Executive Summary: A CVaR Scenario-based Framework For Minimizing Downside Risk In Multi-Asset Class Portfolios
|
|
- Paulina Kelly
- 5 years ago
- Views:
Transcription
1 Executive Summary: A CVaR Scenario-based Framework For Minimizing Downside Risk In Multi-Asset Class Portfolios Axioma, Inc. by Kartik Sivaramakrishnan, PhD, and Robert Stamicar, PhD August 2016 In this paper, which is an executive summary of an Axioma technical report [1], we show how to minimize downside risk in multi-asset class (MAC) portfolios. By comparing the scenario-based Conditional Value at Risk (CVaR) approach with parametric Mean-Variance Optimization (MVO) approaches that linearize all the instruments in the MAC portfolio, we show that (a) the CVaR approach generates MAC portfolios with better downside risk statistics, and that (b) the CVaR hedges return more attractive risk decompositions and stress-test numbers tools commonly used by risk managers to evaluate the quality of hedges. MAC portfolios comprise investments in equities, fixed-income, commodities, foreign-exchange, credit, derivatives, and alternatives, such as real-estate and private equity. Such portfolios often have substantial nonlinear exposure to risk factors, particularly in the presence of derivatives or over longer time horizons. The return for such nonlinear portfolios is asymmetric with significant tail risk. The traditional Markowitz MVO framework, which linearizes all the assets in the portfolio and uses the standard deviation of return as a measure of risk, does not accurately measure risk for such portfolios. To mitigate this problem, we use a CVaR approach. We seek to minimize downside risk in a MAC portfolio by adding appropriate overlays. The CVaR approach uses: (a) (b) Monte Carlo simulations to generate asset return scenarios, and, Scenario-based convex optimization to generate overlay holdings. The calculation returns an optimal portfolio of holdings in the overlay portfolio that minimizes the expected losses beyond a specified probability threshold. The authors would like to thank Diana Rudean, PhD, for her contribution to this paper.
2 1. Introduction Multi-asset class (MAC) portfolios are an integral component of asset-manager, asset-owner and hedge-fund investment, and comprise a broad set of assets that include equities, fixed income, commodities, foreign exchange, credit, and alternatives, such as real estate and private equity (Figure 1). MAC instruments provide a more diversified set of asset allocation opportunities that are based on a wide spectrum of risk and return profiles. For example, adding investment grade bonds to an equity portfolio can improve its risk profile. Figure 1: Multi-asset class (MAC) portfolio composition With a broad set of assets, portfolio construction is challenging in a MAC setting. In Figure 2 below, on the left side, we schematically represent the investment process. This figure is by no means exhaustive but serves to illustrate the complexity of portfolio construction for MAC portfolios. We do not consider portfolio construction in the traditional sense where we adjust all portfolio holdings so as to optimize an objective function in this paper. Instead, we consider the risk management problem of mitigating tail risk from a hedging perspective. Tail risk is a rare event or outcome with a small probability of occurring. The tails are the end portions of a distribution. In this study we concentrate on the left tail of the portfolio return distribution, which reflects the probabilities of worst-case scenarios with severe losses. More specifically, we present a methodology for mitigating downside (left tail) risk of MAC portfolios via multi-asset class overlays. There has been considerable interest in downside risk protection, especially in the wake of the 2008 financial crisis. Our starting point is a MAC portfolio with nonlinear assets that has been constructed, say, from an investment process in a traditional manner or using a sophisticated optimization algorithm. The downside risk of the existing portfolio is then minimized with the addition of MAC hedging overlays over a specified time horizon. A CVaR Scenario-based Framework page 2
3 Figure 2: Moving parts in MAC portfolio construction The Markowitz parametric mean-variance optimization (MVO) framework (see Markowitz [5]), which uses the standard deviation of returns as a risk measure and is widely applied in equity portfolio management, is not suitable for MAC portfolios. In particular, positions with nonlinear payoffs introduce asymmetry between positive and negative returns. MVO is not suitable because linear models do not capture asymmetric returns. Moreover, parametric higher moment optimization, which also incorporates the skew and the kurtosis of the returns, is fairly limited in the size of problems that it can handle. To illustrate how standard deviation understates the tail risk in a MAC portfolio, consider Figure 3 that shows the cumulative return distributions for the S&P 500 and a covered call on the S&P 500 (long 100 shares in index and short a call contract on index). Note that the cumulative distribution for the S&P 500 is normal and symmetric about the origin. This implies that a positive return for the index of between 6% and 10% is equally likely as a negative return between -10% and -6%. The upside of the covered call portfolio, however, is capped at 5% by the strike of the call. This is because the counterparty will exercise the call option once the index price exceeds the strike price. As we see in Figure 3, the covered call has a zero probability of a positive return between 6% and 10%, while it has a nonzero probability of a negative return between -10% and -6%. In particular, the covered call has a nonlinear asymmetric return distribution with a long left tail. In this study we present a scenario-based hedging framework to mitigate the tail risk for MAC portfolios that contain nonlinear instruments with asymmetric payoffs. The framework consists of two phases. In the first phase, we generate Monte Carlo simulations for asset and hedging position returns. These scenarios are generated via appropriate pricing engines for the different instruments. The pricing engine captures the nonlinearity of the instrument returns. For example, we use the Black-Scholes pricing engine to price an equity index option that reflects the nonlinear relationship between the index option returns and risk factors, such as the underlying and the implied volatility returns that drive the option price. In the second phase, the simulations from the first phase are fed into a scenario-based convex optimization problem where tail risk is minimized by selecting overlay A CVaR Scenario-based Framework page 3
