Rolling Black-Litterman Implied Returns for Out-of-Sample Portfolios

Summary

The document considers an out-of-sample portfolio process that updates monthly. It uses a rolling 36-month covariance estimate to construct a minimum-variance portfolio, reverse-optimizes those weights into implied returns, combines the estimates with investor views, and optimizes again to obtain portfolio weights. The central question is whether recalculating implied returns each month is appropriate when some published approaches show only one set.

The text does not include an answer or empirical results. It raises the possibility that implied returns should vary as the covariance estimate, portfolio weights, or market capitalization inputs change. A rolling process is therefore a modeling choice to examine, not a conclusion established here. Any evaluation would need to specify the reverse-optimization assumptions and ensure that all inputs at each rebalance date use only information available then, while accounting for estimation noise and turnover.

Key ideas

• A monthly out-of-sample process can recompute covariance estimates and minimum-variance weights.
• Reverse optimization maps portfolio weights and risk inputs into implied returns.
• The document asks whether those implied returns should be updated at each rebalance.
• It provides no empirical comparison, and rolling inputs may introduce estimation noise and turnover.

Tags

# Black-Litterman implied returns using rolling window


# Black-Litterman implied returns using rolling window












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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.