EMA Alpha Toolbox

Statistically Robust Factor Models for Alpha development

Risky and risk-free returns – “alpha” – are unavoidably tied up with one another as they together make up total returns and what is assigned to one component is deducted from the other. Whatever is assessed as risk affects the perception of what “riskless” alpha remains.

In particular, a risk model should not be designed around the investment process itself – using the manager’s valuation measures as factors, for example – as that will make it more likely that the model will not account for the unintended systematic bets in a portfolio – and it is the identification of these in which the true value of a risk system lies.

Instead, when seeking to develop a quantitative estimate of alpha, there is a case for building a custom risk model that spans the systematic risk space but which is correctly able to distinguish risk from alpha. This will increase the probability that any apparent superior returns from a backtest are not simply compensation for risk taken.

The EMA Alpha Toolbox models correct for this “contemporaneous/simultaneous estimation bias” to allow for use of full-information maximum likelihood (FIML) estimation techniques for risk-adjusted testing of valuation/trading models. FIML estimation avoids issues associated with having to divide data sets into two groups, one for risk-parameter estimation (beta) and a second for performance measurement (alpha). FIML estimation also allows for the use of securities with partially missing returns histories.

The Toolbox can be used in the model building process by creating user specified sub-period alpha measures synchronized to measure performance immediately following updated fundamental/technical valuation model variables utilizing weighted regression analysis. It can also be used in testing a completed multi-variable valuation model based on the buy/sell signals of the model.


  1. Robust non-Normal models of residual variance remove undue influence from outliers and avoid Contemporaneous Estimation bias caused by heteroskedasticity
  2. Full Information Maximum Likelihood estimation routine using all data for more efficient estimation, including securities with partially missing returns
  3. Optimal attribute creation from a combination of other attributes
  4. Valuation Model/Trading Strategy-testing using user-supplied period-by-period buy-sell indicator matrix
  5. Bootstrapping test results to determine significance and remove bias
  6. The MATLAB interface provides access to the Alpha Toolbox methods without C# programming. The MATLAB interface can be used with MATLAB’s wide array of data analysis tools.

The EMA Alpha Toolbox supports the quantitative investment manager in securing superior risk-adjusted returns.