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?

#QuantitativeFinance

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Comments

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 - 6 years ago

Apart from trying to bound the roots of the characteristic equation, what other ways can we use?

Calvin Lin Staff - 6 years ago

Non-negativity of the determinant would yield the same necessary result.

Abhishek Sinha - 6 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$