4 hedges, which are constrained by a budget. The convex optimization can conceivably be extended to include other objectives and constraints that model manager preferences and institutional mandates. Figure 3: Cumulative return distribution for a covered call portfolio and underlying stock index It is important to highlight two key points. First, the simulation-based approach is only as good as the pricing engines and the risk factors that are used to generate instrument return scenarios. Second, we acknowledge that the scenario-based approach, however useful, should not be a standalone analysis. It is a complement to existing tools in the arsenal of the risk manager, such as stress testing, risk decomposition, delta-hedging, what-if analysis, etc. 2. The CVaR Downside Risk Measure Downside risk measures are one-sided risk measures meant to identify potential negative outcomes. They better reflect the left-sided tail risk in MAC portfolios. The most popular downside risk measures include Value at Risk (VaR) and Conditional Value at Risk (CVaR), also known as Expected Shortfall. VaR at confidence level ε is the (1 ε) percentile of the portfolio return distribution. VaR has a simple interpretation: A portfolio VaR at the 95% confidence level over a 10 day period of $10 million implies that we are 95% confident that the portfolio will not suffer losses greater than $10 million over a 10 day period. CVaR at confidence level ε is the expected value of the loss exceeding VaR. These concepts are graphically illustrated in Figure 4, where (a) VaR at the 95% confidence level is the 5% percentile of the portfolio return distribution, and (b) CVaR at the 95% confidence level is the VaR at the 95% confidence level plus the area of the shaded region divided by the length of the axis under the shaded region (excess loss exceeding VaR). A CVaR Scenario-based Framework page 4
5 CVaR was introduced to overcome some of the shortcomings of VaR. First, CVaR is a coherent risk measure encouraging diversification (see Artzner et al. [2]). Second, it is a tail statistic that measures the length of the left tail of the portfolio return distribution. Third, it is easy to optimize. Optimizing CVaR can be done by solving a scenario-based linear optimization problem (see Rockafellar and Uryasev [6]). CVaR will replace VaR as the risk standard in early 2018, and it will be used for all risk and capital calculations under the Basel Committee s FRTB (fundamental review of the trading book; see FTRB link [7]). Figure 4: VaR and CVaR Graphical Representation 3. CVaR Scenario-Based Framework and Results Our approach involves a scenario-based CVaR framework for minimizing the downside risk of an existing MAC portfolio. In the first step, we generate return scenarios for the different MAC instruments in the portfolio using Monte Carlo simulations (see Glasserman [3]). In the second step, we employ a scenario-based convex optimization model that takes the Monte Carlo scenarios as inputs and then generates the overlay hedges. We refer the interested reader to the extended version of this paper for more details on the two phases of the scenario-based framework. We must emphasize that there is a good deal of flexibility in the choice of risk factors and the pricing engines in Phase 1 (Monte Carlo scenario generation) of the algorithm. We analyze several MAC case studies in the extended version of the paper (see Sivaramakrishnan and Stamicar [1]) where we keep the holdings of the original or base portfolio fixed and adjust the weights of hedging/overlay positions to minimize the CVaR at the 95% confidence level. We discuss the second example from the paper below. In this test we want to hedge a callable bond portfolio by purchasing interest rate caps with different strikes and times to expiration, with 1% to 5% budgets (current market value of the base portfolio) in increments of 1%. Most of the risk in the callable bond portfolio is interest rate (IR) risk. We want to hedge this portfolio against an increase in interest rates with over-the-counter (OTC) interest rate caps. Note that both the base portfolio and the hedging overlays are nonlinear instruments. Callable bonds have fat left tails since their upside is capped when interest rates decrease. This is because the issuer of the callable bond may call, i.e., redeem the bond A CVaR Scenario-based Framework page 5
6 when its value increase beyond the call price. We consider a fixed-income portfolio with 48 US callable bonds on May 2, We chose this analysis date since the Fed had increased the key rate 15 straight times until then, and there was a high probability that the Fed would raise rates in the near future. Our strategy is as follows: 1. Hedge callable bond portfolio with OTC interest rate caps over a six-month horizon. There are 10 OTC interest rate caps with varying strikes and times to expiration: (a) Floating rate is based on the six-month LIBOR rate. The prevailing six-month LIBOR rate on May 2, 2006 is 5.34%. (b) Strikes are chosen to the prevailing six-month LIBOR rate. (c) Short-term caps expire on June 30, 2008 and long-term caps expire on June 30, (d) Each caplet tenor is six months. 2. Maintain the callable bond holdings in the portfolio. 3. Experiment with budgets of 1% and 5% of the total market value of the callable bond portfolio. 4. Compare the CVaR and MVO hedges over a six-month hedging horizon. Here is a brief description of the Monte Carlo pricing engine used to generate the asset scenarios: 1. The single factor Hull-White engine (see Hull [4]) is used to price the callable bonds, where the pricing factors include the US sovereign, swap, issuer credit, and swaption volatility factors. 2. Black s formula (see Hull [4]) is used to price the caps as a sequence of caplets, where the pricing factors include the US sovereign, swap, issuer credit, and the cap volatility surface factors. The MVO approach linearizes both the callable bonds (base portfolio) and the IR caps (hedging overlays) to arrive at a covariance matrix for the portfolio that is minimized in a parametric risk term. Figure 5 shows the smoothed kernel density plots of 20,000 realizations of the CVaR and the MVO hedged portfolio returns at the end of the six-month hedging horizon, when the option budget is 1% and 5% of the reference size of the callable bond portfolio, respectively. Notice that the unhedged callable bond portfolio has a fat left tail since the upside of this portfolio is capped when the bonds are redeemed by the issuer. Importantly, both the CVaR and the MVO approaches reduce the tail risk but the CVaR approach offers better downside protection. A CVaR Scenario-based Framework page 6
