Risk Management interview preparation

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1. 066What does it mean if an estimator is BLUE?Statistics and quant foundationsHardtechnicalUBSRisk Management · Zurich · 2021

   Say this

   Best Linear Unbiased Estimator. Among all estimators that are linear in the data and unbiased, it has the smallest variance. That's the Gauss-Markov result: ordinary least squares is BLUE provided a specific set of assumptions holds.

   Then walk it

   1. Unpack each word, because that's what the question is testing. Linear in the observations. Unbiased, so its expected value equals the true parameter. Best, meaning minimum variance within that class.
   2. The Gauss-Markov conditions: correct linear specification, errors with zero conditional mean, homoskedasticity, no autocorrelation, and no perfect multicollinearity. Notice normality is not required for BLUE. You need normality for the t and F tests in small samples, not for OLS to be efficient.
   3. The restriction that matters is 'linear'. A biased or non-linear estimator can easily beat OLS on mean squared error. Ridge and lasso are deliberately biased and often predict better, and James-Stein shrinkage famously dominates the sample mean. So BLUE is optimality within a box, not optimality.
   4. In finance the assumptions fail routinely. Returns are heteroskedastic and volatility clusters, so OLS stays unbiased but the standard errors are wrong, which means your t-statistics lie. That's the practical consequence and it's the one to lead with when asked what breaks.
   5. The fixes: White or Newey-West robust standard errors for heteroskedasticity and autocorrelation, generalised least squares if you know the error structure, and instrumental variables if the regressor is endogenous. Endogeneity is the serious one, because it destroys unbiasedness rather than just efficiency.
   6. The distinction to keep straight: heteroskedasticity and autocorrelation cost you efficiency and valid inference. Omitted variables, measurement error in a regressor and simultaneity cost you unbiasedness. Those are different problems needing different fixes.
   7. So the answer I'd close with: BLUE is a useful benchmark and a weak guarantee. In a risk model I care more about whether the specification is right and whether the relationship is stable than about being efficient within the linear unbiased class.

   Where candidates lose it

   Expanding the acronym and stopping, or claiming normality is a Gauss-Markov requirement. It isn't. The two answers that separate candidates are that 'best' is only within linear unbiased estimators, so biased shrinkage estimators can beat it, and that in finance the binding violation is heteroskedasticity making your standard errors wrong.

   Expect next

   • Is normality required for OLS to be BLUE?
   • Which Gauss-Markov assumption fails most often in financial data?
   • Can a biased estimator ever be preferable?

   Reported by candidates at UBS (Risk Management, Zurich, 2021). Source: Wall Street Oasis.

Firm tags come from public, anonymous candidate reports on Wall Street Oasis: strong signal, not sworn testimony. Firms are named as the places a question was reported, not as partners of Fin Maverick. Answers are written for this page to show how to think out loud; they are not scripts to recite.