I am trying to combine multiple forecasts on each of N assets in line with Grinold and Kahn's methodology, taken from Active Portfolio Management, 2nd ed. On p.311, they suggest transforming the raw forecasts g into a set of uncorrelated (orthogonal) forecasts y. This is done as follows: \begin{align*} Var\{g\} = H^T\cdot H\\ y \equiv (H^T)^{-1}\cdot[g-E\{g\}] \end{align*} Can someone please explain what the matrix H is and what process is going on here?


I do not have access to this book but I suppose the decomposition is the cholesky decomposition (if you use R, simply generate it with


where g is a matrix with forecasts.
What the transformation is doing are essentially two steps: 1. You replace the forecasts g with the normalized forecasts g-E(g). This can be done by demeaning the matrix (R: demean) 2. Your normalize the variaton by 'dividing' with the part of the cholesky decompostion. Recall: In the univariate case the part $(H^T)^{-1}$ would correspond to the standard deviation.

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    $\begingroup$ Thanks - i'm working in Python so chol = np.linalg.cholesky(np.cov(old_signals, rowvar = False)) new_signals =np.linalg.inv(chol)*old_signals $\endgroup$ – William Dorsey Feb 8 '17 at 18:49

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