Axioma Global Multi-Asset Class Risk Model Fact Sheet. AXGMM Version 2.0. May 2018

Transcription

1 Axioma Global Multi-Asset Class Risk Fact Sheet AXGMM Version 2.0 May 2018 Axioma s Global Multi-Asset Class Risk (Global MAC ) is intended to capture the investment risk of a multi-asset class portfolio by explaining asset returns as a combination of exposures to risk factor returns. The model is available as a factor covariance matrix, updated weekly, together with a matrix of asset exposures to the factors, which can be downloaded for integration with risk reporting and attribution systems. 1 Introduction Axioma s Global MAC offers users an intuitive decomposition of a multi asset class portfolio. The model is designed for a broadbased analysis of global multi asset class holdings. As such, the resolution of the factors targets understanding sources of risk across a broad portfolio. The model contains factors derived from an integrated set of pricing models calibrated to tradeable asset prices for a wide range of asset classes. This allows portfolio managers to analyze the risk and performance of their portfolios across all assets in a consistent and rigorous manner. The Global MAC combines the coverage of Axioma s global equity risk model with coverage of the fixed-income and commodities markets. Leveraging the expertise embedded in Axioma Robust Equity s and an extensive universe of fixed-income factors, the Global MAC allows portfolio managers holding a wide range of assets to use a consistent set of models to analyze their risk and attribute performance. Axioma s factor models are designed to separate and quantify systematic and idiosyncratic components of risk. The systematic factors captured in the model include: Yield curve Volatility Credit Sector Currency Inflation Commodity curves Country Equity Style The Global MAC is produced by Axioma s Enterprise Risk Platform Axioma Risk. This cloud-based platform allows extensive flexibility in factor definition, risk model construction, stress testing, risk analysis, and reporting. The Global MAC provides for a streamlined portfolio risk analysis, while Axioma Risk offers a fully customizable enterprise risk system. 2 Top Level Structure of the Global MAC Risk The Global MAC is a linear, parametric risk model composed of i) a global set of risk factors for which factor returns and an associated covariance matrix are computed; and ii) a set of exposures to these risk factors for each asset in the covered universe. If there are N A assets in the portfolio and N F risk factors, we can define Axioma 1

2 an N A N F exposure matrix B with the i th row containing the exposures of asset i to all the factors. The portfolio risk (i.e. the volatility of the portfolio return) is then computed as σ Π = ( ) 1/2 w T BΣ F B T w where Σ F is the covariance matrix of the factor returns and w is the vector of dollar position weights for each asset. Axioma provides the factor return covariance matrix and the exposure matrix for a specific portfolio as the weekly Global MAC deliverable, while the user provides the universe and position data. factor returns are then calculated off a cross sectional regression model carried out on an estimation universe. 3.2 Global Fixed-Income Factor The Global Fixed-Income Factor derives rate curves, spread curves and volatility surfaces from market prices and estimates factors that drive changes in the curves. The factors are designed to separate and quantify systematic and idiosyncratic components of risk. The systematic factors within a typical fixed-income portfolio include changes in: 3 Risk Factors in the Global MAC The set of risk factors for the Global MAC is comprised of the Axioma Global Equity Fundamental (the World-Wide Fundamental, version 4.0), the Axioma Global Fixed-Income Factor, and a commodity model based on constant maturity futures curves, as well as volatility factors derived from swaption data. Summary information for specific asset classes are described here, detailed information is available in the risk model handbook. 3.1 Global Equity Fundamental Factor For equities, the Global MAC imposes a structure on the asset returns by identifying common factors within the market that is, factors that drive asset returns. Returns can then be modeled as a function of a relatively small number of parameters, and estimating potentially millions of asset covariances can thus be simplified to calculating a much smaller set of numbers. The factors used in the Global Equity Fundamental Factor fall into several broad categories, namely Industry, Country, & Style factors. Calculation of the exposures to these factors is described in the Section 4. Once the exposures to these factors have been determined, rates spreads Spot FX rates Corporate credit spreads by rating and rating/gics sector Break-even inflation rates Asset-backed security spreads Covered bond spreads Other government, GRE and Supranational spreads Derivatives: tion Volatilities, CDS spreads The table in Appendix A lists the number of such curves/factors grouped by category. 3.3 Commodities Commodity futures contracts are modeled in Axioma Risk using Constant Maturity Futures (CMF) curves. The model uses daily futures settlement prices and maturities to construct the CMF curves as a set of interpolated nodes at fixed maturities. The nodes of the CMF curves are the risk factors, and the CMF curves are constructed using the one day log returns of the futures prices. Axioma 2

