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Finance Quant Interview - II

For what values of \(p\) is

\[ \begin{pmatrix} 1 & p & 0.6 \\ p & 1 & -0.8 \\ 0.6 & -0.8 & 1 \\ \end{pmatrix} \]

a correlation matrix?

Note by Calvin Lin
2 years, 3 months ago

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A correlation matrix must be Symmetric and Positive Semi-Definite and hence all its eigenvalues must be real and non-negative. Writing out the characteristic equation for the above matrix and requiring the above condition yields \[-0.96 \leq p \leq 0\] Abhishek Sinha · 2 years, 3 months ago

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@Abhishek Sinha Apart from trying to bound the roots of the characteristic equation, what other ways can we use? Calvin Lin Staff · 2 years, 3 months ago

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@Calvin Lin Non-negativity of the determinant would yield the same necessary result. Abhishek Sinha · 2 years, 3 months ago

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