7 Figure 5: Density plots of portfolio returns at end of rebalancing period Table 1 presents the downside risk statistics for the different portfolios. Notice that the CVaR portfolio has superior downside risk statistics, even for the small 1% budget. In particular, the worst-case return, CVaR and VaR of the left tail of the return distribution, and standard deviation are much smaller than that of the MVO portfolio. The MVO portfolio does not use its entire budget of 1% and so the results are unchanged when one increases the budget to 5%. On the other hand, the downside risk statistics for the CVaR portfolio get better when the budget is 5%. Statistic CVaR 1% Scenario-based CVaR 5% Scenario-based MVO Unhedged CVaR 3.58% 2.45% 4.41% 5.08% VaR 2.86% 1.93% 3.49% 3.85% Worst Loss -7.30% -4.92% -8.10% -9.13% StdDev 1.71% 1.18% 1.99% 2.25% Right CVaR 3.48% 2.40% 3.85% 4.27% Table 1: Downside risk statistics Figure 6 plots the profit and losses (P/Ls) for the CVaR, MVO, and unhedged portfolios, when the portfolios are subject to instantaneous interest rate shocks ranging from -1% to 1%. An interest rate shock of 1% implies that we move the entire yield curve up by 1%. When a shock of 1% is applied, the base portfolio loses 6%, the MVO portfolio loses 4%, the CVaR portfolio with 1% budget loses 2%, and the CVaR portfolio with 5% budget loses nothing. On the other hand, when the entire yield curve moves down by 1%, the base portfolio gains 5%, the MVO and the CVaR portfolios with 1% budget gain 4%, and the CVaR portfolio with 5% budget gains 2%. Notice that the CVaR portfolio with 1% budget (shown by the dashed blue line in Figure 6) has a smaller downside than the MVO portfolio (shown by the solid red line in Figure 6) while both portfolios have the same upside. A CVaR Scenario-based Framework page 7
8 Figure 6: Interest Rate Stress Tests In conclusion, when comparing the CVaR hedging approach with the MVO approach, which linearizes both the callable bonds (the underlying instruments) and the IR caps (hedging overlays), we find that CVaR hedge returns have the best downside risk statistics: smallest CVaR, Worst-Case Loss, VaR, and Standard Deviation. The CVaR hedge also returns the best statistics when all the portfolios are subjected to instantaneous interest rate stress tests. We refer the reader to the extended version of this paper for two other MAC hedging use-cases. In general, we expect these results to extend to other MAC portfolio hedges as well. That is, the CVaR approach generates portfolios with better downside risk statistics than the traditional parametric MVO approaches, without taking much away from the upside. The CVaR hedges also return more attractive statistics on stress tests and on other tools commonly used by risk managers to evaluate the quality of hedges. 4. Conclusions We present a two-phase scenario-based CVaR hedging approach for minimizing the downside risk in MAC portfolios. The base portfolio is fixed and the hedging approach determines the overlay holdings by minimizing the CVaR of the overall portfolio. The first phase of the hedging approach uses a Monte Carlo framework for generating the scenarios for the different instruments in the portfolio. The second phase incorporates these scenarios in a scenario-based convex optimization problem to generate the overlay holdings. We compare the CVaR approach with MVO-based approaches that linearize all the instruments in the portfolio on three examples and show that (a) the CVaR portfolio has better downside risk statistics, and (b) the CVaR portfolio returns more attractive stress-test and risk-decomposition statistics tools commonly used by risk managers to evaluate the quality of hedges. A CVaR Scenario-based Framework page 8
9 We must emphasize that the CVaR hedging approach is flexible. This includes (a) the choice of the risk factors and the pricing models in the Monte Carlo framework, and (b) the setup of the scenario-based convex optimization, including how it is regularized to return stable optimal solutions. We refer the interested reader to the extended version of the paper for more details on the two-phase CVaR approach and other use-cases. Ultimately, the CVaR hedging approach is not a standalone analysis and the flexibility should be used wisely and in conjunction with other tools in the arsenal of the risk manager, such as risk decomposition, deltahedging and stress testing. References [1] K. Sivaramakrishnan and R. Stamicar (2016). A CVaR Scenario-based Framework: Minimizing Downside Risk of Multi-asset Class Portfolios, Technical Report 66, Axioma, May [2] P. Artzner, F. Delbaen, J.M. Eber, and D. Heath (1999). Coherent Measures of Risk, Mathematical Finance, 9(3), [3] P. Glasserman (2003). Monte Carlo Methods in Financial Engineering, Springer. [4] J.C. Hull (2008). Options, Futures, and Other Derivatives, 7th edition, Prentice Hall. [5] H. Markowitz (1959). Portfolio Selection: Efficient Diversification of Instruments, Wiley. [6] R.T. Rockafellar and S. Uryasev (2000). Optimization of Conditional Value-at- Risk, Journal of Risk, 2, [7] FTRB Regulations: A CVaR Scenario-based Framework page 9
10 Contact us to learn more about how Axioma can bring more information and insights to your investment process. United States and Canada: Europe: Asia: Sales: Client Support: Careers:
Axioma Research Paper No. 66. May 25, 2016
Axioma Research Paper No. 66 May 25, 2016 : Minimizing Downside Risk of Multi-asset Class Portfolios Multi-asset class (MAC) portfolios can be comprised of investments in equities, fixed-income, commodities,
More informationPortfolio Optimization using Conditional Sharpe Ratio
International Letters of Chemistry, Physics and Astronomy Online: 2015-07-01 ISSN: 2299-3843, Vol. 53, pp 130-136 doi:10.18052/www.scipress.com/ilcpa.53.130 2015 SciPress Ltd., Switzerland Portfolio Optimization
More informationCalculating VaR. There are several approaches for calculating the Value at Risk figure. The most popular are the
VaR Pro and Contra Pro: Easy to calculate and to understand. It is a common language of communication within the organizations as well as outside (e.g. regulators, auditors, shareholders). It is not really
More informationAxioma Multi-Asset Class Risk Monitor
Analysis Date 2018-06-08 Axioma Multi-Asset Class Risk Monitor Figure 1. Factor Correlations (60 days) and Changes in Correlations (vs previous 60 days) 1. Correlations are unweighted and based on daily
More informationMarket Risk Analysis Volume IV. Value-at-Risk Models
Market Risk Analysis Volume IV Value-at-Risk Models Carol Alexander John Wiley & Sons, Ltd List of Figures List of Tables List of Examples Foreword Preface to Volume IV xiii xvi xxi xxv xxix IV.l Value
More informationAsset Allocation Model with Tail Risk Parity
Proceedings of the Asia Pacific Industrial Engineering & Management Systems Conference 2017 Asset Allocation Model with Tail Risk Parity Hirotaka Kato Graduate School of Science and Technology Keio University,
More informationRISKMETRICS. Dr Philip Symes
1 RISKMETRICS Dr Philip Symes 1. Introduction 2 RiskMetrics is JP Morgan's risk management methodology. It was released in 1994 This was to standardise risk analysis in the industry. Scenarios are generated
More informationVaR vs CVaR in Risk Management and Optimization
VaR vs CVaR in Risk Management and Optimization Stan Uryasev Joint presentation with Sergey Sarykalin, Gaia Serraino and Konstantin Kalinchenko Risk Management and Financial Engineering Lab, University
More informationStress Testing Best Practices
Stress Testing Best Practices ˇ Iulian Cotoi and Robert Stamicar June 2017 Why Stress Tests In our last note, we discussed how optimization techniques can help fixed-income managers construct portfolios.
