portfolios without human
intervention.
In this paper, we show that the mean-variance optimization approach
is mainly driven by arbitrage factors that are related to the
concept of hedging portfolios. This is why regularization and
sparsity are necessary to define robust asset allocation. However,
this mathematical framework is more complex and requires
understanding how norm penalties impacts portfolio optimization. From a
numerical point of view, it also requires the implementation of
non-traditional algorithms based on ADMM methods and proximal operators.
Keywords
Robo-advisor, asset allocation, active management, portfolio optimization, Black-Litterman model, spectral
filtering, machine learning, Tikhonov regularization, mixed penalty, ridge regression, lasso method, sparsity, ADMM algorithm, proximal operator.
- Download the PDF file
- Portfolio Allocation with Skewness Risk: A Practical Guide
Authors
E. Lezmi, H. Malongo, T. Roncalli and R. Sobotka
Date
June 2018
Abstract
In this article, we show how to take into account skewness risk in portfolio
allocation. Until recently, this issue has been seen as a purely statistical
problem, since skewness corresponds to the third statistical moment of a
probability distribution. However, in finance, the concept of skewness is
more related to extreme events that produce portfolio losses. More precisely,
the skewness measures the outcome resulting from bad times and adverse
scenarios in financial markets. Based on this interpretation of the skewness
risk, we focus on two approaches that are closely connected. The first one is
based on the Gaussian mixture model with two regimes: a normal regime and a
turbulent regime. The second approach directly incorporates a stress scenario using
jump-diffusion modeling. This second approach can be seen as a special case
of the first approach. However, it has the advantage of being clearer and
more in line with the experience of professionals in financial markets:
skewness is due to negative jumps in asset prices. After presenting the
mathematical framework, we analyze an investment portfolio that mixes risk
premia, more specifically risk parity, momentum and carry strategies. We show
that traditional portfolio management based on the volatility risk measure is
biased and corresponds to a short-sighted approach to bad times. We then
propose to replace the volatility risk measure by a skewness risk measure,
which is calculated as an expected shortfall that incorporates a stress
scenario. We conclude that constant-mix portfolios may be better adapted than
actively managed portfolios, when the investment universe is composed of
negatively skewed financial assets.
Keywords
Skewness, volatility, expected shortfall, stress scenario, market regime, drawdown, risk budgeting, equal risk contribution,
Gaussian mixture model, jump-diffusion process
- Download the PDF file
- The Active Versus Passive Management Debate
Author
T. Roncalli
Date
April 2018
Conference slides
- Download the PDF file
- Keep Up the Momentum
Authors
T. Roncalli
Date
December 2017
Abstract
The momentum risk premium is one of the most important alternative risk premia alongside the carry risk premium.
However, it appears that it is not always well understood. For example, is it an alpha or a beta exposure? Is it a
skewness risk premium or a market anomaly? Does it pursue a performance objective or a hedging objective?
What are the differences between time-series and cross-section momentum? What are the main drivers of
momentum returns? What does it mean when we say that it is a convex and not a concave strategy?
Why is the momentum risk premium a diversifying engine, and not an absolute return strategy?
The goal of this paper is to provide specific and relevant answers to all these questions.
The answers can already be found in the technical paper "Understanding the Momentum Risk Premium"
published recently by Jusselin et al. (2017). However, the underlying mathematics can be daunting to readers.
Therefore, this discussion paper presents the key messages and the associated financial insights behind these results.
Among the main findings, one result is of the most importance. To trend is to diversify in bad times. In good times,
trend-following strategies offer no significant diversification power. Indeed, they are beta strategies. This is not
a problem, since investors do not need to be diversified at all times. In particular, they do not need diversification in good
times, because they do not want that the positive returns generated by some assets to be canceled out by negative returns on
other assets. This is why diversification may destroy portfolio performance in good times.
Investors only need diversification in bad economic times and stressed markets.
This diversification asymmetry is essential when investing in beta strategies like alternative risk premia.
On the contrary, this diversification asymmetry is irrelevant when investing in absolute return strategies.
However, we know that generating performance with alpha strategies is much more difficult than generating
performance with beta strategies. Therefore, beta is beautiful, but convex beta is precious and scarce.
Among risk premia, momentum is one of the few strategies to offer this diversification asymmetry.
This is why investing in momentum is a decision of portfolio construction, and not a search for alpha.
Keywords
Momentum, Trend-Following, Diversification, Payoff
- Download the PDF file
- Understanding the Momentum Risk Premium: An In-Depth Journey Through Trend-Following Strategies
Authors
P. Jusselin, E. Lezmi, H. Malongo, C. Masselin, T. Roncalli and T-L. Dao
Date
September 2017
Abstract
Momentum risk premium is one of the most important alternative risk premia.
Since it is considered a market anomaly, it is not always well understood.
Many publications on this topic are therefore based on backtesting and
empirical results. However, some academic studies have developed a
theoretical framework that allows us to understand the behavior of such
strategies. In this paper, we extend the model of Bruder and Gaussel (2011)
to the multivariate case. We can find the main properties found in academic
literature, and obtain new theoretical findings on the momentum risk premium.
In particular, we revisit the payoff of trend-following strategies, and
analyze the impact of the asset universe on the risk/return profile. We also
compare empirical stylized facts with the theoretical results obtained from
our model. Finally, we study the hedging properties of trend-following
strategies.
Keywords
Momentum risk premium, trend-following strategy, cross-section momentum, time-series momentum, alternative risk premium, market anomaly, diversification, correlation,
payoff, trading impact, hedging, skewness, Gaussian quadratic forms, Kalman filter, EWMA
- Download the PDF file
- The Quest for Diversification: Why Does It Make Sense to Mix Risk Parity, Carry and Momentum Risk Premia?
Authors
A. Burgues, E. Knockaert, E. Lezmi, H. Malongo, T. Roncalli and R. Sobotka
Date
September 2017
Abstract
Diversification should be the first objective of any large institutions because managing risk is a
key source of long-term performance. However, building a diversified portfolio cannot only be reduced to the
allocation policy between asset classes, such as stocks and bonds. Diversification can be improved by using alternative risk premia,
in particular carry and momentum. Mixing traditional and alternative risk premia will then become the standard of diversified management in the near future.
The traditional diversification approach consists in optimising the volatility of a portfolio.
This approach is inadequate for managing diversification because it focuses on arbitrage risk
factors and not on common risk factors. When considering traditional risk premia, the standard approach today is to use the risk parity model.
With an enlarged investment universe of traditional and alternative risk premia, the "correlation diversification approach" must be replaced by
the "payoff diversification approach" because the relationships between assets are non-linear. Indeed, correlation models
are not able to take into account the convexity characteristics of these assets, which is not the case of payoff models.
The payoff approach implies mixing concave and convex strategies in order to diversify the skewness risk of diversified portfolios.
This is why it makes sense to allocate between traditional, carry and momentum risk premia. Nevertheless, this approach recognises that
diversification cannot be obtained in every state of nature, and must mainly focus on the adverse states instead of the positive ones.
In this case, budgeting the skewness risk is the right way to manage diversification and reduce the residual tail risk.
Keywords
Diversification, correlation, payoff, alternative risk premium, skewness risk, carry, momentum, multi-asset allocation
- Download the Discussion paper
- Alternative Risk Premia: What Do We Know?
Author
T. Roncalli
Date
February 2017
Abstract
The concept of alternative risk premia is an extension of the factor
investing approach. Factor investing consists in building long-only equity
portfolios, which are directly exposed to common risk factors like size,
value or momentum. Alternative risk premia designate non-traditional risk
premia other than a long exposure to equities and bonds. They may involve
equities, rates, credit, currencies or commodities and correspond to
long/short portfolios. However, contrary to traditional risk premia, it is
more difficult to define alternative risk premia and which risk premia really
matter. In fact, the term alternative risk
premia encompasses two different types of systematic risk
factor: skewness risk premia and market anomalies. For example, the most
frequent alternative risk premia are carry and momentum, which are
respectively a skewness risk premium and a market anomaly. Because the
returns of alternative risk premia exhibit heterogeneous patterns in terms of
statistical properties, option profile and drawdown, asset allocation is more
complex than with traditional risk premia. In this context, risk
diversification cannot be reduced to volatility diversification and skewness
risk becomes a key component of portfolio optimization. Understanding these
different concepts and how they interconnect is essential for improving
multi-asset allocation.
Keywords
Alternative risk premium, factor investing, skewness risk, market anomalies, systematic risk factor,
diversification, carry, momentum, value, low beta, short volatility,
payoff function, alternative beta, hedge funds, multi-asset allocation
- Download the PDF file
- Download the viewpoint
- Portfolio Diversification & Asset Allocation: What Does It Mean?
