The classical risk modeling approach relies upon one risk estimate. Regrettably, portfolio managers are often disappointed at the accuracy of the risk model. One must never forget that a risk model is an attempt to simplify reality to provide an estimate. Axioma Portfolio incorporates both the Axioma Alpha Factor as well as the flexibility to incorporate more than one risk model. Clients can then decompose, validate and stress-test their portfolios relative to a number of different methodologies as a means of "triangulating" on what is real.
The classical portfolio rebalancing approach maximizes expected return for a given level of risk through the solution of an optimization problem. In Axioma Portfolio, risk may be included as a constraint or in the objective with a risk-aversion coefficient. Realistic strategies for managing portfolios often include additional quantities in the objective, such as market impact costs and additional restrictions on the structure of the final portfolio and trade list-features not present in the classical model. Axioma Portfolio offers a comprehensive list of goals (objectives) and rules (constraints) for creating optimization strategies. Any possible combination of objectives and constraints is supported by Axioma Portfolio's proprietary optimization engine.
Key Features
Fully Integrated Market Data: With Axioma Portfolio, market data and Axioma Robust Risk Models are available as an option within the application. The addition of data greatly decreases the time required to create the data environment in Axioma Portfolio, allowing the user to focus on portfolio analysis and optimization.
Robust Risk Models: Many practitioners know that risk models tend to oversimplify reality. The result is that estimates rarely succeed in becoming reality. Approaching the problem from a new perspective, Axioma has developed models that dynamically find what is missing in a risk model based upon client-specific portfolios. This new technology, named the Axioma Alpha Factor, significantly improves accuracy and minimizes the ill effects of estimation error in portfolio analysis and rebalancings.
Robust Optimization: Robust optimization allows information about estimation error in expected returns to be explicitly incorporated in the optimization process. This provides portfolios that are more likely to perform well over a wide range of future market outcomes, through the direct incorporation of parameter uncertainty in the portfolio rebalancing problem
Hierarchical Optimization: Axioma Portfolio pioneered a technique called hierarchical optimization. This feature handles infeasibilities in the optimization model in a very 'smart' way. Hierarchical optimization allows the user to assign a priority to each constraint in the model. If it is not possible to find a solution that satisfies all the constraints simultaneously, Axioma Portfolio will find the solution that minimizes the constraint violations, based on the priority assigned to each constraint.
Greater Data Flexibility: Axioma Portfolio incorporates data manipulation tools that simplify the creation of powerful constraints. For example: the user may create the restriction "do not hold securities with a price under $10." Axioma Portfolio will automatically update the list of assets affected, based on the current asset prices.
Flexible Risk Control: Multiple risk models may be used to measure risk in a single strategy. Common factor risk and specific risk may be treated separately in objectives and constraints. Constraints on Marginal Contribution to Risk can be imposed on risk factors, as well as individual assets. Marginal contributions may be calculated relative to a benchmark if desired.
Composite Assets, such as futures and ETFs, are seamlessly supported in Axioma Portfolio. The application also includes tools for specifying user-defined composites and new constraint classes to control exposure attributes of portfolios that include composites.
Available Objectives [within Portfolio Rebalancing]
Axioma Portfolio gives users the ability to customize their analyses by allowing the following objectives to be used individually or in combination:
Expected Return - Robust* Return or standard Expected Return
Risk - variance or standard deviation, absolute terms or benchmark-relative, specific risk and factor risk may be weighted separately
Transaction Costs - linear, piecewise-linear, quadratic, or 3/2 power
Tax Liability - exact tax calculation using HIFO, LIFO, or specific lot accounting
Net Tax Gains - harvest tax losses or reduce realized gains
Any linear function of the net, long, or short holdings
Any quadratic function of the holdings
*Robust MVO is a proprietary methodology only available in Axioma Portfolio.
Available Constraints
The table below lists the quantities that can be constrained. For each constraint type we indicate whether a maximum or minimum limit (or both) may be imposed. We also indicate whether the type can be applied to individual assets, weighted groups of assets, or the global list of assets. The Units column lists the available units for expressing the restriction. The Benchmark Relative column indicates whether the restriction can be placed on the active holdings or risk. The final column indicates whether or not the restriction can be softened. Many of the constraints in Axioma Portfolio may be softened, that is, the constraint bound may be violated by paying a penalty that is either linear or quadratic in the size of the violation.
