Before revision: Factor models are commonly used in financial applications to analyze portfolio risk and to decompose it to loadings of risk factors. A linear factor model often depends on a small number of carefully-chosen factors and it has been assumed that an arbitrary selection of factors does not yield a feasible factor model. We develop a statistical factor model, the random factor model, in which factors are chosen at random based on the random projection method.
After revision: In a very high-dimensional vector space, two randomly-chosen vectors are almost orthogonal with high probability. Starting from this observation, we develop a statistical factor model, the random factor model, in which factors are chosen at random based on the random projection method.