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Creating portfolio risk and return models [20]

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Bullet points include: Most PCA algorithms calculate all eigenvectors/eigenvalues simultaneously However, suppose V is an n x n covariance matrix with (sorted) eigenvalues 1, 2, ..., n (largest is lambda 1) and corresponding (normalised) eigenvectors q1, q2, ..., qn. Suppose our importance criterion involves f(a) = aTVa, and |a|=1 Then a can be expressed as a = a1q1 + ... + anqn with a12 + ... + an2 = 1 And f(a) = a121 + ... + an2n so f(a) is maximised when a = q1 And eigenvectors are orthogonal, so removing one from output signals leaves remainder still to be extracted

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