Correlation, co-dependency and risk aggregation [14]

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Bullet points include: Aim is to characterise distributions of returns (movements) for each instrument (asset or liability) in a parsimonious manner. Usually proceed as follows, for j’th instrument’s return in period t. Here beta j,k is the exposure (beta) of the instrument to the k’th factor, xk,t is the return on the k’th factor (for period t) and epsilon j,t are residual (idiosyncratic) components. Portfolio described by a vector of (active) weights a then has expected return of a.alpha and (expected future) tracking error (standard deviation of returns) as follows (where beta is matrix formed by beta j,k):

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