Author
T. Roncalli
Date
November 2016
Conference slides
- University of Bordeaux, Advances in Quantitative Asset Management, November 25, 2016 (Bordeaux)
- AFG, Agoras de la Gestion Financière, November 8, 2016 (Paris)
- Download the PDF file
- Size, Interconnectedness and the Regulation of Systemic Risk
Authors
A. Nikeghbali and T. Roncalli
Date
November 2016
Conference slides
- Download the PDF file
- New Trends in Asset Management
Author
T. Roncalli
Date
October 2016
Conference slides
- Download the PDF file
- Portfolio Allocation with Skewness Risk
Authors
B. Bruder, N. Kostyuchyk and T. Roncalli
Date
October 2016
Conference slides
- Download the PDF file
- Risk Parity Portfolios with Skewness Risk: An Application to Factor Investing and Alternative Risk Premia
Authors
B. Bruder, N. Kostyuchyk and T. Roncalli
Date
September 2016
Abstract
This article develops a model that takes into account skewness risk in risk parity
portfolios. In this framework, asset returns are viewed as stochastic processes with
jumps or random variables generated by a Gaussian mixture distribution. This dual
representation allows us to show that skewness and jump risks are equivalent. As the
mixture representation is simple, we obtain analytical formulas for computing asset
risk contributions of a given portfolio. Therefore, we define risk budgeting portfolios
and derive existence and uniqueness conditions. We then apply our model to the
equity/bond/volatility asset mix policy. When assets exhibit jump risks like the short
volatility strategy, we show that skewness-based risk parity portfolios produce better
allocation than volatility-based risk parity portfolios. Finally, we illustrate how this
model is suitable to manage the skewness risk of long-only equity factor portfolios and
to allocate between alternative risk premia.
Keywords
Risk parity, equal risk contribution, expected shortfall, skewness, jump difusion,
Gaussian mixture model, EM algorithm, filtering theory, factor investing, alternative
risk premia, short volatility strategy, diversification, skewness hedging, CTA strategy
- Download the PDF file
- Alternative Risk Premia: What Do We know?
Authors
T. Roncalli and B. Zheng
Date
May 2016
Conference slides
- Download the PDF file
- A Primer on Alternative Risk Premia
Authors
R. Hamdan, F. Pavlowsky, T. Roncalli and B. Zheng
Date
April 2016
Abstract
The concept of alternative risk premia can be viewed as an extension of the factor investing approach.
Factor investing is a term that is generally dedicated to long-only equity risk factors.
A typical example is the value equity strategy. Alternative risk premia designate non-traditional
risk premia other than long exposure to equities and bonds. They may concern equities, rates, credit,
currencies or commodities and correspond to long/short portfolios. For instance, the value strategy can
be extended to credit, currencies and commodities. This paper provides an overview of the different
alternative risk premia to be found in the academic and professional spheres. Using a database of
commercial indices, we estimate the generic cumulative returns of 59 alternative risk premia in order
to analyze their risk, diversification power and payoff function. From this, it is clear that the
term "alternative risk premia" encompasses two different types of risk factor: skewness risk premia
and market anomalies. We then reconsider portfolio allocation in light of this framework. Indeed,
we show that skewness aggregation is considerably more complex than volatility aggregation, and we illustrate
that the volatility risk measure is less appropriate and pertinent when managing a portfolio with these risk premia.
The development of alternative risk premia shall also affect the risk/return analysis of non-linear strategies,
e.g. hedge fund strategies. In particular, using alternative risk factors instead of traditional risk factors
leads to an extension of the alternative beta framework. Therefore, we apply the previously estimated risk premia
to a universe of hedge fund indices. To that end, we develop a model selection based on the lasso regression to
identify the most pertinent risk premia for each hedge fund strategy. It appears that many traditional risk
factors, with the exception of long equity and credit exposure on developed markets, vanish when we include alternative risk premia.
Keywords
Alternative Risk Premium, Factor Investing, Skewness Risk Premium, Market Anomaly,
Risk Factor, Carry, Event, Growth, Liquidity, Low Beta, Low Volatility, Momentum, Quality,
Reversal, Value, Short Volatility, Size, Skewness, Drawdown, Option Profile, Alternative Beta, Hedge Funds
- Download the PDF file
- Asset Management, Asset Managers & Systemic Risk
Authors
T. Roncalli and G. Weisang
Date
December 2015
Conference slides
- Download the PDF file
- Smart Beta: Managing Diversification of Minimum Variance Portfolios
Authors
J-C. Richard and T. Roncalli
Date
November 2015
Conference slides
- Download the PDF file
- Asset Management and Systemic Risk
Authors
T. Roncalli and G. Weisang
Date
May 2015
Abstract
As regulators around the world progress towards prudential reforms of the global financial
system to address the issue of systemic risk, the sweeping scope of the task touches
areas and actors of the financial markets that have typically not been seen as
systemically important before. The idea that the asset management industry can
contribute to systemic risk is new, and warrants detailed examination in order
to shape adequate policies. In this paper, after reviewing the definition of systemic
risk and how systemically important banks and insurance are designated, we review
the activities of the asset management industry and the ways they can contribute to
the transmission of systemic risk. We then look in detail at the March 2015 proposal by
FSB-IOSCO for an assessment methodology for the identification of non-bank non-insurance
systemically important financial institutions. We compare and discuss with empirical data
how the methodology fairs against what the literature and the aftermath of the 2007-2008
crisis reveals about the role of the asset management industry in contributing to systemic
risk. We find that the current proposal in part fails to adequately identify natural
candidates for the systemically important designation and perhaps confuses large
institutions with systemically strategic institutions giving wealth loss too much
importance over the potential for real economic disruption and market dislocation.
Finally, we call for a more robust and risk-sensitive approach to identifying
systemically important financial institutions.
Keywords
Systemic risk, SIFI, asset managers,
asset owners, interconnectedness, liquidity risk, reputational risk,
business risk, counterparty credit risk, market risk, liquidation
period, index funds, money market funds, exchange traded funds, hedge funds.
- Download the PDF file
- Smart Beta: Managing Diversification of Minimum Variance Portfolios
Authors
J-C. Richard and T. Roncalli
Date
March 2015
Abstract
In this article, we consider a new framework to understand risk-based
portfolios (GMV, EW, ERC and MDP). This framework is similar to the constrained
minimum variance model of Jurczenko et al. (2013), but with another definition of
the diversification constraint. The corresponding optimization problem can then be
solved using the CCD algorithm. This allows us to extend the results of Cazalet
et al. (2014) and to better understand the trade-off relationships between volatility
reduction, tracking error and risk diversification. In particular, we show that
the smart beta portfolios differ because they implicitly target different levels
of volatility reduction. We also develop new smart beta strategies by managing the
level of volatility reduction and show that they present appealing properties
compared with the traditional risk-based portfolios.
Keywords
Smart beta, risk-based allocation, minimum variance portfolio, GMV,
EW, ERC, MDP, portfolio optimization, CCD algorithm.
- Download the PDF file
- Factor Investing & Equity Portfolio Construction
Author
T. Roncalli
Date
January 2015
Conference slides
- Download the PDF file
- Facts and Fantasies About Factor Investing
Authors
Z. Cazalet and T. Roncalli
Date
October 2014
Abstract
The capital asset pricing model (CAPM) developed by Sharpe (1964) is
the starting point for the arbitrage pricing theory (APT). It uses a
single risk factor to model the risk premium of an asset class.
However, the CAPM has been the subject of important research, which
has highlighted numerous empirical contradictions. Based on the APT
theory proposed by Ross (1976), Fama and French (1992) and Carhart
(1997) introduce other common factors models to capture new risk
premia. For instance, they consequently define equity risk factors,
such as market, value, size and momentum. In recent years, a new
framework based on this literature has emerged to define strategic
asset allocation. Similarly, index providers and asset managers now
offer the opportunity to invest in these risk factors through factor
indexes and mutual funds. These two approaches led to a new paradigm
called `factor investing' (Ang, 2014). Factor investing seems to
solve some of the portfolio management issues that emerged in the
past, in particular for long-term investors. However, some questions
arise, especially with the number of risk factors growing over the
last few years (Cochrane, 2011). What is a risk factor? Are all risk
factors well-rewarded? What is their level of stability and
robustness? How should we allocate between them? The main purpose of
this paper is to understand and analyze the factor investing
approach in order to answer these questions.
Keywords
Factor investing, risk premium, CAPM,
risk factor model, anomaly, size, value, momentum, volatility,
idiosyncratic risk, liquidity, carry, quality, mutual funds, hedge
funds, alternative beta, strategic asset allocation.
- Download the PDF file
- Big Data in Asset Management
Author
T. Roncalli
Date
March 2014
Conference slides
- Download the PDF file
- Introducing Expected Returns into Risk Parity Portfolios: A New Framework for Asset Allocation
Author
T. Roncalli
Date
April 2014
Abstract
Risk parity is an allocation method used to build diversified
portfolios that does not rely on any assumptions of expected
returns, thus placing risk management at the heart of the strategy.
This explains why risk parity became a popular investment model
after the global financial crisis in 2008. However, risk parity has
also been criticized because it focuses on managing risk
concentration rather than portfolio performance, and is therefore
seen as being closer to passive management than active management.
In this article, we show how to introduce assumptions of expected
returns into risk parity portfolios. To do this, we consider a
generalized risk measure that takes into account both the portfolio
return and volatility. However, the trade-off between performance
and volatility contributions creates some difficulty, while the risk
budgeting problem must be clearly defined. After deriving the
theoretical properties of such risk budgeting portfolios, we apply
this new model to asset allocation. First, we consider long-term
investment policy and the determination of strategic asset
allocation. We then consider dynamic allocation and show how to
build risk parity funds that depend on expected returns.