More informationMotif Capital Horizon Models: A robust asset allocation framework
Motif Capital Horizon Models: A robust asset allocation framework Executive Summary By some estimates, over 93% of the variation in a portfolio s returns can be attributed to the allocation to broad asset
More informationUniversity of Colorado at Boulder Leeds School of Business Dr. Roberto Caccia
Applied Derivatives Risk Management Value at Risk Risk Management, ok but what s risk? risk is the pain of being wrong Market Risk: Risk of loss due to a change in market price Counterparty Risk: Risk
More informationBloomberg. Portfolio Value-at-Risk. Sridhar Gollamudi & Bryan Weber. September 22, Version 1.0
Portfolio Value-at-Risk Sridhar Gollamudi & Bryan Weber September 22, 2011 Version 1.0 Table of Contents 1 Portfolio Value-at-Risk 2 2 Fundamental Factor Models 3 3 Valuation methodology 5 3.1 Linear factor
More informationCHAPTER II LITERATURE STUDY
CHAPTER II LITERATURE STUDY 2.1. Risk Management Monetary crisis that strike Indonesia during 1998 and 1999 has caused bad impact to numerous government s and commercial s bank. Most of those banks eventually
More informationRisk e-learning. Modules Overview.
Risk e-learning Modules Overview Risk Sensitivities Market Risk Foundation (Banks) Understand delta risk sensitivity as an introduction to a broader set of risk sensitivities Explore the principles of
More informationNOTES ON THE BANK OF ENGLAND OPTION IMPLIED PROBABILITY DENSITY FUNCTIONS
1 NOTES ON THE BANK OF ENGLAND OPTION IMPLIED PROBABILITY DENSITY FUNCTIONS Options are contracts used to insure against or speculate/take a view on uncertainty about the future prices of a wide range
More informationAxioma s new Multi-Asset Class (MAC) Risk Monitor highlights recent trends in market and portfolio
Introducing the New Axioma Multi-Asset Class Risk Monitor Christoph Schon, CFA, CIPM Axioma s new Multi-Asset Class (MAC) Risk Monitor highlights recent trends in market and portfolio risk. The report
More informationNorthern Trust Corporation
Northern Trust Corporation Market Risk Disclosures June 30, 2015 Market Risk Disclosures Effective January 1, 2013, Northern Trust Corporation (Northern Trust) adopted revised risk based capital guidelines
More informationComparison of Estimation For Conditional Value at Risk
-1- University of Piraeus Department of Banking and Financial Management Postgraduate Program in Banking and Financial Management Comparison of Estimation For Conditional Value at Risk Georgantza Georgia
More informationThe risk/return trade-off has been a
Efficient Risk/Return Frontiers for Credit Risk HELMUT MAUSSER AND DAN ROSEN HELMUT MAUSSER is a mathematician at Algorithmics Inc. in Toronto, Canada. DAN ROSEN is the director of research at Algorithmics
More informationAccelerated Option Pricing Multiple Scenarios
Accelerated Option Pricing in Multiple Scenarios 04.07.2008 Stefan Dirnstorfer (stefan@thetaris.com) Andreas J. Grau (grau@thetaris.com) 1 Abstract This paper covers a massive acceleration of Monte-Carlo
More informationRho-Works Advanced Analytical Systems. CVaR E pert. Product information
Advanced Analytical Systems CVaR E pert Product information Presentation Value-at-Risk (VaR) is the most widely used measure of market risk for individual assets and portfolios. Conditional Value-at-Risk
More informationStress Testing using Factor Risk Models in Axioma Portfolio Analytics
Stress Testing using Factor Risk Models in Axioma Portfolio Analytics November 2013 1 Introduction Portfolio stress testing provides a means to quantify how a portfolio would perform under extreme economic
More informationNext Generation Fund of Funds Optimization
Next Generation Fund of Funds Optimization Tom Idzorek, CFA Global Chief Investment Officer March 16, 2012 2012 Morningstar Associates, LLC. All rights reserved. Morningstar Associates is a registered
More informationAsset Allocation in the 21 st Century
Asset Allocation in the 21 st Century Paul D. Kaplan, Ph.D., CFA Quantitative Research Director, Morningstar Europe, Ltd. 2012 Morningstar Europe, Inc. All rights reserved. Harry Markowitz and Mean-Variance
More informationClassic and Modern Measures of Risk in Fixed
Classic and Modern Measures of Risk in Fixed Income Portfolio Optimization Miguel Ángel Martín Mato Ph. D in Economic Science Professor of Finance CENTRUM Pontificia Universidad Católica del Perú. C/ Nueve
More informationRobustness of Conditional Value-at-Risk (CVaR) for Measuring Market Risk
STOCKHOLM SCHOOL OF ECONOMICS MASTER S THESIS IN FINANCE Robustness of Conditional Value-at-Risk (CVaR) for Measuring Market Risk Mattias Letmark a & Markus Ringström b a 869@student.hhs.se; b 846@student.hhs.se
More informationValue at Risk, Expected Shortfall, and Marginal Risk Contribution, in: Szego, G. (ed.): Risk Measures for the 21st Century, p , Wiley 2004.
