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Sounds like PCA is not the approach you're looking for. If you're looking to transform a risk vector in terms of securities V into a risk vector in terms of securities W, then the basic approach would be to perform a linear regression of V against W. The resulting regression coefficients will form a matrix B which will give a change of basis between V and W. ...


This is the challenge for below-mean semivariance in optimization. Since the mean becomes a moving target, the observations that impact the min function change. Estrada proposed a heuristic method for optimization and Beach(2011) discusses the decomposition and semi covariances. Below target semivariance assumes investors do not change their target ...


The best solution is to matrix-price these bonds first. For each bond, either find a comparable bond or use your own judgment to determine the appropriate spread to a benchmark curve (e.g., OAS to LIBOR), then use the daily LIBOR curve and the corresponding OAS to obtain the daily prices.

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