Keywords
Risk parity, risk budgeting, expected
returns, ERC portfolio, value-at-risk, expected shortfall, active management, tactical asset allocation, strategic asset allocation.
- Download the PDF file
- The Risk Dimension of Asset Returns in Risk Parity Portfolios
Author
T. Roncalli
Date
April 2014
Conference slides
- Download the PDF file
- Improving the Efficiency of the European ETF Market: Implications for Regulators, Providers, Exchanges and Investors
Author
T. Roncalli
Date
February 2014
Conference slides
- Download the PDF file
- Measuring the Liquidity of ETFs: An Application to the European Market
Authors
T. Roncalli and B. Zheng
Date
February 2014
Abstract
The liquidity of exchange traded funds is of utmost importance for
regulators, investors and providers. However, the study of
liquidity is still in its infancy. In this work, we show some
stylised facts of liquidity statistics (daily/intraday spread,
trading volume, etc.). We also propose a new liquidity measure
combining these statistics. In this case, liquidity is a power
function of the spread where the parameters are determined by
actual trading volumes. We also study the relationship between the
liquidity of ETFs and the liquidity of the underlying index. We show
that they are correlated on a daily basis, but not in terms of intraday
frequency. We also define a measure of liquidity improvement
and apply it to the EURO STOXX 50 index.
Keywords
Exchange traded fund, liquidity, spread, trading volume, order book, liquidity improvement.
- Download the PDF file
- A Risk Parity Approach to Manage Risk Factors for Strategic Asset Allocation
Authors
T. Roncalli and G. Weisang
Date
October 2013
Conference slides
- Download the PDF file
- Risk Parity: A (New) Tool for Asset Management
Author
T. Roncalli
Date
October 2013
Conference slides
- Download the PDF file
- A Fast Algorithm for Computing High-dimensional Risk Parity Portfolios
Authors
T. Griveau-Billion, J-C. Richard and T. Roncalli
Date
September 2013
Abstract
In this paper we propose a cyclical coordinate descent (CCD) algorithm for solving
high dimensional risk parity problems. We show that this algorithm
converges and is very fast even with large covariance matrices (n > 500).
Comparison with existing algorithms also shows that it is one of the most
efficient algorithms.
Keywords
Risk parity, risk budgeting, ERC portfolio, cyclical coordinate descent algorithm, SQP algorithm,
Jacobi algorithm, Newton algorithm, Nesterov algorithm.
- Download the PDF file
- The Smart Beta Indexing Puzzle
Authors
Z. Cazalet, P. Grison and T. Roncalli
Date
July 2013
Abstract
In this article, we consider smart beta indexing, which is an
alternative to capitalization-weighted (CW) indexing. In
particular, we focus on risk-based (RB) indexing, the aim of which
is to capture the equity risk premium more effectively. To achieve this,
portfolios are built which are more diversified and less volatile than
CW portfolios. However, RB portfolios are less liquid than CW
portfolios by construction. Moreover, they also present two risks in
terms of passive management: tracking difference risk and tracking
error risk. Smart beta investors then have to a puzzle out
the trade-off between diversification, volatility,
liquidity and tracking error. This article examines the trade-off
relationships. It also defines the return components of smart beta indexes.
Keywords
Smart beta, risk-based indexing,
minimum variance portfolio, risk parity, equally weighted portfolio, equal
risk contribution portfolio, diversification, low beta anomaly, low volatility
anomaly, tracking error, liquidity.
- Download the PDF file
- Regularization of Portfolio Allocation
Authors
B. Bruder, N. Gaussel, J-C. Richard and T. Roncalli
Date
June 2013
Abstract
The mean-variance optimization (MVO) theory of Markowitz (1952) for
portfolio selection is one of the most important methods used in
quantitative finance. This portfolio allocation needs two input
parameters, the vector of expected returns and the covariance matrix
of asset returns. This process leads to estimation errors, which may
have a large impact on portfolio weights. In this paper we review
different methods which aim to stabilize the mean-variance
allocation. In particular, we consider recent results from machine
learning theory to obtain more robust allocation.
Keywords
Portfolio optimization, active
management, estimation error, shrinkage estimator, resampling
methods, eigendecomposition, norm constraints, Lasso regression,
ridge regression, information matrix, hedging portfolio, sparsity.
- Download the PDF file
- Measuring Efficiency of Exchange Traded Funds
Author
T. Roncalli
Date
February 2013
Conference slides
- Download the PDF file
- Measuring Performance of Exchange Traded Funds
Authors
M. Hassine and T. Roncalli
Date
February 2013
Abstract
Fund selection is an important issue for investors. This topic has spawned abundant academic
literature. Nonetheless, most of the time, these works concern only active management,
whereas many investors, such as institutional investors, prefer to invest in index funds.
The tools developed in the case of active management are also not suitable for evaluating the
performance of these index funds. This explains why information ratios are usually used
to compare the performance of passive funds. However, we show that this measure is not pertinent,
especially when the tracking error volatility of the index fund is small. The objective of
an exchange traded fund (ETF) is precisely to offer an investment vehicle that presents
a very low tracking error compared to its benchmark. In this paper, we propose a performance
measure based on the value-at-risk framework, which is perfectly adapted to passive management and ETFs.
Depending on three parameters (performance difference, tracking error volatility and liquidity spread),
this efficiency measure is easy to compute and may help investors in their fund selection process.
We provide some examples, and show how liquidity is more of an issue for institutional investors than retail investors.
Keywords
Passive management, index fund, ETF, information ratio, tracking error, liquidity, spread, value-at-risk.
- Download the PDF file
- Beyond Risk Parity: Using Non-Gaussian Risk Measures and Risk Factors
Authors
T. Roncalli and G. Weisang
Date
November 2012
Conference slides
- Download the PDF file
- Risk Parity Portfolios with Risk Factors
Authors
T. Roncalli and G. Weisang
Date
September 2012
Abstract
Portfolio construction and risk budgeting are the focus of many studies by academics
and practitioners. In particular, diversification has spawn much interest and has
been defined very differently. In this paper, we analyze a method to achieve portfolio
diversification based on the decomposition of the portfolio's risk into risk factor contributions.
First, we expose the relationship between risk factor and asset contributions.
Secondly, we formulate the diversification problem in terms of risk factors as an optimization
program. Finally, we illustrate our methodology with some real life examples
and backtests, which are: budgeting the risk of Fama-French equity factors, maximizing
the diversification of an hedge fund portfolio and building a strategic asset allocation
based on economic factors.
Keywords
Risk parity, risk budgeting, factor model, ERC portfolio, diversification, concentration, Fama-French model, hedge fund allocation, strategic asset allocation.
- Download the PDF file
- How to Design Target-Date Funds?
Authors
B. Bruder, L. Culerier and T. Roncalli
Date
September 2012
Abstract
Several years ago, the concept of target-date funds emerged to
complement traditional balanced funds in defined-contribution
pension plans. The main idea is to delegate the dynamic allocation
with respect to the retirement date of individuals to the portfolio
manager. Owing to its long-term horizon, a target-date fund is
unique and cannot be compared to a mutual fund. Moreover, the
objective of the individual is to contribute throughout their
working life by investing a part of their income in order to
maximise their pension benefits. The main purpose of this article is
to analyse and understand dynamic allocation in a target-date fund
framework. We show that the optimal exposure in the risky portfolio
varies over time and is very sensitive to the parameters of both the
market and the investor's. We then deduce some practical guidelines
to better design target-date funds for the asset management industry.
Keywords
Target-date fund, lifecycle fund, retirement system, dynamic asset allocation, stochastic optimal control, market portfolio, risk aversion, stock/bond asset mix policy.
- Download the PDF file
- It is Time for Multi-Indexing
Author
T. Roncalli
Date
June 2012
Conference slides
- Download the PDF file
- From Portfolio Optimization to Risk Parity
Author
T. Roncalli
Date
June 2012
Conference slides
- Download the PDF file
- Managing Sovereign Risk Through a Risk Budgeting Approach
Author
T. Roncalli
Date
June 2012
Conference slides
- Download the PDF file
- On the Market Portfolio for Multi-Asset Classes
Authors
R. Louis and T. Roncalli
Date
April 2012
Abstract
The influence of the CAPM theory on the financial theory of investment
has increased with the development of passive management. Today, equity
or fixed-income market portfolios can easily be defined using equity and
fixed-income indexes. These indexes also play an important role in active
management as they serve as benchmarks. The case of multi-asset classes is
more complex. Indeed, indexes taking into account both stocks and bonds do
not exist today. However, most investors need such references as their
principal problem is to define their stock/bond asset mix policy. It is
especially true for institutional investors like pension funds and
long-term investors. In this article, we show how to compute the market
portfolio of equity and fixed-income instruments. We then analyse the
specificity of such a portfolio according to countries or regions and
how this portfolio has changed over the last thirty years. The dynamics
of the market portfolio also gives useful information about the evolution
of ex-ante risk premia of stocks and bonds. Finally, we illustrate how
the market portfolio could be used to benchmark diversified funds and
to characterize the bets of long-term investment policy.
Keywords
Market portfolio, benchmark, multi-assets allocation, multi-indexation, active management, risk premium, strategic asset allocation, long-term investment policy.
