An excellent analysis of the reality of equity curves, Jim, but I respectfully point out that I see them as having a different, and very useful, purpose.
For me, equity curves are simply a tool to compare the relative performance and stability of various strategies or concepts. I use them as a visual compilation of many statistics: slope, stability, standard deviation, consistency, etc.
They’re an excellent way to verify that a trading strategy is valid; if this and this happens, would it be prudent to enter a trade?
I don’t expect to be taking $1M trades. I just want to apply the same set of rules & criteria consistently over a long period of time in a variety of conditions, with different types of instruments to validate a theory. The equity curve is merely a graph of the results, another way to “see” the statistics - and an excellent way to compare the relative merits of various systems.
That said, you’ve presented a number of excellent ideas over the years for measuring risk and mitigating its effect that I’d like to see incorporated.