I would tend to go with the definition in the textbooks I have read. Or Wikipedia.
But you can define it however you wish 
I think this is an inaccurate description of regression toward the mean. And it is more a theorem than a definition. Once you define correlation you really cannot get away from it—assuming the correlation is not one.
[quote]
Final questions for the audience: Given that sharing of our own alpha contributes to our own alpha-decay, are their situations in which selective sharing within a closed system (i.e., a cabal) results in a net increase one’s alpha (i.e, increases information arbitrage faster than information diffusion)?
[/quote]I am again going to take the liberty to reword your question and address the new question:
Q. When does it pay to share your secret sauce?
A #1. When you are selling your services. The performance will go down, but your profit may go up from subscribers and/or investors. For example, by sharing a designer model, you may make more money from subscriptions than you lose in investment gains.
A #2. When you learn by teaching. I have learned many things from writing. Sometimes I get a good suggestion for an improvement. More often, the process of writing forces me to look up the data and the studies that I took for granted which may teach me something new. It also pushes me to think things through. Besides, I have found that people are less interested in my intellectual property than I am, which means that they don’t clone it as much as I would have expected.
A #3. Collaboration. No matter how good you get, there are always going to be things that someone else is better at. If we collaborate with a small group of talented people, each one of us may end up with better results than we would have been able to do individually.
Jim -
I admit I had never heard of statistical mean regression as opposed to mean reversion in the finance sense. Wikipedia has two very different entries for “Regression to the mean” and “Mean reversion (finance).”
We’re talking about alpha decay here. That’s mean reversion in the finance sense, not mean regression in the statistics sense. Mean reversion is essentially symmetrical. Stock prices revert to the mean. The question is whether strategies and factors do too.
One of the foundations of modern portfolio theory is that alpha is unsustainable. Jensen and Sharpe both tried to prove that; Malkiel took the same position. I take more of a Warren Buffet position: I believe that no matter what the future holds, careful use of fundamentals will, in the long run, beat the market. In other words, some alpha does not revert to the mean. Maybe it regresses to the mean in some instances (though I’m not exactly sure what that means), but it bounces right back.
But you probably agree with me so this is just a semantic quibble.
It would be a quibble only if—for some reason—I were not allowed to make my own inferences from your data.
Me, I am happy to investigate whether mean reversion, mean regression and regression toward the mean are, in fact, different concepts. Or as Galton originally called it: “reversion towards mediocrity.” Maybe Galton was talking about my portfolio and not statistics at all:-)
I’m happy to investigate whether the field of finance is really using the terms differently, for their correlations, than statisticians do. And why, if that is the case. Many people in finance are quite capable mathematically and it would be hard to imagine that any published differences are by accident.
I appreciate the opportunity to discuss this.
Thanks!
-Jim