- Download the PDF file
- Managing Sovereign Credit Risk in Bond Portfolios using the Risk Budgeting Approach
Author
T. Roncalli
Date
March 2012
Conference slides
- Download the PDF file (Paris version)
- Download the PDF file (Nantes version)
- Managing Risk Exposures using the Risk Budgeting Approach
Authors
B. Bruder and T. Roncalli
Date
January 2012
Abstract
The ongoing economic crisis has profoundly changed the industry of
the asset management, by putting risk management at the heart of
most investment processes. This new risk-based investment style does
not rely on returns forecasts and is therefore assumed to be more
robust. In 2011, it has particularly encountered a great success
with the achievement of minimum variance, ERC and risk parity
strategies in portfolios of several large institutional investors.
These portfolio constructions are special cases of a more general
class of allocation models, known as the risk budgeting approach. In
a risk budgeting portfolio, the risk contribution from each
component is equal to the budget of risk defined by the portfolio
manager. Unfortunately, even if risk budgeting techniques are widely
used by market practitioners, they are few results about the
behavior of such portfolios in the academic literature. In this
paper, we derive the theoretical properties of the risk budgeting
portfolio and show that its volatility is located between those of
minimum variance and weight budgeting portfolios. We also discuss
the existence, uniqueness and optimality of such a portfolio. In a
second part of the paper, we propose several applications of risk
budgeting techniques for risk-based allocation, like risk parity
funds and strategic asset allocation, and equity and bond alternative indexations.
Keywords
Risk budgeting, risk management, risk-based allocation, equal risk contribution, diversification,
concentration, risk parity, alternative indexation, strategic asset allocation.
- Download the PDF file
- Portfolio Optimization versus Risk-Budgeting Allocation
Author
T. Roncalli
Date
January 2012
Abstract
Portfolio allocation is generally based on optimization method (Minimum variance,
Markowitz, Merton, Black-Litterman, etc.). The first part of this presentation is
to show that portfolio optimization faces several drawbacks in terms of concentration,
stability and management. We will show that risk-budgeting techniques is an alternative
method which appears more robust. In particular, we will focus the second part of the
presentation in one of the most simple risk-budgeting methods, when the risk budgets
are the same. In this case, we obtain the ERC (Equal Risk Contribution) portfolio. After
giving the mathematical properties of the ERC portfolio, we will present some applications
to manage equity funds (like alternative-weighted indexes) and diversified funds (like risk
parity funds). In the third part of the presentation, we will focus on risk-budgeting methods,
when the risk budgets are not the same. We will generalize some properties of the ERC portfolio
and present an application to manage the sovereign credit risk in bond portfolios.
Keywords
Portfolio optimization, ERC portfolio, risk budgeting, risk parity.
Conference slides
- ESSEC, WG RISK, Paris, January 18, 2012
- Download the PDF file
- Trend Filtering Methods for Momentum Strategies
Authors
B. Bruder, T-L. Dao, J-C. Richard and T. Roncalli
Date
December 2011
Abstract
This paper studies trend filtering methods. These methods are widely used in momentum
strategies, which correspond to an investment style based only on the history
of past prices. For example, the CTA strategy used by hedge funds is one of the
best-known momentum strategies. In this paper, we review the different econometric
estimators to extract a trend of a time series. We distinguish between linear and nonlinear
models as well as univariate and multivariate filtering. For each approach, we
provide a comprehensive presentation, an overview of its advantages and disadvantages
and an application to the S&P 500 index. We also consider the calibration problem of
these filters. We illustrate the two main solutions, the first based on prediction error,
and the second using a benchmark estimator. We conclude the paper by listing some
issues to consider when implementing a momentum strategy.
Keywords
Momentum strategy, trend following, moving average, filtering, trend extraction.
- Download the PDF file
- Strategic Asset Allocation -- An Update Following the Sovereign Debt Crisis
Authors
K. Eychenne and T. Roncalli
Date
December 2011
Abstract
This short paper is an update of Lyxor White Paper #6 -- Strategic Asset
Allocation -- published in March 2011. This white paper was written
with a view to helping investors understand the goal of strategic asset
allocation (SAA), which is part of any long-term investment policy with
tactical asset allocation (TAA). SAA requires long-term assumptions of
asset risk/return characteristics as a key input.
Acknowledging the occurrence of key dramatic events since the beginning
of 2011, we have decided to update the results of our strategic asset allocation
model. We discuss the long-lasting adverse effects of the ongoing
crisis on the long-term path of the economy and long-run asset returns,
notably as a consequence of large fiscal imbalances and continuing financial
fragilities. In particular, we focus on plausible risk scenarios that
could alter asset return forecasts.
Keywords
Long-term investment policy, strategic asset allocation, tactical asset allocation, risk premium, long-run economic growth, Solow model, Phillips curve.
- Download the PDF file
- Managing Sovereign Credit Risk in Bond Portfolios
Authors
B. Bruder, P. Hereil and T. Roncalli
Date
October, 2011
Abstract
With the recent development of the European debt crisis, traditional index bond management
has been severely called into question. We focus here on the risk issues raised by the classical
market-capitalization weighting scheme. We propose an approach to properly measure sovereign
credit risk in a fixed-income portfolio. For that, we assume that CDS spreads follow a
SABR process and we derive a sovereign credit risk measure based on CDS spreads and
duration of portfolio bonds. We then consider two alternative weighting methods which are
fundamental indexation and risk-based indexation. Fundamental indexation is based on GDP
indexation whereas risk-based indexation uses a risk-budgeting approach based on our
sovereign credit risk measure. We then compare all these methods in terms of risk,
diversification and performance. We show that the risk-budgeting approach is the
most appropriate scheme to manage sovereign risk in bond portfolios and gives
very appealing results with respect to active management of bond portfolios.
Keywords
Sovereign credit risk, credit spread, convex risk measure, sabr model, CDS, bond indices, fundamental indexation, risk-based indexation, risk budgeting.
- Download the PDF file
- Managing Sovereign Credit Risk in Bond Portfolios
Authors
B. Bruder, P. Hereil and T. Roncalli
Date
October, 2011
Conference slides
- CFA France, BNP Paribas Investment Partners, Paris, October 13, 2011
- AFGAP, Association Française des Gestionnaires Actif-Passif, Cercle Républicain, Paris, November 17, 2011
- Download the PDF file
- Strategic Asset Allocation and Long-Term Investment Policy
Author
T. Roncalli
Date
March, 2011
Conference slides
- Download the PDF file
- Strategic Asset Allocation
Authors
K. Eychenne, S. Martinetti and T. Roncalli
Date
March 2011
Abstract
To implement strategic asset allocation, we must determine
risk and return expectations for the various asset classes.
Starting from the paradigm that long-run asset returns are determined by the
long-run fundamentals of the economy, a fair value approach to building expectations
is crucial. This paper proposes to formalize a quantitative and
systematic methodology for optimizing portfolios,
from the determination of long-run fundamental pillars through the
modeling of asset returns and the assessment of market risks. We
apply forecasting models and build in the specific of the main asset
classes (equities, bonds and alternative investments)
depending on the uncertainties they represent for the risk-averse
investor. Our resulting allocations within the equity asset class,
and with regard to the place of alternative investments, question the
choices of long-term institutional investors such as pension funds that have shifted their
long-run allocations in response to the recent financial crisis.
Keywords
Long-term investment policy, strategic asset allocation, tactical asset allocation, risk premium, long-run economic growth, Solow model, Phillips curve.
- Download the PDF file
- How Quantitative Methods Can Help To Understand Some Asset Management Problems?
Author
T. Roncalli
Date
March 10, 2011
Conference slides
- Download the PDF file
- Understanding the Weights Constraints in Portfolio Theory
Author
T. Roncalli
Date
January 2011
Abstract
In this article, we analyze the impact of weights constraints in portfolio
theory using the seminal work of Jagannathan and Ma (2003). They show that
solving the global minimum variance portfolio problem with some constraints on
weights is equivalent to use a shrinkage estimate of the covariance matrix.
These results may be easily extended to mean variance and tangency
portfolios. From a financial point of view, the shrinkage estimate of the
covariance matrix may be interpreted as an implied covariance matrix of the
portfolio manager. Using the universe of the DJ Eurostoxx 50, we study the
impact of weights constraints on the global minimum variance portfolio and the
tangency portfolio. We illustrate how imposing lower and upper bounds on
weights modify some properties of the empirical covariance matrix. Finally,
we draw some conclusions in the light of recent developments in the asset
management industry.
Keywords
Global minimum variance portfolio, Markowitz optimization, tangency portfolio, Lagrange coefficients, shrinkage methods, covariance matrix.
- Download the PDF file
- Portfolio Allocation of Hedge Funds
Authors
B. Bruder, S. Darolles, A. Koudiraty and T. Roncalli
Date
January 2011
Abstract
Research in hedge fund investing proposes different solutions to
build optimal hedge fund portfolios. However, these solutions are direct extensions of the usual mean-variance
framework, and still suffer from model risks. More complex approaches start to be
used but are related to numerous estimation risks. We compare in this paper the
out-sample properties of different
allocation models through a dynamic investment exercise using hedge fund
indices. We show that the best out-of-sample properties are obtained
by allocation models that take into account the specific statistical
properties of hedge fund returns.
Keywords
Hedge funds, portfolio allocation, higher-order moments, regime-switching models.
