Let me give you a long and winding answer (gee, how out-of-character for me!!!) that may set important context before addressing the specifics.
There is no such thing as a mathematical or statistical series or phenomenon. When we speak of them, we are using verbal shorthand to describe something else. (Actually, that can probably be said for every field to which statistics applies.) For those who are knowledgable about investing (or whatever other field may be applicable), the notion that statistical information is just a shorthand description of something else is so well known, it need not be stated over and over again. And in fact, people who do state it again and again find it hard to participate in sensible conversation and are likely to be shunned as a-holes.
Example: Stock price momentum. It doesn’t exist. It never existed. It never will exist. And because old-time academicians thought investors really believed in it, they came up with all sorts of nonsense to refute it, such as the random walk theory, etc. When legit folks are talking about momentum, what they are really talking about, even if they don’t verbalize it (and they pretty-much never do) is this: On day 1, a stock moves because of reason A. If reason A continues to exist on days 2, 3, 4, etc., the stock will continue to move as it did on day 1. It’s a lot easier to talk in terms of momentum rather than in terms of the sustainability of the underlying reason for the price action. And since the world does tend to change in more of an evolutionary than revolutionary manner, we usually have enough sustainability to create the conditions that empiricists see and refer to as the momentum factor.
This applies all over the place. In technical analysis, we speak of support-and-resistance, overbought-oversold, MACD, RSI, etc., etc., etc. All flow from behavioral phenomenon that are so well accepted that they need not be referred to in discussion (and are best not referred to lest the speaker come to be seen as an overly pedantic jerk).
The same holds true of mean reversion. It’s a verbal shorthand way of addressing a very very well established body of knowledge relating to what known is known to happen when conditions become extreme. There is an inherent tendency to exhaust and reverse. Lao Tzu noticed it and described it in the Tao Teh Ching. Aristotle learned of it and it forms the foundation for Nicomacean Ethics. In Economics 101, they describe it by discussing, for example, how excess profits attract additional suppliers into a market and how this keeps happening until profits recede to the point of unacceptability, at which time suppliers start to exit and things move in the other direction. Sometimes these things play out quickly (technical analysis). Sometimes, they play out generationally (the current Democratic Left representing a corrective stage that started when Regan and the Republicans took over DC back in 1980). Etc., etc., etc.
So starting with your third topic, regression to the mean, yes it exists. Its built into the human condition (actually, we never regress “to” the mean; we tend to regress (or, rather, move) “to and then beyond” the mean in the other direction and back and forth.
As to whether a good performing model will regress to the mean, the answer is tied not to the model’s performance but to the market phenomenon to which the model is tying itself. The more a model tilts toward market extremes, the more confidently we can assume its performance will regress as extremes correct. (This is why I am so bothered by things like MktCap-smaller-is- better and similar items. I know it’s pushing toward the “risk-on” extreme and that as good as it can perform when the market is friendly toward high levels of risk, I also know how ugly it will get when the market climate changes — and I have seen too many p123 users, including most of the 1st generation Designer Model community, ignore warnings about it, and we all know what happened.) The challenge is one of timing. We can never know how long the pendulum will swing. Sometimes, its fast. But we are seeing the business cycle is lengthening; ditto the interest rate cycle, etc. And external factors always intervene to mess things up because the world as an irritating way of always changing. (Considering where interest rates have been for a while now, we should be experiencing rampant inflation; that we aren’t is testament to how much the world (external variables) has changed since traditional notions came into being.
So to choose one model vs another based on an assumption of regression to the mean, one would have to follow and understand the markets; what they are doing and how things develop, Modeling is useless. We’ve already busted all the relevant historically established precedents so we’re all in new territory.
If one isn’t/doesn’t want to become proficient in understanding market dynamics, the most prudent course is to aim a model at central tendencies that are likely to perform badly under some extremes, wonderfully under others, but on the whole, more or less middle of the road. (This, by the way, is why there’s such a Quality bias in the Invest models I built, even though its hurting relative performance now. In that business/advisory model, its not feasible for me to swap models in and out all the time based on what I think of the market, so I push them to a place better likely to tolerate auto-pilot. I aimed to do likewise in Designer Models; my goal is sustainability, not to win a performance contest in any particular month.)
So I have to disagree about well-designed models performing better. Well designed models are those that are more proficient in producing stocks consistent with one’s goal, but no amount of model design can influence what the market wants to favor or not favor in any particular time period.
Moving up to question 2, it’s a similar answer. Always pick the model that best delivers what one wants. One can always want the best performance, but that often leads to anger or disappointment because it often doesn’t match what the real world can deliver. And the longer it takes for Mr. Market to switch gears, the more shocking it is to those who got caught. (This is why a generation ago, when mutual fund families got big, they worked so hard, often in vain, to discourage the public and fund newsletters, from chasing the highest performing funds.) It’s the goal that counts. Here’s a link to a year-or-so-ago article in which I actually wrote-up and chose a model that tested badly (and explained why).
https://seekingalpha.com/article/4185747-screening-shield-reit-yield-hogs-butchers-knife?source=all_articles_title
As to the first question, item “d” alone seals the deal. If that occurs, ditch the model without even bothering to define over-optimized. Items “a,” “b” and “c” are things that should prompt serious thought about over optimizing, although none are silver bullets. Even slippage: For liquid stocks, we need not even bother, except insofar as we use slippage as a proxy for commissions because bid-ask spread differentials vaporize over the course of even weekly hold periods. For illiquid stocks, real-world slippage can be much higher than any p123 member would ever assume in a model. In the real world, any alpha above zero makes the portfolio manager a hero, so in sim, where even the best designers inevitably have some 20-20 hindsight, I’d say any alpha above 3-5% is suspect, the higher the alpha, the bigger the danger. Small numbers of holdings are definitely a danger factor (but we have to be sure to define “small” differently between stocks and ETFs; for the latter, 5 positions can be too many.)