Rau-Bredow, Hans: Value at Risk, Expected Shortfall, and Marginal Risk Contribution, in: Szego, G. (ed.): Risk Measures for the 21st Century, p. 61-68, Wiley 2004. Copyright geschützt 5 Value-at-Risk,
More informationGN47: Stochastic Modelling of Economic Risks in Life Insurance
GN47: Stochastic Modelling of Economic Risks in Life Insurance Classification Recommended Practice MEMBERS ARE REMINDED THAT THEY MUST ALWAYS COMPLY WITH THE PROFESSIONAL CONDUCT STANDARDS (PCS) AND THAT
More informationRISK-BASED APPROACH IN PORTFOLIO MANAGEMENT ON POLISH POWER EXCHANGE AND EUROPEAN ENERGY EXCHANGE
Grażyna rzpiot Alicja Ganczarek-Gamrot Justyna Majewska Uniwersytet Ekonomiczny w Katowicach RISK-BASED APPROACH IN PORFOLIO MANAGEMEN ON POLISH POWER EXCHANGE AND EUROPEAN ENERGY EXCHANGE Introduction
More informationDeterministic interest rate shocks are widely
s in Value-d Measures of Interest Rate Risk By Michael R. Arnold and Dai Zhao Relying on rate shocks as the basis for measuring value-based interest rate risk may understate risk. Deterministic interest
More informationCOMPARISON OF NATURAL HEDGES FROM DIVERSIFICATION AND DERIVATE INSTRUMENTS AGAINST COMMODITY PRICE RISK : A CASE STUDY OF PT ANEKA TAMBANG TBK
THE INDONESIAN JOURNAL OF BUSINESS ADMINISTRATION Vol. 2, No. 13, 2013:1651-1664 COMPARISON OF NATURAL HEDGES FROM DIVERSIFICATION AND DERIVATE INSTRUMENTS AGAINST COMMODITY PRICE RISK : A CASE STUDY OF
More informationIntroduction to Risk Parity and Budgeting
Chapman & Hall/CRC FINANCIAL MATHEMATICS SERIES Introduction to Risk Parity and Budgeting Thierry Roncalli CRC Press Taylor &. Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor
More informationAPPLICATION OF KRIGING METHOD FOR ESTIMATING THE CONDITIONAL VALUE AT RISK IN ASSET PORTFOLIO RISK OPTIMIZATION
APPLICATION OF KRIGING METHOD FOR ESTIMATING THE CONDITIONAL VALUE AT RISK IN ASSET PORTFOLIO RISK OPTIMIZATION Celma de Oliveira Ribeiro Escola Politécnica da Universidade de São Paulo Av. Professor Almeida
More informationNATIONWIDE ASSET ALLOCATION INVESTMENT PROCESS
Nationwide Funds A Nationwide White Paper NATIONWIDE ASSET ALLOCATION INVESTMENT PROCESS May 2017 INTRODUCTION In the market decline of 2008, the S&P 500 Index lost more than 37%, numerous equity strategies
More informationCredit Risk Modelling: A Primer. By: A V Vedpuriswar
Credit Risk Modelling: A Primer By: A V Vedpuriswar September 8, 2017 Market Risk vs Credit Risk Modelling Compared to market risk modeling, credit risk modeling is relatively new. Credit risk is more
More informationMarket risk measurement in practice
Lecture notes on risk management, public policy, and the financial system Allan M. Malz Columbia University 2018 Allan M. Malz Last updated: October 23, 2018 2/32 Outline Nonlinearity in market risk Market
More informationA Framework for Understanding Defensive Equity Investing
A Framework for Understanding Defensive Equity Investing Nick Alonso, CFA and Mark Barnes, Ph.D. December 2017 At a basketball game, you always hear the home crowd chanting 'DEFENSE! DEFENSE!' when the
More informationHANDBOOK OF. Market Risk CHRISTIAN SZYLAR WILEY
HANDBOOK OF Market Risk CHRISTIAN SZYLAR WILEY Contents FOREWORD ACKNOWLEDGMENTS ABOUT THE AUTHOR INTRODUCTION XV XVII XIX XXI 1 INTRODUCTION TO FINANCIAL MARKETS t 1.1 The Money Market 4 1.2 The Capital
More informationPortfolios of Everything
Portfolios of Everything Paul D. Kaplan, Ph.D., CFA Quantitative Research Director Morningstar Europe Sam Savage, Ph.D. Consulting Professor, Management Science & Engineering Stanford University 2010 Morningstar,
More informationAlternative Risk Measures for Alternative Investments
Alternative Risk Measures for Alternative Investments A. Chabaane BNP Paribas ACA Consulting Y. Malevergne ISFA Actuarial School Lyon JP. Laurent ISFA Actuarial School Lyon BNP Paribas F. Turpin BNP Paribas
More informationHandbook of Financial Risk Management
Handbook of Financial Risk Management Simulations and Case Studies N.H. Chan H.Y. Wong The Chinese University of Hong Kong WILEY Contents Preface xi 1 An Introduction to Excel VBA 1 1.1 How to Start Excel
More informationAn Application of Extreme Value Theory for Measuring Financial Risk in the Uruguayan Pension Fund 1
An Application of Extreme Value Theory for Measuring Financial Risk in the Uruguayan Pension Fund 1 Guillermo Magnou 23 January 2016 Abstract Traditional methods for financial risk measures adopts normal
More informationTarget Date Glide Paths: BALANCING PLAN SPONSOR GOALS 1
PRICE PERSPECTIVE In-depth analysis and insights to inform your decision-making. Target Date Glide Paths: BALANCING PLAN SPONSOR GOALS 1 EXECUTIVE SUMMARY We believe that target date portfolios are well
More informationINTEREST RATES AND FX MODELS
INTEREST RATES AND FX MODELS 7. Risk Management Andrew Lesniewski Courant Institute of Mathematical Sciences New York University New York March 8, 2012 2 Interest Rates & FX Models Contents 1 Introduction