- Download the PDF file
- Mutual Fund Ratings and Performance Persistence
Authors
P. Hereil, P. Mitaine, N. Moussavi and T. Roncalli
Date
June 2010
Abstract
This paper studies the persistence of mutual fund performance.
Academic research often focuses on fund returns, sometimes
adjusted for style and market cap biases. Because fund rating
systems play a central role in the asset management industry, we
consider another approach in this paper. Using a Markov modeling of
these ratings, we illustrate that the persistence of the performance
is relatively poor with respect to the time horizon of investors. We
show that two facts may explain these results. First, the rating
system is not necessarily time-homogeneous. Second, the importance
of style is crucial when comparing the ratings of mutual funds. However, we
show that it is extremely difficult to characterize quantitatively
the style of a mutual fund. We conclude that fund selection is more
art than science, and that quantitative analysis must be combined with
qualitative insight.
Keywords
Mutual funds, rating system, style analysis, Markov chain, active management.
- Download the PDF file
- Risk-Based Indexation (with a Focus on the ERC Method)
Author
T. Roncalli
Date
May 12, 2010
Conference slides
- Download the PDF file
- Risk-Based Indexation
Authors
P. Demey, S. Maillard and T. Roncalli
Date
March 2010
Abstract
A capitalization-weighted index is the most common way to gain access to broad
equity market performance. These portfolios are generally
concentrated in a few stocks and present some lack of diversification. In order to avoid
this drawback or to simply diversify market exposure,
alternative indexation methods have recently prompted great interest,
both from academic researchers and market practitioners. Fundamental
indexation computes weights with regard to economic measures, while risk-based
indexation focuses on risk and diversification criteria. This paper
describes risk-based indexation methodologies,
highlights potential practical issues when implemented, and
illustrates these issues as it applies to the Euro Stoxx 50 universe.
Keywords
Risk-based indexation, fundamental indexation, market capitalization, equity indexes, diversification, portfolio optimization, robust estimation,
minimum-variance indexation, equally-weighted indexation, erc indexation, mdp/msr indexation.
- Download the PDF file
- Exploring non linearities in Hedge Funds: An application of Particle Filters to Hedge Fund Replication
Authors
T. Roncalli and G. Weisang
Date
September 2009
Abstract
Of the three main challenges of hedge fund replication, only replication of the well known
nonlinearities of their returns remains undisputed. Recent advances in hedge fund replication
using factor models have shown that the use of Bayesian filters helps greatly
in capturing the dynamic allocation of assets of hedge fund managers, particularly in the
case of aggregates of hedge funds. Furthermore, from a practitioner's perspective,
access to the alpha of the funds can be provided on top of capturing the dynamic exposures
by adopting a core/satellite approach to building the replication portfolio. In this
working paper, we explore tentatively the solutions that Bayesian filters could provide to
the replication of hedge fund nonlinearities. Although, not entirely successful, our results
show promises and open new grounds for the field.
Keywords
Particle filters, hedge funds, non-linearity.
- Download the PDF file
- Risk Management Lessons from Madoff Fraud
Authors
P. Clauss, T. Roncalli and G. Weisang
Date
November 12, 2009
Conference slides
- Northeastern Section of the Mathematical Association of America, Spring 2009 Meeting, Fairfield University, May 29-30, 2009
- The 23rd New England Statistics Symposium, University of Connecticut, April 25, 2009
- Conseil Scientifique de l'AMF, Paris, November 12, 2009
- Download the PDF file
- Risk Management Lessons from Madoff Fraud
Authors
P. Clauss, T. Roncalli and G. Weisang
Date
March 2, 2009
Abstract
In December 2008, as the financial and economic crisis continued on
its devastating course, a new scandal bursts. After the 1998's
failure of Long-Term Capital Management, Madoff's fraud brings once
again the discredit on the hedge funds industry. This one is however
of a different kind. Indeed, Madoff's firm is not a standard hedge
fund but a developed Ponzi scheme. By explaining Madoff's system and
exploring the reasons to its collapse, this paper draws risk
management lessons from this fraud, especially for operational risk
management. Risk management rules as applied nowadays partially
failed to prevent Madoff's scandal. This paper presents the issues
for risk capital requirements raised by Madoff collapse.
Implications for due diligence processes, including the use of
quantitative replication to assess hedge fund performance's
credibility, are also considered. Finally, consideration is given to
the regulatory and standardizing approaches of the hedge fund
industry as an answer to frauds of Madoff's kind.
Keywords
Madoff fraud, Ponzi scheme, operational risk, due diligence, supervision, hedge funds, bull spread strategy, split strike conversion.
- Download the PDF file
- Hedge Fund Replication and Alternative Beta
Authors
T. Roncalli and G. Weisang
Date
February 11, 2009
Conference slides
- Brown Bag Seminar Series, IE Business School, Madrid, November 18, 2008
- Petits Déjeuners de la Finance, Palais Brogniart, Paris, February 11, 2009
- Laboratoire J. A. Dieudonné, Université de Nice Sophia-Antipolis, April 29, 2009
- Download the PDF file
- Tracking Problems, Hedge Fund Replication and Alternative Beta
Authors
T. Roncalli and G. Weisang
Date
December 24, 2008
Abstract
As hedge fund replication based on factor models has encountered
growing interest among professionals and academics, and despite the
launch of numerous products (indexes and mutual funds) in the past
year, it faced many critics. In this paper, we consider three of the
main critiques, namely the lack of reactivity of hedge fund
replication and its deficiency in capturing tactical allocations;
its failure to apprehend non-linear positions of the underlying
hedge fund industry and higher moments of hedge fund returns; and,
finally, the lack of access to the alpha of hedge funds. To address
these problems, we consider hedge fund replication as a general
tracking problem which may be solved by means of Bayesian filters.
Using the linear Gaussian model as a basis for discussion, we
provide the reader with an intuition for the inner tenets of the
Kalman filter and illustrate the results' sensitivity to the
algorithm specification choices. This part of the paper includes
considerations on the type of strategies which can be replicated, as
well as the problem of selecting factors. We then apply more
advanced Bayesian filters' algorithms, known as particle filters, to
capture the non-normality and non-linearities documented on hedge
fund returns. Finally, we address the problem of accessing the pure
alpha by proposing a core/satellite approach of alternative
investments between high-liquid alternative beta and less liquid
investments.
Keywords
Tracking problem, hedge fund replication,
alternative beta, global tactical asset allocation, Bayes filter, Kalman filter, particle filter, numerical algorithms (SIS, GPP, SIR and RPF),
skewness, kurtosis, non-linear exposure, alpha.
- Download the PDF file
- Download the GAUSS library of Particle Filters
- Equally-weighted risk contributions: a new method to build risk balanced diversified portfolios
Authors
S. Maillard, T. Roncalli and J. Teiletche
Date
September 2008
Abstract
Slides (not yet presented)
Keywords
risk contributions, minimum-variance, 1/n portfolio,
diversification, equity market neutral hedge funds.
- Download the PDF file
- On the property of equally-weighted risk contributions portfolios
Authors
S. Maillard, T. Roncalli and J. Teiletche
Date
July 1, 2008
Abstract
Minimum variance and equally-weighted portfolios have recently
prompted great interest both from academic researchers and market
practitioners, as their construction does not rely on expected
average returns and is therefore assumed to be robust. In this
paper, we consider a related approach, where the risk contribution
from each portfolio components is made equal, which maximizes
diversification of risk (at least on an ex-ante basis). Roughly
speaking, the resulting portfolio is similar to a minimum variance
portfolio subject to a diversification constraint on the weights of
its components. We derive the theoretical properties of such a
portfolio and show that its volatility is located between those of
minimum variance and equally-weighted portfolios. Empirical
applications confirm that ranking. All in all, equally-weighted risk
contributions portfolios appear to be an attractive alternative to
minimum variance and equally-weighted portfolios and might be
considered a good trade-off between those two approaches in terms of
absolute level of risk, risk budgeting and diversification.
Keywords
Asset allocation, risk contributions, minimum-variance, portfolio construction, risk budgeting, portfolio diversification.
- Download the PDF file
- Fund Rating Systems and Performance Predictability
Authors
A-S. Duret, P. Hereil, P. Mitaine, N. Moussavi and T. Roncalli
Date
April 16, 2008
Abstract
This paper studies the performance predictability of external fund rating systems.
Most investors use 5 stars rated funds to build their portfolios. The underlying idea is
that funds which were the best during the last three years will be better performers than the
other funds in the future. It implies that the 5 stars rating is a good persistence measure
of the performance. Using a Markov modelling and the seminal empirical work of Garnier and Pujol (2007),
we show that ratings persistence is poor. It means that fund selection or a fund picking process
may not be reduced to choose funds in a 5 stars rated universe.
Keywords
fund ratings, performance predictability,
markov generator, transition matrix, hurst exponent, fund picking, statistical persistence.
- Download the PDF file
- An Alternative Approach to Alternative Beta
Authors
T. Roncalli and J. Teiletche
Date
April 1, 2007
Abstract
Hedge fund replication based on factor models is encountering growing interest.
In this paper, we investigate the implications of substituting standard rolling windows
regressions, which appear ad-hoc, with more efficient methodologies like the Kalman Filter.
