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The math behind portfolio optimization has a problem. If you have N stocks and only T days of data, your correlation matrix is mostly noise. In this video, only 8 eigenvalues out of 400 were real signal. The other 392 were statistical illusion. The fix comes from nuclear physics. In 1955 Wigner used random matrix theory to model the energy levels of uranium nuclei. In 1967 Marchenko and Pastur extended his framework to sample covariance matrices, giving the exact formula for which eigenvalues ar
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The dot product is a way to combine two vectors to get a single number. You multiply the matching components of the two vectors and then add those results together. For example, if you have two 2D vectors, you multiply the x-values together and the y-values together, then add those two numbers. The result tells you something about how much the two vectors point in the same direction. If the result is zero, the vectors are at a right angle to each other. There’s also a geometric way to understand
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