3 4 Exposure Calculation in the Global MAC Calculation of the sensitivity of an asset price return to the various risk factors is handled differently across the broad asset groupings: Equity, Fixed-Income, and Commodities. Summary information for risk factor groups is provided in this section with detailed information available in the risk model handbook. 4.1 Exposure to Equity Risk Factors Exposure to the industry and country factors in the equity risk model are binary, either 0 or 1. These are determined by the GICS industry classification of the company and the country of incorporation. Exposure to the style factors is computed based on a Z-score transformation of a combination of financial ratios or performance measures associated with the definition of the style factor. The models are constructed to maximize the explanatory power of the style factors driven by the definitions of these exposures. Industry and country exposures are generally static, while most style factor exposures are updated when new financial performance data are released. T ). When the maturity of the contract lies between two nodes, the contract has exposure to the two surrounding nodes and each exposure is computed as the proportional linear distance from the maturity to the node maturity. 4.4 Exposure to Volatility and Currency Risk Factors Because the volatility and currency risk factors are computed as log returns, the exposure is computed as β = X P A P A X (1) where X is either the volatility level σ or the spot exchange rate. For non-us dollar denominated assets with no currency exposure other than the reporting currency exchange-rate risk, this formula corresponds to a currency risk exposure of 1. 5 Global MAC Parameters The Global MAC includes a covariance matrix estimated from the time series of the relevant factors for a given portfolio. Details of the parameter choices for the covariance estimation calculation are given here. 4.2 Exposure to Fixed-Income Risk Factors For all fixed-income rate and spread risk factors, the exposure is computed as the price return sensitivity to changes in the factor. Axioma has implemented detailed pricing functions for all fixed-income assets covered and computes exposures to the underlying risk factors based on these pricing functions. 4.3 Exposure to Commodity Risk Factors As the risk factors for commodity future contracts are log-return CMF curves, the exposure of a contract with the same maturity as a node point is exactly 1 (i.e. the volatility of the commodity future contract with maturity T is the same as the volatility of the CMF curve at point 5.1 History Monthly covariance matrix history from January 2012 onward; daily factor returns from January Reporting Currency USD. 5.3 Factor Volatility / Covariance Calculation Parameters The covariance matrix for the model is estimated based on five years of daily factor-return data using the following estimation procedure. The daily factor returns are aggregated into overlapping weekly returns, thus creating a time series of approximately 1250 observations of weekly returns. Note that weekly returns are used Axioma 3

4 to minimize the impact of asynchronous timing of returns reporting and potentially stale fixedincome pricing. Overlapping returns are used to ensure that the model still responds quickly to market shocks, as well as to increase the effective sample size used in the covariance estimation. An exponentially decaying weighting scheme is used to more heavily weight the recent return behavior. A half-life of 250 daily observations (one year) is used to compute both variances and correlations. 5.4 Specific Risk For assets with sufficient data and idiosyncratic drivers of risk, specific risk (i.e. additional volatility uncorrelated with the factors in the model) is estimated and included in the model. The methodology implemented varies by asset class in the model: For equity assets, specific risk is defined as the volatility of the residual that is not explained by the factors. Specific risk for fixed-income corporate securities is estimated, where the data are available, from single-name issuer-curve volatilities. 6 Data Deliverables The Axioma Global Multi-Asset Class is accessible through Axioma s SFTP site. 1. Availability: The covariance and exposure matrices are updated weekly and available to download via SFTP. 2. Historical Coverage: A monthly history of covariance and exposure matrices is available going back to January Daily factor returns are available going back to January Data Format: Delimited text files (flatfiles) Axioma 4