We show that the copycats constructed this way offer risk-return profiles which share several
characteristics with the ones posted by hedge funds indices: Sharpe ratios above buy-and-hold
strategies on standard assets, moderate correlation with standard assets and limited drawdowns
during equity downward trends. An interesting result is that the shortfall risk seems less important
than with hedge fund indices and regressions based-trackers. We finally propose new breakdowns of
hedge fund performance into alpha, traditional beta and alternative beta.
Keywords
Hedge funds, factor models, beta, alpha, replication, Kalman filter.
- Download the PDF file
- Prise en compte du skew de corrélation dans le princing des CDO^2
Auteur
T. Roncalli
Date
3 Juin 2005
Résumé
Dans cette note, on propose une approche économique pour expliquer et donc prendre en
compte le skew de corrélation des CDO. On présente des premiers résultats basés sur l'indice iTraxx.
Mots-clés
CDO, skew correlation, copula.
- Télécharger la fichier PDF
- Interpretation and Estimation of Default Correlations
Authors
P. Demey and T. Roncalli
Date
September 29, 2004
Abstract
Slides of the seminar
"Petit Déjeuner de la Finance" organized by Frontiers in Finance.
Keywords
Default probability, maximum likelihood, spread jumps,
- Download the PDF file
- Maximum Likelihood Estimate of Default Correlations
Authors
P. Demey, J-F. Jouanin, C. Roget and T. Roncalli
Date
November 2004
Abstract
Estimating asset correlations is difficult in practice since there is little available data and
many parameters have to be found. Paul Demey, Jean-Frédéric Jouanin, Céline Roget and
Thierry Roncalli present a tractable version of the multi-factor Merton model in which firms
are sorted into homogeneous risk classes. They derive a simplified maximum likelihood
approach that provides estimates in a reasonable computational time. As an application of
this methodology, industrial sector correlations are estimated from S&P's data.
Keywords
default correlations, factor models.
- Download the PDF file
- Download the correction note
- The Correlation Problem in Operational Risk
Authors
A. Frachot, T. Roncalli and E. Salomon
Date
January 23, 2004
Abstract
This paper demonstrates that aggregate losses are necessarily low as long as we remain under the
standard assumptions of LDA models. Moreover empirical findings show that the correlation between two
aggregate losses is typically below 5%, which opens a wide scope for large diversification effects, much larger
than those the Basel Committee seems to have in mind. In other words, summing up capital charges is in
substantial contradiction with the type of correlation consistent with the standard LDA model.
Keywords
Operational risk, LDA model,
severity correlation, frequency correlation, aggregate loss correlation.
- Download the PDF file
- Financial Applications of Copula Functions
Authors
J-F. Jouanin, G. Riboulet and T. Roncalli
Date
July 15, 2003
Abstract
Copula functions have been introduced recently in finance. They are a general tool to construct
multivariate distributions and to investigate dependence structure between random variables. In this
paper, we show that copula functions may be extensively used to solve many financial problems. As
examples we show how to monitor the market risk of basket products, to measure the credit risk
of a large pool of loans and to compute capital requirements for operational risk.
Keywords
copula, risk management, market risk, credit risk, operational risk.
- Download the PDF file
- Download the zipped PS file
- Loss Distribution Approach in Practice
Authors
A. Frachot, O. Moudoulaud and T. Roncalli
Date
May 07, 2003
Abstract
This paper follows the different steps necessary for implementing a LDA in practice:
- Step 1: Severity Estimation
- Step 2: Frequency Estimation
- Step 3: Capital Charge Computations
- Step 4: Confidence Interval
- Step 5: Self Assesment and Scenario Analysis
For each of these steps, we try to give illustrative examples and we gather all demanding mathematics
into subsections named Technical Appendix. We hope it will allow for a more reader-friendly paper.
Keywords
Operational risk, estimation,
confidence interval, self assesment and scenario analysis.
- Download the PDF file
- A critical approach to the copula model for credit derivatives
Author
J-F. Jouanin, G. Riboulet and T. Roncalli
Date
February 7, 2003
Abstract
Slides of the conference "Risque de Crédit", Evry.
Keywords
Credit derivatives, pricing, hedging.
- Download the PDF file
- Some pratical issues on credit risk
Author
T. Roncalli
Date
February 6, 2003
Abstract
Slides of the conference "Séminaire CREST / LFA", Paris.
Keywords
Basle II, credit risk measurement,
credit portfolio management, time-inconsistency problems.
- Download the PDF file
- How to avoid over-estimating capital charge for operational risk?
Authors
N. Baud, A. Frachot and T. Roncalli
Date
December 01, 2002
Abstract
Intense reflections are being conducted at the moment regarding the way to pool heteregenous data
coming from both banks' internal systems and industry-pooled databases. We propose here a sound
methodology. As it relies on maximum likelihood principle, it is thus statistically rigorous and should
be accepted by supervisors. We believe that it solves the most part of data heterogeneity and scaling
issues.
Keywords
Operational risk, capital charge,
threshold, conditional distribution, maximum likelihood.
- Download the PDF file
- Internal data, external data and consortium data -- How to mix them for measuring operational risk
Authors
N. Baud, A. Frachot and T. Roncalli
Date
June 01, 2002
Abstract
It is widely recognized that calibration on internal data may not
suffice for computing an accurate capital charge against
operational risk. However, pooling external and internal data lead
to unacceptable capital charges as external data are generally
skewed toward large losses. In a previous paper, we have
developped a statistical methodology to ensure that merging both
internal and external data leads to unbiased estimates of the loss
distribution. This paper shows that this methodology is applicable
in real-life risk management and that it permits to pool internal
and external data together in an appropriate way. The paper is
organized as follows.\ We first discuss how external databases are
designed and how their design may result in statistical flaws.
Then we develop a model for the data generating process which
underlies external data.\ In this model, the bias comes simply
from the fact that external data are truncated above a specific
threshold while this threshold may be either constant but known,
or constant but unknown, or finally stochastic. We describe the
rationale behind these three cases and we provide for each of them
a methodology to circumvent the related bias. In each case,
numerical simulations and practical evidences are given.
Keywords
Operational risk, internal data,
external data, consortium data, threshold.
- Download the PDF file
- An internal model for operational risk computation
Authors
N. Baud, A. Frachot and T. Roncalli
Date
May 22, 2002
Abstract
Slides of the conference
"Seminarios de Matematica Financiera", Instituto MEFF -
Risklab, Madrid.
Keywords
Operational risk, LDA, internal data, external data, implied threshold.
- Download the PDF file
- Beyond conditionnally independent defaults
Authors
J-F. Jouanin, G. Riboulet and T. Roncalli
Date
January 31, 2002
Abstract
Non-technical version of the paper
"Modelling dependence for credit derivatives with copulas".
Keywords
Copulas, intensity models, Moody's diversity score.
- Download the PDF file
- Mixing internal and external data for managing operational risk
Authors
A. Frachot and T. Roncalli
Date
Januray 29, 2002
Abstract
The Loss Distribution Approach has many appealing features since it is expected to be much more
risk-sensitive than any other methods taken into consideration by the last proposals by the Basel
Committee. Thus this approach is expected to provide significantly lower capital charges for banks
whose track record is particularly good relatively to their exposures and compared with industry-wide
benchmarks.
Unfortunately LDA when calibrated only on internal data is far from being satisfactory from a regu-
latory perspective as it could likely underestimate the necessary capital charge. This happens for two
reasons. First if a bank has experienced a lower-than-average number of events, it will benefit from
a lower-than-average capital charge even though its good track record happened by chance and does
not result from better-than-average risk management practices. As a consequence, LDA is acceptable
as long as internal frequency data are tempered by industry-wide references. As such, it immediately
raises the issue of how to cope with both internal frequency data and external benchmarks. This
paper proposes a solution based on credibility theory which is widely used in the insurance industry
to tackle analogous problems. As a result, we show how to make the statistical adjustment to temper
the information conveyed by internal frequency data with the use of external references.
Similarly if the calibration of severity parameters ignores external data, then the severity distribution
will likely be biased towards low-severity losses since internal losses are typically lower than those
recorded in industry-wide databases. Again from a regulatory perspective LDA cannot be accepted
unless both internal and external data are merged and the merged database is used in the calibration
process. Here again it raises the issue regarding the best way to merge these data. Obviously it cannot
be done without any care since if internal databases are directly fuelled with external data, severity
distributions will be strongly biased towards high-severity losses. This paper proposes also a statistical
adjustment to make internal and external databases comparable with one another in order to permit
a safe and unbiased merging.
Keywords
Operational risk, LDA, internal data, external data, credibility theory.
- Download the PDF file
- Pricing multi-asset options and credit derivatives with copulas
Author
T. Roncalli
Date
October 26, 2001
Abstract
Slides of the conference
"Séminaire de Mathématiques et Finance Louis Bachelier", Institut Henri Poincaré.
Keywords
Copulas, credit derivatives, multi-asset options.
- Download the PDF file
- Copulas, multivariate risk-neutral distributions and implied dependence functions
Authors
S. Coutant, V. Durrleman, G. Rapuch and T. Roncalli
Date
September 5, 2001
Abstract
In this paper, we use copulas to define multivariate risk-neutral
distributions. We can then derive general pricing formulas for multi-asset
options and best possible bounds with given volatility smiles. Finally, we
then apply the copula framework to define `forward-looking' indicators of
the dependence function between asset returns.
