Questions / Quant research, Portfolio & factor risk
A tiny risk eigenvalue can attract enormous leverage
Along one covariance eigenvector, expected return is 0.002 and estimated variance is 0.00001. An unconstrained mean–variance objective is μx−(2/2)λx². What exposure x does the optimizer choose?
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Answer: 100 exposure units
- The solution is x=0.002/(2×0.00001)=100. A small apparent variance makes the inverse-covariance allocation extremely large even for a modest forecast.
Interview shortcut. x = μ/(λ × 2 × var): a tiny variance means a huge position.
In the app this has a follow-up where one thing about the setup changes. Try the follow-up.