More informationLinda Allen, Jacob Boudoukh and Anthony Saunders, Understanding Market, Credit and Operational Risk: The Value at Risk Approach
P1.T4. Valuation & Risk Models Linda Allen, Jacob Boudoukh and Anthony Saunders, Understanding Market, Credit and Operational Risk: The Value at Risk Approach Bionic Turtle FRM Study Notes Reading 26 By
More informationManaging Personal Wealth in Volatile Markets
Click to edit Master title style Managing Personal Wealth in Volatile Markets An ERM Approach Jerry A. Miccolis, CFA, CFP, FCAS March 15, 2011 Call 800.364.2468 :: Visit brintoneaton.com By way of (re)introduction
More informationEnterprise risk management has been
KJETIL HØYLAND is first vice president in the Department of Asset and Risk Allocation at Gjensidige NOR Asset Management, Norway. kjetil.hoyland@dnbnor.no ERIK RANBERG is senior vice president in charge
More informationTail Risk Literature Review
RESEARCH REVIEW Research Review Tail Risk Literature Review Altan Pazarbasi CISDM Research Associate University of Massachusetts, Amherst 18 Alternative Investment Analyst Review Tail Risk Literature Review
More informationBENEFITS OF ALLOCATION OF TRADITIONAL PORTFOLIOS TO HEDGE FUNDS. Lodovico Gandini (*)
BENEFITS OF ALLOCATION OF TRADITIONAL PORTFOLIOS TO HEDGE FUNDS Lodovico Gandini (*) Spring 2004 ABSTRACT In this paper we show that allocation of traditional portfolios to hedge funds is beneficial in
More informationNon-normality of Market Returns A framework for asset allocation decision-making
Non-normality of Market Returns A framework for asset allocation decision-making Executive Summary In this paper, the authors investigate nonnormality of market returns, as well as its potential impact
More informationValue at Risk Risk Management in Practice. Nikolett Gyori (Morgan Stanley, Internal Audit) September 26, 2017
Value at Risk Risk Management in Practice Nikolett Gyori (Morgan Stanley, Internal Audit) September 26, 2017 Overview Value at Risk: the Wake of the Beast Stop-loss Limits Value at Risk: What is VaR? Value
More informationPortfolio Management
Portfolio Management 010-011 1. Consider the following prices (calculated under the assumption of absence of arbitrage) corresponding to three sets of options on the Dow Jones index. Each point of the
More informationFinancial Risk Forecasting Chapter 6 Analytical value-at-risk for options and bonds
Financial Risk Forecasting Chapter 6 Analytical value-at-risk for options and bonds Jon Danielsson 2017 London School of Economics To accompany Financial Risk Forecasting www.financialriskforecasting.com
More informationInstitute of Actuaries of India. Subject. ST6 Finance and Investment B. For 2018 Examinationspecialist Technical B. Syllabus
Institute of Actuaries of India Subject ST6 Finance and Investment B For 2018 Examinationspecialist Technical B Syllabus Aim The aim of the second finance and investment technical subject is to instil
More informationScenario-Based Value-at-Risk Optimization
Scenario-Based Value-at-Risk Optimization Oleksandr Romanko Quantitative Research Group, Algorithmics Incorporated, an IBM Company Joint work with Helmut Mausser Fields Industrial Optimization Seminar
More informationBasel II and the Risk Management of Basket Options with Time-Varying Correlations
Basel II and the Risk Management of Basket Options with Time-Varying Correlations AmyS.K.Wong Tinbergen Institute Erasmus University Rotterdam The impact of jumps, regime switches, and linearly changing
More informationTuomo Lampinen Silicon Cloud Technologies LLC
Tuomo Lampinen Silicon Cloud Technologies LLC www.portfoliovisualizer.com Background and Motivation Portfolio Visualizer Tools for Investors Overview of tools and related theoretical background Investment
More informationConcentrated Investments, Uncompensated Risk and Hedging Strategies
Concentrated Investments, Uncompensated Risk and Hedging Strategies by Craig McCann, PhD, CFA and Dengpan Luo, PhD 1 Investors holding concentrated investments are exposed to uncompensated risk additional
More informationOvernight Index Rate: Model, calibration and simulation
Research Article Overnight Index Rate: Model, calibration and simulation Olga Yashkir and Yuri Yashkir Cogent Economics & Finance (2014), 2: 936955 Page 1 of 11 Research Article Overnight Index Rate: Model,
More informationKevin Dowd, Measuring Market Risk, 2nd Edition
P1.T4. Valuation & Risk Models Kevin Dowd, Measuring Market Risk, 2nd Edition Bionic Turtle FRM Study Notes By David Harper, CFA FRM CIPM www.bionicturtle.com Dowd, Chapter 2: Measures of Financial Risk
More informationSOLVENCY AND CAPITAL ALLOCATION
SOLVENCY AND CAPITAL ALLOCATION HARRY PANJER University of Waterloo JIA JING Tianjin University of Economics and Finance Abstract This paper discusses a new criterion for allocation of required capital.
