a book that I am currently reading states:
First, by combining stocks into a portfolio, we reduce risk through diversification. Because the prices of the stocks do not move identically, some of the risk is averaged out into a portfolio. Second, the amount of risk that is eliminated in a portfolio depends on the degree to which the stocks face common risks and their prices move together.
As to my understanding: A stocks return moves up or down either because of firm-specific or market wide risk. Firm-specific risk is uncorrelated across companies and is averaged out, so diversified, in large portfolios. Some companies of my portfolio will experience good (firm-specific) news and some bad news. In the long run, good and bad news should average out in a large portfolio, leaving me with the systematic risk of my portfolio, which cannot be diversified.
However, why does it states that the amount of risk that is eliminated (or remains) depends on the degree to which my stocks face common, so systematic, risks? Wouldn’t this statement imply that I am able to get rid of systematic risk when I find two stocks whose returns are perfectly negatively correlated? Of course, finding those stocks in practice is impossible but here I am more interested in a theoretical consideration.
Consider an equally weighted two-stock portfolio. One stock has a ß of 1 and the other of -1.
From a theoretical point of view, my portfolio would have no systematic risk. Would this not also be considered a diversification of systematic risk?