Keywords
Copulas, risk-neutral distribution, change of numéraire, option pricing, implied multivariate RND.
- Download the PDF file
- Modelling dependence for credit derivatives with copulas
Authors
J-F. Jouanin, G. Rapuch, G. Riboulet and T. Roncalli
Date
August 25, 2001
Abstract
In this paper, we address the problem of incorporating default dependency in
intensity-based credit risk models. Following the works of Li [2000], Giesecke [2001] and
Schonbucher and Schubert [2001], we use copulas to model the joint distribution of the
default times. Two approaches are considered. The first one consists in
modelling the joint survival function directly with survival copulas of
default times, whereas in the second approach, copulas are used to correlate
the threshold exponential random variables. We compare these two approaches
and give some results about their relationships. Then we try some
simulations of simple products, such as first-to-defaults. Finally, we
discuss the calibration issue according to Moody's diversity score.
Keywords
Copulas, intensity models, Cox processes, Bessel processes, Moody's diversity score.
- Download the PDF file
- Some remarks on two-asset options pricing and stochastic dependence of asset prices
Authors
G. Rapuch and T. Roncalli
Date
July 16, 2001
Abstract
In this short note, we consider some problems of two-asset options pricing.
In particular, we investigate the relationship between options prices and
the `correlation' parameter in the Black-Scholes model. Then, we consider
the general case in the framework of the copula construction of risk-neutral
distributions. This extension involves results on the supermodular order
applied to the Feynman-Kac representation. We show that it could be viewed
as a generalization of a maximum principle for parabolic PDE.
Keywords
Copulas, two-asset options (Spread, Basket, Min, Max, BestOf, WorstOf),
supermodular order, concordance order, Fréchet bounds, Feynman-Kac representation, maximum principle, parabolic PDE.
- Download the PDF file
- Modelling dependence in finance using copulas
Author
T. Roncalli
Date
July 8, 2001
Abstract
Slides of the conference
"Statistics 2001", Concordia University, Montréal, Canada.
Keywords
Copulas, gaussian assumption,
operational risk, risk-neutral copula, Heston model.
- Download the PDF file
- Multivariate survival modelling: a unified approach with copulas
Authors
P. Georges, A-G. Lamy, E. Nicolas, G. Quibel and T. Roncalli
Date
May 28, 2001
Abstract
In this paper, we review the use of copulas for multivariate survival modelling.
In particular, we study properties of survival copulas and discuss the dependence measures associated to this construction.
Then, we consider the problem of competing risks. We derive the distribution of the failure time and order statistics.
After having presented statistical inference, we finally provide financial applications which concern the life time
value (attrition models), the link between default, prepayment and credit life, the measure of risk for a credit
portfolio and the pricing of credit derivatives.
Keywords
Survival copula, frailty model, ageing concepts, competing risks,
failure time, order statistics, prepayment, credit risk measure, default mode, correlated defaults, risk-bucket capital
charge, default digital put, credit default swap, first-to-default.
- Download the PDF file
- Understanding the dependence in financial models
Author
T. Roncalli
Date
April 23, 2001
Abstract
Slides of the seminar
"Stochastic Models in Finance", Ecole Polytechnique, Paris, 23/04/2001.
Keywords
Copulas, quantile regression, markov copulas,
credit risk, uniform convergence, operations on distribution functions.
- Download the PDF file
- Loss Distribution Approach for operational risk
Authors
A. Frachot, P. Georges and T. Roncalli
Date
March 30, 2001
Abstract
In this paper, we explore the Loss Distribution Approach (LDA)
for computing the capital charge of a bank for operational risk where LDA refers to statistical/actuarial
methods for modelling the loss distribution. In this framework, the capital charge is calculated using a
Value-at-Risk measure. In the first part of the paper, we give a detailed description of the LDA
implementation and we explain how it could be used for economic capital allocation. In particular, we show
- how to compute the aggregate loss distribution by compounding the loss severity distribution and the
loss frequency distribution,
- how to compute the total Capital-at-Risk using copulas,
- how to control the upper tail of the loss severity distribution with order statistics.
In the second part of the paper, we compare LDA with the Internal Measurement Approach (IMA) proposed by the Basel
Committee on Banking Supervision to calculate regulatory capital for operational risk. LDA and IMA
are bottom-up internal measurement models which are apparently different. Nevertheless, we could map LDA
into IMA and give then some justifications about the choice done by regulators to define IMA. Finally, we
provide alternative ways of mapping both methods together.
Keywords
Operational risk, aggregated loss,
compound distribution, loss severity, loss frequency, Panjer algorithm, Capital-at-Risk, economic capital allocation,
order statistics, LDA, IMA, RPI, copulas.
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- What are the most important copulas in finance?
Authors
V. Durrleman, A.Nikeghbali and T. Roncalli
Date
March 17, 2001
Abstract
Slides for the
International Finance Conference, Hammam-Sousse, Tunisia, 03/17/2001.
Keywords
Copulas, risky
dependence function, singular copulas, extreme points, quantile aggregation,
spread option.
- Download the PDF file
- Copulas: a tool for modelling dependence in finance
Author
T. Roncalli
Date
January 26, 2001
Abstract
Slides of the seminar
"Statistical Methods in Integrated Risk Management" organized by Frontiers in Finance.
Keywords
Copulas, 2D option pricing,
markov processes, credit risk, CreditMetrics, CreditRisk+, first-to-default.
- Download the PDF file
- Non-uniform grids for PDE in finance
Authors
J. Bodeau, G. Riboulet and T. Roncalli
Date
December 15, 2000
Abstract
In this paper,
we consider non-uniform grids to solve PDE. We derive the theta-scheme
algorithm based on finite difference methods and show its consistency.
We then apply it to different option pricing problems.
Keywords
Theta-scheme, non-uniform
grids, temporal grids, cubic spline interpolation, european option,
american option, barrier option.
- Download the PDF file
- Download the corresponding GAUSS library
- Financial applications of copulas
Author
T. Roncalli
Date
November 16, 2000
Abstract
Slides of the seminar
"Financial Applications of Copulas".
Keywords
Copulas, financial
applications, risk management, statistical modelling, probabilistic
metric spaces, markov operators, quasi-copulas.
- Download the PDF file
- A note about the conjecture on Spearman's rho and Kendall's tau
Authors
V. Durrleman, A.Nikeghbali and T. Roncalli
Date
November 23, 2000
Abstract
In this paper,
we consider the open question on Spearman's rho and Kendall's
tau of Nelsen [1991]. Using a technical hypothesis, we can answer
in the positive. One question remains open: how can we understand
the technical hypothesis? Because this hypothesis is not right
in general, we could find some pathological cases which contradict
Nelsen's conjecture.
Keywords
Spearman's rho, Kendall's tau, cubic copula.
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- Copulas: an open field for risk management
Authors
E. Bouyé, V. Durrleman, A. Nikeghbali G. Riboulet and T. Roncalli
Date
March 23, 2001 (First version: November 10, 2000)
Abstract
In this paper,
we show that copulas are a very powerful tool for risk management
since it fulfills one of its main goals: the modelling of dependence
between the individual risks. That is why this approach is an
open field for risk.
Keywords
Copulas, market risk,
credit risk, operational risk.
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- Revisiting the dependence between financial markets with copulas
Authors
A. Costinot, T.Roncalli and J. Teïletche
Date
October 24, 2000
Abstract
We consider the
problem of modelling the dependence between financial markets.
In financial economics, the classical tool is the Pearson (or
linear correlation) coefficient to compare the dependence structure. We show
that this coefficient does not give a precise information on the
dependence structure. Instead, we propose a conceptual framework
based on copulas. Two applications are proposed. The first one
concerns the study of extreme dependence between international
equity markets. The second one concerns the analysis of the East
Asian crisis.
Keywords
Linear correlation,
extreme value theory, quantile regression, concordance order,
Deheuvels copula, contagion, Asian crisis.
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- Stress-testing et théorie des valeurs extrêmes : une vision quantifiée du risque extrême
Auteurs
A. Costinot, G. Riboulet et T. Roncalli
Date
September 15, 2000
Résumé
Les banques ont aujourd'hui
la possibilité de mettre en place un modèle interne de risque de marché. L'une des composantes
indispensables de ce modèle est la création d'un programme de stress testing.
Cet article présente un outil potentiel pour la construction d'un tel programme :
la théorie des valeurs extrêmes. Après avoir rappelé la règlementation propre au stress
testing et les principaux résultats de cette théorie, nous montrons comment les utiliser
pour construire des scénarios unidimensionnels, multidimensionnels et enfin pour quantifier
des scénarios de crise élaborés à partir de méthodologies différentes. Aux considérations méthodologiques
sont adjoints les résultats des simulations que nous avons réalisées sur différentes séries financières.
Mots-clés
Copules, fonction de dépendance de queue stable,
théorie des valeurs extrêmes, stress testing.
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- How to get bounds for distribution convolutions? A simulation study and an application to risk management
Authors
V. Durrleman, A. Nikeghbali and T. Roncalli
Date
September 10, 2000
Abstract
In this paper,
we consider the problem of bounds for distribution convolutions
and we present some applications to risk management. We show that
the upper Fréchet bound is not always the more risky dependence
structure. It is in contradiction with the belief in finance that
maximal risk corresponds to the case where the random variables
are comonotonic.