More informationMeasuring Risk in Canadian Portfolios: Is There a Better Way?
J.P. Morgan Asset Management (Canada) Measuring Risk in Canadian Portfolios: Is There a Better Way? May 2010 On the Non-Normality of Asset Classes Serial Correlation Fat left tails Converging Correlations
More informationRisk Reward Optimisation for Long-Run Investors: an Empirical Analysis
GoBack Risk Reward Optimisation for Long-Run Investors: an Empirical Analysis M. Gilli University of Geneva and Swiss Finance Institute E. Schumann University of Geneva AFIR / LIFE Colloquium 2009 München,
More informationIEOR E4602: Quantitative Risk Management
IEOR E4602: Quantitative Risk Management Basic Concepts and Techniques of Risk Management Martin Haugh Department of Industrial Engineering and Operations Research Columbia University Email: martin.b.haugh@gmail.com
More informationDIFFERENCES BETWEEN MEAN-VARIANCE AND MEAN-CVAR PORTFOLIO OPTIMIZATION MODELS
DIFFERENCES BETWEEN MEAN-VARIANCE AND MEAN-CVAR PORTFOLIO OPTIMIZATION MODELS Panna Miskolczi University of Debrecen, Faculty of Economics and Business, Institute of Accounting and Finance, Debrecen, Hungary
More information1 Commodity Quay East Smithfield London, E1W 1AZ
1 Commodity Quay East Smithfield London, E1W 1AZ 14 July 2008 The Committee of European Securities Regulators 11-13 avenue de Friedland 75008 PARIS FRANCE RiskMetrics Group s Reply to CESR s technical
More informationRisk-adjusted Stock Selection Criteria
Department of Statistics and Econometrics Momentum Strategies using Risk-adjusted Stock Selection Criteria Svetlozar (Zari) T. Rachev University of Karlsruhe and University of California at Santa Barbara
More informationRisk-Return Optimization of the Bank Portfolio
Risk-Return Optimization of the Bank Portfolio Ursula Theiler Risk Training, Carl-Zeiss-Str. 11, D-83052 Bruckmuehl, Germany, mailto:theiler@risk-training.org. Abstract In an intensifying competition banks
More informationEconomic capital allocation. Energyforum, ERM Conference London, 1 April 2009 Dr Georg Stapper
Economic capital allocation Energyforum, ERM Conference London, 1 April 2009 Dr Georg Stapper Agenda ERM and risk-adjusted performance measurement Economic capital calculation Aggregation and diversification
More informationJaime Frade Dr. Niu Interest rate modeling
Interest rate modeling Abstract In this paper, three models were used to forecast short term interest rates for the 3 month LIBOR. Each of the models, regression time series, GARCH, and Cox, Ingersoll,
More informationTHE FOREIGN EXCHANGE EXPOSURE OF BALTIC NON- FINANCIAL COMPANIES: MYTH OR REALITY?
THE FOREIGN EXCHANGE EXPOSURE OF BALTIC NON- FINANCIAL COMPANIES: MYTH OR REALITY? Ramona Rupeika-Apoga Roberts Nedovis Abstract The authors of this paper are looking for answers: are domestic companies
More informationField Guide to Internal Models under the Basel Committee s Fundamental review of the trading book framework
Field Guide to Internal Models under the Basel Committee s Fundamental review of the trading book framework Barry Pearce, Director, Skew Vega Limited A R T I C L E I N F O A B S T R A C T Article history:
More informationThe Returns and Risk of Dynamic Investment Strategies: A Simulation Comparison
International Journal of Business and Economics, 2016, Vol. 15, No. 1, 79-83 The Returns and Risk of Dynamic Investment Strategies: A Simulation Comparison Richard Lu Department of Risk Management and
More informationTarget-Date Glide Paths: Balancing Plan Sponsor Goals 1
Target-Date Glide Paths: Balancing Plan Sponsor Goals 1 T. Rowe Price Investment Dialogue November 2014 Authored by: Richard K. Fullmer, CFA James A Tzitzouris, Ph.D. Executive Summary We believe that
More informationOptimizing S-shaped utility and risk management
Optimizing S-shaped utility and risk management Ineffectiveness of VaR and ES constraints John Armstrong (KCL), Damiano Brigo (Imperial) Quant Summit March 2018 Are ES constraints effective against rogue
More informationSkewing Your Diversification
An earlier version of this article is found in the Wiley& Sons Publication: Hedge Funds: Insights in Performance Measurement, Risk Analysis, and Portfolio Allocation (2005) Skewing Your Diversification
More informationCondensed Interim Consolidated Financial Statements of. Canada Pension Plan Investment Board
Condensed Interim Consolidated Financial Statements of Canada Pension Plan Investment Board December 31, 2017 Condensed Interim Consolidated Balance Sheet December 31, 2017 December 31, 2017 March 31,
More informationFinancial Risk Measurement/Management
550.446 Financial Risk Measurement/Management Week of September 23, 2013 Interest Rate Risk & Value at Risk (VaR) 3.1 Where we are Last week: Introduction continued; Insurance company and Investment company
More informationOracle Financial Services Market Risk User Guide
Oracle Financial Services User Guide Release 8.0.4.0.0 March 2017 Contents 1. INTRODUCTION... 1 PURPOSE... 1 SCOPE... 1 2. INSTALLING THE SOLUTION... 3 2.1 MODEL UPLOAD... 3 2.2 LOADING THE DATA... 3 3.
