AxiomaAXWW4World-WideEquityFactorRisk Model

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RISK MODEL FACT SHEETAxioma AXWW4 World-Wide Equity Factor RiskModelEquity Factor Risk ModelsOctober 2017ContentsModel Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2Fundamental Factor Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3Statistical Factor Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5Factor Volatilities / Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5Currency Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5Specific Risks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6Data Deliverables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6Appendix: AXWW4 Industry Factors vs. GICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8Appendix: AXWW4 Results Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10Model Fit and Factor Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10Copyright 2020 Qontigo GmbH

AXWW4MODEL OVERVIEWModel OverviewAsset CoverageAs of 2017, the model covers roughly 42,700 securities (over 77,700 historically), primarily from the following 48 markets:ArgentinaDenmarkIrelandNew adaGreeceLuxembourgPolandTurkeyChileHong olombiaIndiaMoroccoSingaporeCzech Rep.IndonesiaNetherlandsSouth AfricaIn addition, the following 46 emerging markets are included; the first groupwas included in 2003 and the second in 2009 and the third in aLatviaQatarSri mibiaTunisiaTrinidad & TobagoEcuadorKenyaNigeriaUkraineGhanaLebanonSaudi ArabiaVietnamJamaicaMaltaSerbiaZambiaIvory wePalestinianTerritoryBosnia &HerzegovinaEstimation UniverseIncludes assets with sufficient size and liquidity, using selection criteria similarto those employed by major index providers. More granular, localized rulesare also applied on a per-market basis to filter certain exchanges, asset types,etc. In early 2017, the estimation universe comprised 12,700 securities on average.Forecast HorizonMedium-horizon model: 3-6 months; Short-horizon model: 1-2 months.Copyright 2020 Qontigo GmbH2

AXWW4Model Variants (4)FUNDAMENTAL FACTOR MODELMedium- and short-horizon, fundamental and statistical factor models areavailable. Using Axioma Portfolio , the fundamental factor models can be rebased into country- or industry-focused versions, for risk decomposition orperformance attribution tailored to a specific investment process.Estimation FrequencyFactor exposures, returns, covariances and asset-specific risks estimated daily.Fundamental Factor ModelStyle FactorsAXWW4-MH (12)AXWW4-SH (13)Market-Based FactorsMarket Sensitivity2-year weekly beta versus the global market1-year weekly betaVolatility6-month average of absolute returns over cross-Same (3-month average)sectional standard deviation, fully orthogonalized to Market SensitivityShort-Term MomentumN/ACumulative return over past monthLiquidityNatural logarithm of the ratio of 3-month av-Same (1-month average daily volume,erage daily volume and 1-month average mar-3-month Amihud ratio)ket capitalization, inverse of 6-month Amihudilliquidity ratio, and proportion of returns-tradedover last calendar yearExchange Rate Sensitivity2-year weekly beta to returns of currency basketSame (1-year weekly beta)containing USD, EUR, GBP, JPY, CNYMedium-Term MomentumCumulative return over past year excluding the most recent month (same for MH andSizeNatural logarithm of market capitalization (same for MH and SH models)SH models)Fundamental Factors (same for MH and SH models)ValueBook-to-priceEarnings YieldEarnings-to-price and estimated earnings-to-priceLeverageTotal debt (current and long-term liabilities) to total assets and total debt to equityGrowthSales growth, estimated sales growth, earnings growth, estimated earnings growthProfitabilityReturn-on-equity, return-on-assets, cash flow to assets, cash flow to income, grossDividend YieldRatio of sum of the dividends paid (excluding non-recurring, special dividends) overmargin, and sales-to-assetsthe most recent year to average market capitalization(See the AXWW4 Model Supplement Document for exact factor definitions)Industry Factors (68)GICS -based, corresponding to GICS 2016 Industries with 0/1 assignments.Assets with no official GICS are given industry membership based on internalresearch and are explicitly labeled as such in product deliverables.Copyright 2020 Qontigo GmbH3

AXWW4Global Market FactorFUNDAMENTAL FACTOR MODELRegression intercept term; all assets have unit exposure. Allows the model tobetter distinguish between country and industry risk contribution effects.Country Factors0/1 assignments based on an asset’s country of quotation, business activitiesor domicile. In most cases this is equivalent to the market where an assettrades; the issuer’s home country is used for foreign listings, depository receipts, and similar instruments.Currency Factors0/1 assignments to the primary currency of an asset’s country.Local FactorsMeant to capture strong residual structure in certain markets not captured byothers factors. The model currently has one such factor: Domestic China.Returns ModelModels local asset excess returns using five sets of factors: a global marketfactor, countries, industries, styles, and local factors. Currency factors are onlyintroduced in the risk estimation stage.Returns HistoryMedium-horizon model: 4 years of daily returns for factor correlations, 2 yearsof daily returns for factor volatilities.Short-horizon model: 4 years of daily returns for factor correlations, 2 year ofdaily returns for factor volatilities.EstimationConstrained robust linear regression using Huber weight function and squareroot USD capitalization weights. Style, industry and country factors are included in the regression. Local factors are estimated via an auxiliary regression on the residuals. The capitalization-weighted industry and country factorreturns are each constrained to sum to zero. Currency factor returns are computed directly from exchange rates against USD.Numeraire CurrencyCurrency risk is expressed from a U.S. Dollar (USD) perspective, but advancedfeatures in Axioma Portfolio enable users to dynamically re-base the modelinto various other currencies.Copyright 2020 Qontigo GmbH4

