Multi-Factor Risk Attribution Concept and Uses
Introduction Why do we need risk attribution? What are we trying to achieve with it? What is the difference between ex-post and ex-ante risk? What is the multi-factor model for risk? What kinds of analyses can an end investor expect? What are the advantages and disadvantages of the multi-factor risk model? 2/11
Risk Budgeting Process Asset Owners Need Risk Estimates What is it? A quantitative, model-based process for allocating investment risk across portfolios or managers Step 1 Goal Setting What are the benefits? Provides a consistent, objective framework for decision making Helps to identify and quantify unintentional and unmanaged risks Reduces the cost of contracting Increases the latitude that managers have to add value Step 2 Risk Budget/ Asset Allocation Step 3 Manager Weighting/ Guidelines Step 5 Risk Management and Rebalancing Capital Market Assumptions Manager Forecasts Step 4 Portfolio Management 3/11
Risk Estimation and Attribution Goals and Uses Goals Understand the future riskiness of portfolio Based on current portfolio positioning Identify how decisions generate risk Identify how decisions interact with each other from a risk point of view Understand risk sensitivity to portfolio changes What problems do we need to solve to achieve our goals? How to measure risk How to attribute risk 4/11
What is Risk? Ex-post versus Ex-ante Assumption: risk is volatility => standard deviation of return Ex-post Backward-looking estimate Based solely on the time series of observed returns Completely ignores changes in portfolio positioning (i.e. weight in equity, duration of portfolio, existence of alternative asset classes) Ex-ante Forward-looking estimate Requires some kind of a model of portfolio and/or security returns Combines current portfolio positioning with observed variability of model drivers 5/11
Multi-Factor Model for Ex-Ante Risk Fundamental Factor Model Methodology Starting point is return Assumption: return (at security level) can be explained by a linear combination of exposure to systematic factors and their returns plus a security specific return Exposures to systematic factors can be measured at a given point of time Returns to systematic factors are estimated via a multiple linear regression return factors security, period exposure security, factor, begin _ period * factor _ return factor, period Examples of fundamental factors Equity factors: currencies, industries, fundamentals (size, style, momentum), countries Fixed income factors: yield curve factors, Euro country spreads, sector spreads, quality spreads Alternative factors: commodity type, real estate type, hedge fund strategy Return to risk Exposures remain unchanged Factor returns become a covariance matrix (volatility and correlation of factors) Multiplication becomes matrix math Specific return volatility can be ignored for large, diversified portfolios specific _ return security, period 6/11
An Example Overall Portfolio Level For illustrative purposes only, based on Wilshire Associates Risk Model 7/11
An Example Sub-asset Class/Manager Level For illustrative purposes only, based on Wilshire Associates Risk Model 8/11
An Example Manager Positioning Level Sources of Relative Risk Region Country Industry Fundamental Currency Covariance Specific Risk 0.2 0.1 0-0.1-0.2 Fundamentals: Net Exposures and MCTE 2 1 0-1 -2-3 2 1 0-1 Log Market Cap E/P Ratio Book/Price Volatility Momentum Net Z-Score (bars) -2-3 Industry: Net Exposures and MCTE 0.06 0.04 0.02 0-0.02-0.04-0.06-0.08-0.1 9/11 Materials Utilities Energy-EE Food Bev. Tob. Pharma&Biotech Banks Insurance Semiconductors & Telecomm Services Capital Goods Software Real Estate Materials-EE Food & Staples Transportation Consumer Services Comm Services & Auto&Comp Health Eqpt & Srvcs Consumer Durables Retailing Household & Prsnl Energy Tech Hardware & Media Div. Financials Net Weight (bars) For illustrative purposes only, based on Wilshire Associates Risk Model
Why Choose a Multi-Factor Risk Attribution? Advantages and Disadvantages Advantages Full flexibility of attribution (grouping of factors) Asset class, sub-asset class, portfolio manager, manager positioning, security level Consistent methodology for risk budgeting decisions at all levels of investment process Current portfolio positioning is fully captured and reflected in risk estimates and attribution Disadvantages Need a multi-factor risk model Need extensive amounts of data For estimating model Security level data for exposure and returns Almost impossible to do without a dedicated system and know-how 10/11
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