Applications in Finance

“It is interesting, chemically, no doubt,” I answered, “but practically —” Dr. Watson in “Study in Scarlet” Multivariate statistical analysis is frequently used in quantitative finance, risk management, and portfolio optimization. A basic rule says that one should diversify in order to spread financial risk. The question is how to assign weights to the different portfolio positions. Here we analyze a so-called mean-variance optimization that leads to weights that minimize risk given a budget constraint. Equivalently, we may optimize the weights of a portfolio for maximal return given a bound on the risk structure. The discussion naturally leads to links to the capital asset pricing model (CAPM).