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Portfolio Analysis and Optimization Tools

Question: Instead of using quantitative analysis to make investment decisions, are there any quantitative investment tools or strategies that analyze and/or optimize an actively managed portfolio?

Here are some examples to help explain what I am asking.

Example 1: Using variance/covariance calculations to determine the correlation between assets, therefore analyzing diversity of risk.

Example 2: Build models to test a given portfolio's reaction to different economic shocks or past scenarios.

Thank you in advance for any input!