Second Order Risk

TL;DR

This paper introduces a new risk measure that accounts for second order risk, which arises from model uncertainty in portfolio optimization, and demonstrates its effectiveness in predicting portfolio volatility.

Contribution

It proposes a novel risk measure specifically designed to capture second order risk caused by model uncertainty in portfolio management.

Findings

Second order risk significantly impacts realized portfolio volatility.

The proposed measure accurately forecasts out-of-sample portfolio behavior.

Empirical studies confirm the importance of accounting for second order risk.

Abstract

Managing a portfolio to a risk model can tilt the portfolio toward weaknesses of the model. As a result, the optimized portfolio acquires downside exposure to uncertainty in the model itself, what we call "second order risk." We propose a risk measure that accounts for this bias. Studies of real portfolios, in asset-by-asset and factor model contexts, demonstrate that second order risk contributes significantly to realized volatility, and that the proposed measure accurately forecasts the out-of-sample behavior of optimized portfolios.