  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.
