Suppose you could command a phalanx of eager graduate students to perform the following experiment:

- Measure the correlation between the price histories of Gold and Crude Oil
- Run some trading system or another, on Gold and on Crude Oil
- Capture the equity curves when running the trading system on Gold and Crude Oil
- Measure the correlation between the Gold equity cuve and the Crude Oil equity curve
- Which is bigger? The correlation in item (1) or the correlation in item (4)?

There would be numerous choices to make along the way, such as: how many months or years of price history to use; whether to measure correlation on "price" or "price changes"; how big a slice of time to use when measuring correlation; what trading system to simulate; which commodities to use (Gold and Crude Oil may not be your favourite choices); and others. These choices are embedded in any discussion of market correlation and market-system correlation.

Wouldn't it be interesting, if the equity curves from trading Gold and trading Crude Oil, showed significantly more correlation than the price histories of Gold and Crude Oil?

Conversely, wouldn't it be just as interesting, if the equity curves showed significantly less correlation than the price histories? Would that be the ever elusive "free lunch" that investors seek?

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Now suppose you have a second bevy of eager grad students, and you launch them on the following experiment:

- Buy historical price data for >100 commodities for >20 years
- Pick a trading system such as PGO filtered Donchian (here) or VLT Turtle (same link) or another; ideally a profitable and robust system
- Add code to the system so the simulator will print RAR, Robust Sharpe, R-Cubed, and other performance statistics of your liking, on every test.
- Using the random portfolio selector Block kindly provided by nickmar and Jake Carriker (found here), run that trading system on 4000 randomly chosen 20-commodity portfolios out of the 100 commodity universe
- Read the printed statistics file ("Print Output.csv") into Excel and calculate the median values of Robust Sharpe Ratio and the other performance statistics, from the 4000 simulation runs.
- Repeat steps 4&5 but this time, run on 4000 randomly chosen 40-commodity portfolios. Record the median Robust Sharpe Ratio
- Repeat steps 4&5 but this time, run on 4000 randomly chosen 60-commodity portfolios. Record the median Robust Sharpe Ratio
- Make a table of (number of commodities in portfolio) versus (median Robust Sharpe Ratio). What conclusions can you draw?

Perhaps the median Robust Sharpe Ratio gets better and better and better, as you add more and more commodities. Which may have something to say about correlation.

Or perhaps the median Robust Sharpe Ratio stays about constant, getting no better and no worse as you add more and more commodities. Which probably tells you something different about correlation.

Or .... (you get the picture)