Medium · Linear Algebra & Optimization · Numerical · ~8 min · #36

How Negative Can Three Correlations Be?

Real interview · Jump Trading, Citadel Securities

Three random variables have the same pairwise correlation $\rho$ for every pair. What is the smallest possible value of $\rho$ ?

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Worked solution

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Reported in interviews

Jump TradingGlassdoor interview question
Reported for n variables (the lower bound is −1/(n − 1)).
Citadel Securities· Quant ResearcherGlassdoor interview reviews

Candidate-reported and unverified; the firm may phrase it differently or no longer ask it. The wording here is our own paraphrase, and the solution was written and checked independently of any answers posted at the source.

Concepts

Positive semidefinitenessEigenvalues of equicorrelation matrices

Relevant for

Quant ResearcherQuant Trader