5 Appendices Axioma 5

6 Appendix A Global MAC : Curve and Factor Structure Curve/Factor Type Definition Count Reference Curve CO-Commodity Futures Constant Maturity Futures 98 N/A Currency Currency Risk Factors 92 N/A EQ-Country EQ-Industry EQ-Local EQ-Market EQ-Style FI-U.S. IG ABS spread Equity Country Factors from AXWW21 (Global Equity) Equity Industry Factors from AXWW21 (Global Equity) Equity Local Market Residual Factors from AXWW21 (Global Equity) Equity Global Market Factors from AXWW21 (Global Equity) Equity Style Factors from AXWW21 (Global Equity) U.S. Investment Grade Rating Spread FI-Agency Spread U.S. Agency Spread 3 FI-Break Even Inflation FI-CA Provincial Spread FI-Corporate Rating Spread FI-Corporate Sector by Rating Spread Spread of Nominal over Real for Zero Coupon Canadian Provinicial Spread over CA Corporate Rating Spread over Sector Spread over Rating Category 85 N/A 68 N/A 1 N/A 1 N/A 9 N/A Real (BEI Spread = Nominal - Real) (CAD) Rating Curve FI-Covered Bond Spread Spread over 7 FI- Zero Zero Coupon Curve 37 N/A FI- Spread (EUR) Intra-Eurozone Spread over EU FI- Spread EM Spread over US 22 FI-Supranational Spread Supranational Ratings Spread over 15 (EUR) (EUR), FI- Spread Zero Spread 37 FI-Interest Rate Volatility 2 Year 2 Year swaption 19 N/A Total Curve Count 782 Total FI & Equity Factor Count Comments Spot exchange rates for 92. All exchange rates are relative to USD Airline, Auto, CMBS, Credit Card, Equipment, Home Equity, Manufactured Housing, Structured RMBS US Agency Issuers - FHLB, FHLMC, FNMA 17 DM Countries, 12 EM Countries AUD, CAD, CHF, EUR, GBP, JPY, USD 5 Rating Categories DE, DE-Jumbo, DK, ES, FR, SE-EUR, SE-SEK 15 DM Countries, EUR, 22 EM Countries 15 Eurozone Countries 22 EM Countries issuing USD bonds EUR AAA, EUR IG, USD AAA, USD IG 15 DM Currencies, 22 EM Currencies 13 DM Currencies, 6 EM Currencies Table 1: AXGMM Factor Definitions & Coverage Axioma 6

7 United States and Canada: Europe: +44 (0) Asia: New York 17 State Street Suite 2700 New York, NY Phone: Fax: Frankfurt Axioma Deutschland GmbH Mainzer Landstrasse 41 D Frankfurt am Main Germany Phone: +49-(0) Atlanta 400 Northridge Road Suite 850 Atlanta, GA Phone: Fax: Geneva Axioma CH Rue du Rhone 69, 2 nd Floor 1207 Geneva, Switzerland Phone: Chicago 2 N LaSalle Street Suite 1400 Chicago, IL Phone: Fax: Hong Kong Axioma, (HK) Ltd. Unit B, 17/F, Entertainment Bldg 30 Queen s Road Central Hong Kong Phone: Fax: London Axioma, (UK) Ltd. St. Clements House Clements Lane London, EC4N 7AE Phone: Fax: +44-(0) Melbourne Axioma (AU) Ltd 31 st Floor 120 Collins Street Melbourne, VIC 3000 Australia Phone: +61-(0) Paris Axioma (FR) 19 Boulevard Malesherbes 75008, Paris, France Phone: +33-(0) San Francisco 201 Mission Street Suite 2150 San Francisco, CA Phone: Fax: Singapore Axioma, (Asia) PTE Ltd. 30 Raffles Place #23-00 Chevron House Singapore Phone: Fax: Tokyo Axioma, Japan Tekko Building 4F Marunouchi, Chiyoda-ku Tokyo Japan Phone: Sales: sales@axioma.com Client Support: support@axioma.com Careers: careers@axioma.com