Understanding what is Risk & Alpha?

Say you are a L/S equity HF PM managing a book. If you returned 10% (after hedging out market risk) and say 6% of your returns are attributable to factor risk, is the 4% residual alpha risk free, driven by arbitraging away market mispricings? Or is that 4% residual actually driven by mainly idiosyncratic risk? Or is it a mixture of both?

We also assume that no other undiscovered common factor return exists within the residual.

I guess what I’m asking is, what are we exactly paying for “manager skill”?


If market neutral, it’s residual (I’m using residual loosely).

If you are long KO, short PEP: the risk free in the long cancels out with the short.


Sorry I didn’t clarify what I meant. Like yes, by going L/S market neutral, you are hedging the market equity risk premium + the risk free rate. However, within the returns EXCESS of the market & risk free rate, the attribution of these excess returns is driven by factor returns and selection.

My main question is: what exactly is selection?

Is it idiosyncratic risk? Or is it a riskless return if you spot a mispricing within the market? Or is it a mixture of both?


It can be anything - it’s typically idiosyncratic. That’s the hedge fund model. There’s always risk even if something is mispriced. Just lower or higher risk/reward.


The formal definition is the excess performance relative to a benchmark, though I've seen that conflated with the amount of returns generated from idiosyncratic risk.


Performance over benchmark = alpha

Returns not otherwise explained by market factors = returns attributable to idiosyncratic risk

I think alpha may get conflated with idio returns the closer beta is to 1.


Alpha is fully described by whatever you consider risk, not the other way around. Lets say that your only "risk" is beta/market risk - then going long or short factors like value/growth will be considered alpha in this context. Alpha is whatever return cant be explained by whatever risk model you are using.


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