Black–Litterman Weights for Overlapping Funds and Securities

Summary

The document raises a portfolio construction problem for applying Black–Litterman when selected instruments overlap in their underlying holdings. Examples combine a broad equity fund, a clean energy fund, and individual stocks that may be constituents of those funds or fit multiple sector definitions. The question is how to assign market capitalization weights without counting the same underlying companies repeatedly.

It also asks whether expected returns can then be estimated through reverse optimization. The document offers no weighting procedure, model specification, or empirical comparison, so it does not establish how to resolve overlap or whether standard reverse optimization applies unchanged. Its contribution is to identify an implementation issue that arises when portfolios mix broad funds, sector funds, and single-name exposures.

Key ideas

• Fund holdings can overlap with one another and with directly selected stocks.
• Overlapping exposures complicate market capitalization weighting because underlying capitalization may be counted more than once.
• The question concerns portfolios mixing broad funds, sector funds, and individual securities.
• The document asks whether reverse optimization remains applicable but provides no answer or implementation method.

Tags

# Black-Litterman Weights for Intersecting Asset Classes


# Black-Litterman Weights for Intersecting Asset Classes












I'm trying to implement Black-Litterman for an arbitrary selection of assets some of which might be subsets or intersect with others.

For example, one portfolio might be

- US Equities (VTI)

- A global clean energy sector ETF (ICLN) which would include some US equities

- VWDRY that's a constituent stock/holding of ICLN

- TSLA that might be considered part of the clean energy sector

Another example portfolio might be

- CARZ, an automobile ETF

- ICLN, global clean energy ETF with some members overlapping with CARZ

- TSLA, which could be considered part of both

What would be the best way to calculate the "market capitalization weights" for these instruments given that there might be overlap between these instruments in terms of market cap sizing?

Once market cap sizing is done, would I be able to estimate expected returns in the same way using the reverse optimization method?

Thank you!

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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