AXWW4CURRENCY RISKStatistical Factor ModelStatistical Factors (20)All assets have exposure to the statistical factors.Currency Factors0/1 assignments to the primary currency of an asset’s country.EstimationTwo-Pass Asymptotic Principal Components factor analysis with residual variance adjusted returns. One year of daily local excess returns are used. Currency factor returns are taken from the same currency risk model used by thefundamental factor model.Numeraire CurrencyCurrency risk is expressed from a U.S. Dollar (USD) perspective, but advancedfeatures in Axioma Portfolio enable users to dynamically re-base the modelinto various other currencies.Factor Volatilities / CorrelationsEstimationCovariance of exponentially-weighted daily factor returns.Half-life ParametersMedium-horizon model: 125 days for variances, 250 days for correlations.Short-horizon model: 60 days for variances, 125 days for correlations.AutocorrelationNewey-West adjustment accounting for three days of autocorrelation. A fixedlag of 1 day is used for statistical factors.Returns AsynchronicityReturns-timing technique is applied to the factor estimation process to compensate for non-synchronous trading between world stock markets.AdjustmentsAxioma’s proprietary Dynamic Volatility Adjustment (DVA) procedure is used toanalyze trends in factor returns dispersion and adjust risk estimation accordingly to allow for heightened responsiveness in risk forecasts and adaptabilityto the prevailing volatility regime.Currency RiskMiscellaneousCurrency risks in all models are taken from the Axioma Global Currency RiskModel, ensuring that all regional/global risk models share consistent estimatesof currency risks and covariances.EstimationPrincipal components analysis using 1 year of exchange rate returns and 12statistical factors, estimated from a pool of core currencies: USD, EUR, GBP,JPY, CHF, CAD, AUD, BRL, MXN, SGD, KRW, ZAR and PLN.Copyright 2020 Qontigo GmbH5

AXWW4DATA DELIVERABLESSpecific RisksEstimationVariance of exponentially-weighted daily specific returns.Half-life ParametersMedium-horizon model: 125 days, Short-horizon model: 60 days.HistoryMedium-horizon model: 500 days.Short-horizon model: 500 days.AutocorrelationNewey-West adjustment accounting for 1 day of autocorrelation.Other AdjustmentsIssuer Specific Covariance (ISC) captures covariances between security lines ofthe same issuer, using a cointegration model of price behavior. Applies onlyto portfolios containing two or more securities from the same issuer.Data DeliverablesAvailabilityUpdated daily and downloadable via FTP and SFTP.Historical CoverageDaily history from Jan. 1997 onwards.Data FormatDelimited text file (“flat files”) or proprietary database format for seamless integration into Axioma Portfolio and Axioma Backtester .BenchmarksGlobal and regional benchmarks are available in a format compatible with Axioma software products.ExchangeTradedFunds(ETFs)Broad coverage of regional, single country, and index linked ETFs. ETF coverage for the model is determined by the model’s full coverage of the underlyingconstituents in order to ensure consistency in the instrument’s risk and exposure measures.Factor Mimicking PortfoliosFor MH Fundamental Model Style factors (daily update).(FMPs)Statistical Model Factor Re-250 days of Statistical factor returns history (daily update).turns (PRET)Asset IdentifiersAxioma ID, SEDOL, CUSIP, ISIN, local ticker, issuer/company ID.Copyright 2020 Qontigo GmbH6

AXWW4Market DataDATA DELIVERABLESAsset-level data including: Price, market capitalization 1-, 5-, 20-, and 60-day returns 5- and 20-day average daily volume Historical and predicted betaSome items of market data may not be available in delimited text file format.Copyright 2020 Qontigo GmbH7