More informationMarket Risk: FROM VALUE AT RISK TO STRESS TESTING. Agenda. Agenda (Cont.) Traditional Measures of Market Risk
Market Risk: FROM VALUE AT RISK TO STRESS TESTING Agenda The Notional Amount Approach Price Sensitivity Measure for Derivatives Weakness of the Greek Measure Define Value at Risk 1 Day to VaR to 10 Day
More informationDownside Risk: Implications for Financial Management Robert Engle NYU Stern School of Business Carlos III, May 24,2004
Downside Risk: Implications for Financial Management Robert Engle NYU Stern School of Business Carlos III, May 24,2004 WHAT IS ARCH? Autoregressive Conditional Heteroskedasticity Predictive (conditional)
More informationMS&E 348 Winter 2011 BOND PORTFOLIO MANAGEMENT: INCORPORATING CORPORATE BOND DEFAULT
MS&E 348 Winter 2011 BOND PORTFOLIO MANAGEMENT: INCORPORATING CORPORATE BOND DEFAULT March 19, 2011 Assignment Overview In this project, we sought to design a system for optimal bond management. Within
More informationStatistical Models and Methods for Financial Markets
Tze Leung Lai/ Haipeng Xing Statistical Models and Methods for Financial Markets B 374756 4Q Springer Preface \ vii Part I Basic Statistical Methods and Financial Applications 1 Linear Regression Models
More informationQuantitative Risk Management
Quantitative Risk Management Asset Allocation and Risk Management Martin B. Haugh Department of Industrial Engineering and Operations Research Columbia University Outline Review of Mean-Variance Analysis
More informationINVESTMENT SERVICES RULES FOR RETAIL COLLECTIVE INVESTMENT SCHEMES
INVESTMENT SERVICES RULES FOR RETAIL COLLECTIVE INVESTMENT SCHEMES PART B: STANDARD LICENCE CONDITIONS Appendix VI Supplementary Licence Conditions on Risk Management, Counterparty Risk Exposure and Issuer
More informationMarket Risk VaR: Model- Building Approach. Chapter 15
Market Risk VaR: Model- Building Approach Chapter 15 Risk Management and Financial Institutions 3e, Chapter 15, Copyright John C. Hull 01 1 The Model-Building Approach The main alternative to historical
More informationFinancial Risk Measurement/Management
550.446 Financial Risk Measurement/Management Week of September 23, 2013 Interest Rate Risk & Value at Risk (VaR) 3.1 Where we are Last week: Introduction continued; Insurance company and Investment company
More informationPurpose Driven Investing
Purpose Driven Investing Stephanie A. Chedid, AIF LeadingAge New York, September 11, 2013 Business Assets An often overlooked aspect that can lead to issues of over allocation, reduced diversification
More informationBeyond VaR: Triangular Risk Decomposition
Beyond VaR: Triangular Risk Decomposition Helmut Mausser and Dan Rosen This paper describes triangular risk decomposition, which provides a useful, geometric view of the relationship between the risk of
More informationPortfolio selection with multiple risk measures
Portfolio selection with multiple risk measures Garud Iyengar Columbia University Industrial Engineering and Operations Research Joint work with Carlos Abad Outline Portfolio selection and risk measures
More informationValue-at-Risk (VaR) a Risk Management tool
Value-at-Risk (VaR) a Risk Management tool Risk Management Key to successful Risk Management of a portfolio lies in identifying & quantifying the risk that the company faces due to price volatility in
More informationThe role of the Model Validation function to manage and mitigate model risk
arxiv:1211.0225v1 [q-fin.rm] 21 Oct 2012 The role of the Model Validation function to manage and mitigate model risk Alberto Elices November 2, 2012 Abstract This paper describes the current taxonomy of
More informationMultistage risk-averse asset allocation with transaction costs
Multistage risk-averse asset allocation with transaction costs 1 Introduction Václav Kozmík 1 Abstract. This paper deals with asset allocation problems formulated as multistage stochastic programming models.
More informationA SUMMARY OF OUR APPROACHES TO THE SABR MODEL
Contents 1 The need for a stochastic volatility model 1 2 Building the model 2 3 Calibrating the model 2 4 SABR in the risk process 5 A SUMMARY OF OUR APPROACHES TO THE SABR MODEL Financial Modelling Agency
More informationUsing Fat Tails to Model Gray Swans
Using Fat Tails to Model Gray Swans Paul D. Kaplan, Ph.D., CFA Vice President, Quantitative Research Morningstar, Inc. 2008 Morningstar, Inc. All rights reserved. Swans: White, Black, & Gray The Black
More informationCALCURIX: a tailor-made RM software
CALCURIX: a tailor-made RM software Ismael Fadiga & Jang Schiltz (LSF) March 15th, 2017 Ismael Fadiga & Jang Schiltz (LSF) CALCURIX: a tailor-made RM software March 15th, 2017 1 / 36 Financial technologies
More informationWorking Paper October Book Review of
Working Paper 04-06 October 2004 Book Review of Credit Risk: Pricing, Measurement, and Management by Darrell Duffie and Kenneth J. Singleton 2003, Princeton University Press, 396 pages Reviewer: Georges
More informationFrom Financial Risk Management. Full book available for purchase here.
From Financial Risk Management. Full book available for purchase here. Contents Preface Acknowledgments xi xvii CHAPTER 1 Introduction 1 Banks and Risk Management 1 Evolution of Bank Capital Regulation
More informationKARACHI UNIVERSITY BUSINESS SCHOOL UNIVERSITY OF KARACHI BS (BBA) VI
88 P a g e B S ( B B A ) S y l l a b u s KARACHI UNIVERSITY BUSINESS SCHOOL UNIVERSITY OF KARACHI BS (BBA) VI Course Title : STATISTICS Course Number : BA(BS) 532 Credit Hours : 03 Course 1. Statistical
More information