Factor Models

Definitions

Factor models are based on the inherent assumption that a set number of factors that are able to explain the differences in returns between different assets or the same assets at different times.
Factors (in this context) can be any time-series including technical analysis factors (relative strength index, Bollinger bands, etc.), macroeconomic factors (CPI, inflation, etc.), sentiment factors (Twitter, MorningStar, etc.), and more.
Factor models are similar to principal component analyses (PCAs) models in that they aim to explain the price action of an asset by decomposing the original price/returns time series into a set of explanatory factors.
PCAs aim to reduce the number of explanatory variables for a given variable forecast based on observed variables. Factor models predict observed variables (forecast variables) based on latent variables.

Factor models are used extensively by Concrete’s collateral risk engine. To be specific, the core price forecasting model for forecasting the probability of collateral depreciation/loan liquidation is a factor model.
Concrete utilizes factor models to generate a range of different time horizon forecasts including 1 day, 1 week, and 1 month.

Example factor model
Factor models seek to maximize variance, while factor models seek to can be optimized towards a given variable and do not have a necessarily unique solution (unlike PCAs).
PCAs are well-suited to explaining variance, but not correlations between factors. Factor models are well-suited to explaining correlations, but not variance.
Let R be an n by 1 vector of returns for n assets, and let F be a k by 1 vector of latent factors that affect the returns. The factor model assumes that the returns of each asset can be represented as a linear combination of the factors, plus an idiosyncratic error term where is an n by 1 vector of intercepts and B is an n by k. represents an n by 1 vector of idiosyncratic terms.
The factor model decomposes the returns into a linear combination of the factors, with each asset’s exposure to each factor given by the corresponding element of the factor loading matrix.
Examples of the initial factors used by Concrete in the context of the collateral risk engine can be seen in the diagram below.