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I am building an active risk-based Portfolio with a risk-based Portfolio such as the minimum variance Portfolio as the neutral starting point. Therefore, I calculate the rolling 36 month covariance matrix, optimize to obtain the Minimum variance portfolio weights and reverse optimize to get the implied return estimates. Merging These estimates with my views and optimizing again yields my final views for the portfolio.

Lets say I want to test my strategy out-of-sample and I want to re-run the optimization at the end of each month. Therefore, each month, I would calculate a new covariance matrix and obtain a new set of weights and implied returns. In the literature I have read, however, only one set of implied returns is given, i.e. no rolling window is used to get the implied returns. See for example the paper by Emmanuel Jurczenko and Jerome Teiletche "Active Risk-Based Investing" (https://jpm.iijournals.com/content/44/3/56).

Am I missing something here or is it fine to get a new set of implied returns each month? It might because I am not using the market cap to get the implied returns, but the market cap also changes over time, therefore getting different implied returns would still make sense. Would really appreciate if someone could make that clear.

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