APPENDIX: AXWW4 INDUSTRY FACTORS VS. GICS AXWW4Appendix: AXWW4 Industry Factors vs. GICS GICS Industry Groups (24)Axioma Industry Factors (68)1010 Energy1510 Materials2010 Capital Goods2020 Commercial & Professional Services2030 Transportation2510 Automobiles & Components2520 Consumer Durables & Apparel2530 Consumer Services101010Energy Equipment & Services101020Oil, Gas & Consumable Fuels151010Chemicals151020Construction Materials151030Containers & Packaging151040Metals & Mining151050Paper & Forest Products201010Aerospace & Defense201020Building Products201030Construction & Engineering201040Electrical Equipment201050Industrial Conglomerates201060Machinery201070Trading Companies & Distributors202010Commercial Services & Supplies202020Professional Services203010Air Freight & Logistics203020Airlines203030Marine203040Road & Rail203050Transportation Infrastructure251010Auto Components251020Automobiles252010Household Durables252020Leisure Products252030Textiles Apparel & Luxury Goods253010Hotels Restaurants & Leisure253020Diversified Consumer Services2540 Media254010Media2550 Retailing255010Distributors255020Internet & Direct Marketing Retail255030Multiline Retail255040Specialty Retail3010 Food & Staples Retailing301010Food & Staples Retailing3020 Food, Beverage & Tobacco302010Beverages302020Food Products302030Tobacco303010Household Products303020Personal Products351010Health Care Equipment & Supplies351020Health Care Providers & Services351030Health Care Technology352010Biotechnology3030 Household & Personal Products3510 Health Care Equipment & Services3520 Pharmaceuticals, Biotechnology & Life SciencesCopyright 2020 Qontigo GmbH8

APPENDIX: AXWW4 INDUSTRY FACTORS VS. GICS AXWW4352020Pharmaceuticals352030Life Sciences Tools & Services401010Commercial Banks401020Thrifts & Mortgage Finance402010Diversified Financial Services402020Consumer Finance402030Capital Markets402040Mortgage Real Estate Investment Trusts (REITs)4030 Insurance403010Insurance4040 Real Estate404020Equity Real Estate Investment Trusts (REITs)404030Real Estate Management & Development451010Internet Software & Services451020IT Services451030Software452010Communications Equipment452020Technology Hardware, Storage & Peripherals452030Electronic Equipment, Instruments & Compo-4530 Semiconductors & Semiconductor Equipment453010Semiconductors & Semiconductor Equipment5010 Telecommunication Services501010Diversified Telecommunication Services501020Wireless Telecommunication Services551010Electric Utilities551020Gas Utilities551030Multi-Utilities551040Water Utilities551050Independent Power & Renewable Electricity Pro-4010 Banks4020 Diversified Financials4510 Software & Services4520 Technology Hardware & Equipmentnents5510 UtilitiesducersCopyright 2020 Qontigo GmbH9

AXWW4APPENDIX: AXWW4 RESULTS OVERVIEWAppendix: AXWW4 Results OverviewModel Fit and Factor PerformanceFigure 1: Average 1-month adjusted R-squared for the model estimation universe, 1997-2017. The results for themedium- and short-horizon Fundamental models are very similar, so we have only shown the results for theFundamental-MH model.Copyright 2020 Qontigo GmbH10

AXWW4APPENDIX: AXWW4 RESULTS OVERVIEWFigure 2: Total risk bias statistics for selected benchmark portfolios, 1997-2017. The vertical lines represent thebounds of the 95% confidence interval. Bias statistics beyond these lines are significantly different from 1.00.Figure 3: Total risk bias statistics for selected benchmark portfolios, 1997-2017. The vertical lines represent thebounds of the 95% confidence interval. Bias statistics beyond these lines are significantly different from 1.00.Copyright 2020 Qontigo GmbH11

AXWW4APPENDIX: AXWW4 RESULTS OVERVIEWFigure 4: Cumulative return to each of the AXWW4-MH Fundamental Style factors, 1997-2017.Figure 5: Cumulative return to each of the AXWW4-MH Market-based Style factors, 1997-2017.Copyright 2020 Qontigo GmbH12

AXWW4APPENDIX: AXWW4 RESULTS OVERVIEWFigure 6: Cumulative return to each of the AXWW4-SH Fundamental Style factors, 1997-2017.Figure 7: Cumulative return to each of the AXWW4-SH Market-based Style factors, 1997-2017.Copyright 2020 Qontigo GmbH13

AXWW4APPENDIX: AXWW4 RESULTS OVERVIEWFigure 8: AXWW4-MH factors’ frequency of statistical significance, 1997-2017. Market Sensitivity, for example, isstatistically significant 78% of the time.Figure 9: AXWW4-SH factors’ frequency of statistical significance, 1997-2017. Market Sensitivity SH, for example,is statistically significant 77% of the time.Copyright 2020 Qontigo GmbH14

Axioma AXWW4 World-Wide Equity Factor RiskModelBy Qontigo GmbHFirst published October 2017This version published 9 March 2020Copyright 2020 Qontigo GmbH.axiomaBlue, Axioma Risk, Axioma Portfolio Analytics,Axioma Portfolio Optimizer, and Axioma Risk Model Machineare trademarks of Axioma, Inc. All other company, organization,product, or service names referenced herein may be trademarksof their owners.

AXWW4 APPENDIX:AXWW4INDUSTRYFACTORSVS.GICS Appendix:AXWW4IndustryFactorsvs.GICS GICS IndustryGroups(24) AxiomaIndustryFactors(68) 1010 Energy 101010 Energy