Keywords
Triangle functions,
dependency bounds, infimal, supremal and sigma-convolutions, Makarov
inequalities, Value-at-Risk, "square root" rule, Dall'aglio problem,
Kantorovich distance.
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- Copulas approximation and new families
Authors
V. Durrleman, A.Nikeghbali and T. Roncalli
Date
August 21, 2000
Abstract
In this paper,
we study the approximation procedures introduced by Li, Mikusinski,
Sherwood and Taylor [1997]. We show that there exists a bijection
between the set of the discretized copulas and the set of the
doubly stochastic matrices. For the Bernstein and checkerboard
approximations, we then provide analytical formulas for the Kendall's
tau and Spearman's rho concordance measures. Moreover, we demonstrate
that these approximations do not exhibit tail dependences. Finally,
we consider the general case of approximations induced by partitions
of unity. Moreover, we show that the set of copulas induced by
partition of unity is a Markov sub-algebra with respect to the
*-product of Darsow, Nguyen and Olsen [1992].
Keywords
Doubly stochastic
matrices, Bernstein polynomials approximation, checkerboard copula,
partitions of unity, Markov algebras, product of copulas.
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- Which copula is the right one?
Authors
V. Durrleman, A.Nikeghbali and T. Roncalli
Date
August 25, 2000
Abstract
In this paper,
we give a few methods for the choice of copulas in financial modelling.
Keywords
Maximum likelihood
method, inference for margins, CML method, point estimator, non
parametric estimation, Deheuvels copula, copula approximation,
discrete $L^{p}$ norm.
- Download the PDF file
- A simple transformation of copulas
Authors
V. Durrleman, A.Nikeghbali and T. Roncalli
Date
July 31, 2000
Abstract
We study how copulas
properties are modified after some suitable transformations. In
particular, we show that using appropriate transformations permits
to fit the dependence structure in a better way.
Keywords
γ-transformation,
Kendall's tau, Spearman's rho, upper tail dependence.
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- Topics on two-state option pricing
Authors
V. Durrleman, A.Kurpiel, G. Riboulet and T. Roncalli
Date
June 14, 2000
Abstract
In this paper,
we consider 2D option pricing. Most of the problems come from
the fact that only few closed-form formulas are available. Numerical
algorithms are also necessary to compute option prices. This paper
examines some topics on this subject.
Keywords
Numerical integration
methods, Gauss quadratures, Monte Carlo, Quasi Monte Carlo, Sobol
sequences, Faure sequences, two-dimensional PDE, Hopscotch, LOD,
ADI, MOL, Stochastic volatility model, Malliavin calculus.
- Paper presented at the 17th International Conference in Finance
organized by the French Finance Association, Paris (June 28, 2000).
- Download the PDF file
- Copulas for finance - a reading guide and some applications
Authors
E. Bouyé, V. Durrleman, A. Nikeghbali, G. Riboulet and T. Roncalli
Date
Mars 7, 2000
Abstract
Copulas are a general
tool to construct multivariate distributions and to investigate
dependence structure between random variables. However, the concept
of copula is not popular in Finance. In this paper, we show that
copulas can be extensively used to solve many financial problems.
Keywords
Multivariate distribution,
dependence structure, concordance measures, scoring, Markov processes,
risk management, extreme value theory, stress testing, operational
risk, market risk, credit risk.
- Paper presented at the 17th International Conference in Finance
organized by the French Finance Association, Paris (June 27, 2000)
and at First World Congress of the Bachelier Finance Society (June 29, 2000).
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- Evaluation des options cachées d'un PEL
Auteurs
N. Baud, P. Demey, D. Jacomy, G. Riboulet et T. Roncalli
Date
1er Mars 2000
Résumé
Comme son nom l'indique, le Plan Epargne Logement est un produit d'épargne
qui permet d'acquérir des droits à prêts pour financer un éventuel achat immobilier. Pour que les établissements
financiers et les particuliers y trouvent un intérêt commun, le législateur a mis en place un système
de prime pendant la phase d'épargne. Celui-ci est perçu comme un système incitatif pour le particulier et doit
permettre d'assurer la rentabilité du produit pour la banque.
Une note rédigée par le Trésor en 1996 conclut à la rentabilité du PEL pour les banques. L'argument
repose sur le fait que les pertes (éventuelles) supportées par la banque pendant la phase d'emprunt sont largement compensées
par les revenus de la phase d'épargne. En réponse à cette note l'AFB s'est attachée à montrer
le contraire en incluant les coûts liés aux risques de taux (Note de l'AFB du 16/12/1996).
Il n'est donc pas du tout certain que le système mis en place soit rentable pour l'établissement financier. D'autant
plus que le Plan Epargne Logement est un produit financier relativement complexe et que celui-ci contient différentes options cachées.
Le calcul de sa rentabilité est donc beaucoup plus difficile que ceux présentés par le Trésor ou l'AFB.
C'est pourquoi le GRO a tenté de modéliser les options cachées du PEL, de les valoriser et de calculer la rentabilité
finale de ce produit.
Mots-clés
Plan d'épargne logement, option cachée de conversion, option américaine, problème de contrôle optimal.
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- An analysis framework for bank capital allocation
Authors
N. Baud, A. Frachot, P. Igigabel, P. Martineu and T. Roncalli
Date
December 1, 1999
Abstract
Capital allocation
within a bank is getting more important as the regulatory requirements
are moving towards economic-based measures of risk. Banks are
urged to build sound internal measures of credit and market risks
for all their activities. Internal models for credit, market and
operational risks are fundamental for bank capital allocation
in a bottom-up approach. But this approach has to be completed
by a top-down approach in order to give to bank managers
a more comprehensive (but less detailed) vision of the allocation
efficiency.
From a top-down viewpoint, we are considering the different
business lines of a bank as assets. Then the capital has to be
allocated in order to balance a portfolio in an optimal way. In
this respect, a bank has to evaluate not only the expected return
and the risk of every business line, but also the correlation
matrix of these business lines returns. If a bank usually has
a good knowledge of its expected returns and risks, the problem
is more complex in the case of the correlation matrix: to cope
with the lack of internal data and information, we develop an
approach based on a Market Factor Model and estimate an implied
correlation matrix using the returns of a panel of banks.
The allocation problem is not exactly the problem a bank is confronted
to. It more precisely deals with capital reallocation. Moving
from an allocation to a new one generates costs that have to be
taken into account to ensure that the new allocation is better
than the former one. That is why reallocation signals are more
interesting: they do not point out the optimal allocation but
they allow the implementation of a dynamic policy that leads to
an optimal situation.
Keywords
Capital allocation,
top-down, bottom-up, factor model, optimisation problem, Lagrange
multipliers.
- Paper presented at "Les petits déjeuners de la Finance",
Paris (January 27, 2000).
- Download the PDF file
- A note on monetary policy with interest-rate contingent claims as indicators
Author
T. Roncalli
Date
January 13, 1999
Abstract
In this paper, we consider the use of interest rate contingent
claims as indicators for the monetary policy. We analyze two approches: one based on the term
structure of zero bonds and another based on interest-rate option derivatives. We show how traditional tools
based on the Black framework could be biased to build indicators for monetary policy.
In fact, the second approach could not be viewed as an alternative approach, but as a complementary
approach of the term structure approach.
Keywords
Yield curve, Hull-White trinomial model, monetary policy.
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- Option hedging with stochastic volatility
Authors
A. Kurpiel and T. Roncalli
Date
December 8, 1998
Abstract
The purpose of this paper is to analyse different
implications of the stochastic behavior of asset prices volatilities for option hedging purposes.
We present a simple stochastic volatility model for option pricing and illustrate its consistency
with financial stylized facts. Then, assuming a stochastic volatility environment, we study the
accuracy of Black and Scholes implied volatility-based hedging. More precisely, we analyse the
hedging ratios biases and investigate different hedging schemes in a dynamic setting.
Keywords
option hedging, stochastic volatility, Heston model, delta, gamma, vega.
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- Hopscotch methods for two state financial models
Authors
A. Kurpiel and T. Roncalli
Date
November 17, 1998
Abstract
In this paper, we consider Hopscotch methods for solving two-state
financial models. We first derive a solution algorithm for two-dimensional partial differential equations with
mixed boundary conditions. We then consider a number of financial applications including stochastic volatility
option pricing, term structure modelling with two states and elliptic irreversible investment problems.
Keywords
Two-dimensional PDE, Hopscotch method, parabolic financial models,
elliptic problems.
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- Download the corresponding GAUSS library
- La structure par terme des taux zéro: modélisation et implémentation numérique
Auteur
T. Roncalli
Date
23 mars 1998
Résumé
Thèse de l'Université de Montesqieu-Bordeaux IV.
Mots-clés
Structure par terme, taux zéro, taux forward, méthode de Nelson-Siegel,
modèles factoriels, processus de diffusion, modèle de Black-Derman-Toy, modèle de Hull-White.
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- Télécharger la bibliothèque Gauss
- La détermination des cours de conversion bilatéraux entre les monnaies qualifiées : entre les
souhaits des autorités et le verdict du marché
- Should ERM exchange rates be fixed to their current central parities? A market-view assessment