One last thing - I'm an absolute beginner to all this. So do you know of any resources from where I can learn about what models or inputs are used for what strategies? In other words, how do I build up that "trader's skill" of identifying which model uses the same inputs as the ones that affect a trading strategy? I guess I could refer research papers, but there are so many of them that it's overwhelming to find the "right" research paper/article.

Suppose that I use a strategy of assigning weights to stocks on the basis of their returns. I could use the CAPM model to model the market dynamics, but I'm sure there are other, lesser known models that give an expression for stock returns, but with different inputs. Would a decision on which of those models to use (for representing market dynamics) also depend on the trader's experience and skill?

Thanks, that's a very nice explanation! So from what I understand, the market dynamics could be expressed in the form of a model, for example CAPM. A shift or change in the "market dynamics" could then be detected by estimating the model parameters at different times and noticing at what point a significant change in those parameters occured. My follow-up questions is, how do we know which model to use? Based on what factors do we select our model?

Z-scoring seems to be useful if all the weights in the vector represent the same sector stocks. If we have some vector with $4$ entries - $2$ for one sector and $2$ for another, we could apply Z-scoring to the individual vector subsets. But then how do we account for the relative strength of the signals for the $2$ industries? For example, our original vector may be such that more weights (stronger signals) were assigned to one industry as compared to the other.

Oh okay. I was confused at first because I was using the same formula but with the sample standard deviation.

Could you please explain how $(2.5, 4.0, 7.5)$ got transformed to $(-1.03, -0.32, 1.35)$? I'm not familiar with the concept of Z-scoring. Are there any other techniques apart from Z-scoring that would preserve the strength of the original weights and yet result in new weights adding to $0$?

@muffin1974: We look at the historical data for the 2 stocks (in this case, the past week's price data). Then we calculate the weekly return for each stock. The positions are calculated on a relative basis, that is, weekly return for G and A are 2.5% and 7.5% respectively, so we simply assign them positions 2.5 and 7.5. If we had USD 10 mil to invest, we'd invest USD 2.5 mil in G and USD 7.5 mil in A.