@Grant, you said: “... wouldn't have customers lining up to pay 2/20 for SPY”. Yes indeed, even if some hedge funds do about the equivalent of a SPY return, some even less.
I would add, Q won't see that many paying 2/20 for the risk-free rate either. But, their game plan is different. And, if I understand it correctly, it is very serious business.
Why are the foundations as to the structure of capital markets important even in a gaming environment? It is very simple. Whatever the path that might link all that stuff from point a to point z, if it helps us better understand the game we play, then we can find ways to extract from it what we want.
It is like finding that the coin you will be using in what is suppose to be a 50/50 scenario is in fact biased. Knowing that the coin is biased, you have to find what is the best “betting system” that will not only respect the bias you found but also make it that you will not fail. Can someone lose playing a 90/10 biased coin? Yes, and it will be by going all-in all the time. The ride will be great until the first reverse flip.
The point being: it is our job to find the bias. Some call it predicting. But, whatever. If you find that, on average, some 60% of your bet selection are favorable by whatever means you used to find them, then your game plan should be a lot easier to design and implement. You should simply favor this bias whatever its direction.
It is like when @Thomas says: “...We are looking for alpha which is by definition unrelated to beta (and not present in the CAPM formulation used here).” See: https://www.quantopian.com/posts/beta-constraint-in-risk-model-totally-unnecessary#5a61ec83eb948e03e7c89407
To which I say: yes, and no.
True, the CAPM has no alpha: E[R(p)] = r_f + β∙(E[R(m)] – r_f). The EMH states that there is none to be found, there is no free-lunch. Saying that whatever alpha, it is arbitraged away. However, markets are not that efficient.
In Q's notebook, https://www.quantopian.com/lectures/the-capital-asset-pricing-model-and-arbitrage-pricing-theory they present the SML (security market line) formula as: E[Ri]=RF+ß(E[RM]-RF).
The difference being considering the asset's Ri return in a portfolio instead of the portfolio itself. And fair enough, in this case the beta will be all over the place. The more volatile a stock the higher the beta. However, when they picture the SML, they give it an intercept of zero, when in fact, it should be RF, the risk-free rate. Renaming the intercept as alpha is a misnomer. We already have a definition for the SML. (see: https://en.wikipedia.org/wiki/Security_market_line if need be)
The thing is when you look at a portfolio, you are looking at an ensemble of stocks. And the more stocks you put in a portfolio, the more something funny will happen. The portfolio beta will tend to 1! The CAPM equation will reduce to: E[R(p)] → E[R(m)]. At the limit, buying all the stocks will make it: E[R(p)] = E[R(m)].
But, we all build portfolios with only a few hundred stocks in them. Even there, the portfolio beta is approaching one: β(p) → 1. Therefore, what one should expect is that his/her portfolio will vary in step with the market as a whole. Your portfolio becomes itself a proxy for a market index since being so close to it. In fact, if you keep increasing the number of stocks in your portfolio you will be approaching the expected market return, as they would say in math, almost surely.
We talk about CAPM, EMH, efficient frontiers, efficient and optimal portfolios, and then want to ignore their consequences. They are not perfect models, but they do reasonably explain what we see as a generalized framework.
You want to neutralize the beta, then one way to do it is:
E[R(p)] = r_f + β∙(E[R(m)] – r_f) – β∙E[R(m)]
But that too has a conclusion. And again, there is no alpha in it.
If you want some alpha, you will have to grow it, from the outside by bringing more of your skills to the game, (read a better betting system), and make it yourself:
E[R(p)] = r_f + β∙(E[R(m)] – r_f) – β∙E[R(m)] + α