Hi Christophe,
Good question — this is actually a very common use case for Wolfram Language in finance.
Yes, it is possible to work with members of major indices like DJIA or NASDAQ, but this generally requires using Wolfram Language (Mathematica) rather than plain Wolfram|Alpha queries. Wolfram has built-in financial data functions that make this much easier.
For example, index constituents can be retrieved via entities, such as FinancialIndex and FinancialInstrument. Once you have the list of tickers, you can pull time series data (prices, returns) and then compute correlations using built-in functions like Correlation or CorrelationMatrix.
Regarding fundamentals (market cap, P/E ratio, etc.), Wolfram provides access to many of these properties through entity properties, although coverage can vary by market and by company.
As for automatic financial analysis: Wolfram|Alpha itself is more query-based and limited, but in Wolfram Language you can absolutely automate analysis — from correlation tables to factor comparisons and basic portfolio analytics — provided the data is available.
So in short:
Yes, index members can be selected programmatically
Yes, correlation tables are very feasible
Full automation is much more realistic in Mathematica than in Wolfram|Alpha alone
Hope this helps, and curious to hear if others here are using Wolfram for portfolio or factor analysis.