
Factor Analysis provides a rigorous and transparent approach to understanding the risk of a portfolio.
Background
Factor Analysis is in finance began in the mid-1970s following Stephen Ross's paper on arbitrage pricing theory which decomposed asset returns into a small number of core underlying factors. At its core, factor analysis assumes that the returns of any security can be broken down into a small set of underlying factors, common to all assets, and a security specific, idiosyncratic term. Many versions of factor investing have been developed and is a key tool for understanding portfolio risk and returns.
Approach In Clarity
Many factor models utilize macroeconomic variables, such as sensitivity to inflation & GBP, or fundamentals like market capitalization, value and momentum. While the results of these models are useful, they do not directly translate into an investable portfolio. With Clarity, we take a different approach. All of the factors are calculated directly from the returns of liquid ETFs, currencies and government bonds. This allows for a factor representation that can be easily understood and replicated in the market.
Clarity uses 3 core factors (US Equities - SPY, Nominal Interest Rates - 10YR UST Bond, FX - EURUSD) as the major drivers of risk and then a series of user defined residuals factors (tilts) that represent the risk to market sub-subsectors after the core risk is stripped out. Residual factors include mega-cap (QQQ), high yield (HYG) and EUR interest rates (10YR German Govt Bond).
To take a simple example, consider a portfolio consisting of $100mio of QQQ. The resultant factor risk is concentrated in core equities ($117.25mio of SPY which represents the traditional equity beta, a long $15.6mio position in 10YR UST which identifies that tech firms tend to do better in low interest rate environments, and $100mio in Nasdaq 100 Tilt (the residual factor risk of QQQ after the core market factors are taken out).

Historical Performance
While the core factors are easily observable, the residual factors are calculated using regression model. The performance over the past 2 years of a sample set of residual factors is shown below. Nasdaq 100 (QQQ) has outperformed the core market while energy (XLE) has heavily underperformed.

Relative Value
Factor Analysis may also provide a measure for which sectors of the market offer better relative value.

Resources
For a quick mathematical introduction to factor analysis in finance we would recommend David Hiller's video.
Additional videos link.