# Statistical vs Fundamental

**Machine-learning algorithm plus familiar descriptors**

The essential structure of the most common market risk linear factor models is similar in form, comprising:

- a set of time-series factors
- sensitivity measures (betas) of each asset against each factor and
- the relationships between the factors

However, the means of arriving at these model components varies by risk model vendor, depending on the statistical approach deployed.

Because one of the key objectives of a linear factor model used for risk analysis purposes is to allow the attribution of portfolio risk to a range of underlying sources, it is essential that those underlying sources – the descriptive variables to which risk will be allocated – be defined in the model construction process. To enable this, EMA and its traditional competitors have developed two-stage processes, but the order of the processes, as shown in the table below, is different.

Table 1: Model construction process stages

Model Type |
Stage 1 |
Stage 2 |

Traditional | Judgement based definition of descriptive variables to represent Countries, Sectors, Fundamental attributes etc | Estimate a regression (best fit) model based on the defined descriptive variables and observed historic asset returns |

EMA | Machine learning method to estimate a maximum-likelihood factor model directly from the observed asset returns | Define descriptive variables to represent Countries, Sectors, Fundamental attributes etc and map them to the factors |

So, both types of system carry out the same two steps, but other vendors define the descriptors first and then use those to build the model, while EMA builds the model first and then defines descriptors that map on to the model factors.

The words “Fundamental” and “Statistical” are often used to characterise these two alternative approaches. While both are heavily statistical in nature, the names communicate that in the Fundamental approach the definitions of the model factors rely on a human-determined input – the “fundamental” characteristics of the assets – while the Statistical approach is closer to an “artificial intelligence” system in that the factors are deduced from the observed (asset return) data.