Model Risk in Risk Models: Quantifying Statistical Uncertainty in Active Risk

Abstract

Risk models commonly provide a portfolio’s ex ante active risk as a point forecast. Under the hood of risk models, this forecast relies on a bevy of statistical estimations that introduce uncertainty in the forecast. Failure to incorporate this uncertainty in the risk forecast can present an incomplete picture of the portfolio’s risk profile, particularly in periods of high volatility. This limitation may lead to an unintended risk-taking by portfolio managers. In this article, the author proposes a generalizable methodology to quantify the statistical uncertainty in an active risk forecast. This methodology can be applied to increase the precision with which portfolio managers take active risk, especially when volatility regimes change.

TOPICS: Portfolio management/multi-asset allocation, risk management, volatility measures

Key Findings

• ▪ Active risk of a portfolio is commonly provided only as a point forecast by risk models. Statistical uncertainty in this forecast can be quantified in real time using a bootstrap approach.

• ▪ This uncertainty is on the order of 25% of the risk forecast itself, and the amount of uncertainty generally rises in times of high volatility.

• ▪ Real-time monitoring of the statistical uncertainty in a risk forecast can help increase the precision with which portfolio managers take risk, especially when volatility regimes change.