Portfolio Volatility Contributions of Risk Factors in the Presence of Risk Factors Multi-collinearity

Attributing the volatility of a portfolio to some exogenous risk factors which are not directly invested in by the portfolio may be a topic of interest to asset managers. Without any restriction on the nature of risk factors, we must take into account that their returns may exhibit strong correlations. Risk factor returns multi-collinearity causes severe problems in estimating their portfolio volatility contributions. In order to solve this issue, we propose a risk attributing pipeline that applies an orthogonalisation algorithm to risk factor returns. Most importantly, the risk factors interpretability is preserved, in the sense that the orthogonalised risk factors are the ones attaining the least Frobenius norm of the matrix of deviations from the original risk factors.