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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!

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