alpha is in excess of beta. For example, stocks return 8% with a std of 16% but your stock selection portfolio did 12% with the same risk. That’s “4% alpha” (super simplistic but just an example). If you’re doing trend following then your beta is the benchmark of trend followers.
in the above example, you were able to generate 4% above the benchmark. How? You might say “we found that companies exhibiting XYZ characteristics tend to outperform the market” — that’s an anomaly to EMH right? If EMH says all things are priced in and you find something that’s not, then you found an exception to the rule. Note: if your standard deviation (“std”) goes up then you are in fact aligned to EMH (because in EMH you can only make more returns if you take on more risk).
active risk is the difference between your portfolio and the benchmark. E.g. say a 60/40 portfolio is 60% equity and 40% bonds. Because you’re worried about the market you underweight equities — so your mix looks like 30%/70%. If you beat the 60/40 benchmark, you did so because you took active risk on your equity underweight.
