# Active Return (tracking error) vs. alpha?

So in the book it says that active return = return on portfolio - return on benchmark. How is this really different than alpha? I guess the book definition of alpha is actual return on portfolio - expected return…but in real life…people throw around alpha and it is meant to be the excess return over the benchmark, which seems to me is the same thing as “active return”? am i missing something here?

http://pages.stern.nyu.edu/~eofek/InvBank/Understanding%20Hedge%20Fund%20Performance.pdf check out pg 3 here and the footnotes- the 2 are pretty similar but can’t be used interchangibly b/c of risk. let’s say all of that active return earned were b/c the manager were swinging for the fences on some really risky name. is that really alpha or is the guy just swinging for the fences and got lucky? active return = alpha + (beta - 1)(rm - rf) if beta = 1, then active return = alpha

I still don’t get the difference between Alpha and Active return. Could someone provide me with an explanation? Many thanks!

Hey there,

So let’s first eliminate the notion that active return = alpha. Active return is the return earned by actively managing the portfolio against passive management. Now active return = Exp return on an actively managed portfolio - ex return on a benchmark. As an active manager, I need not always be the best in terms of generating alpha. For example as an active manager if I generate 5% on my portfolio but the benchmark generated say 10%, this is still active management but there is no alpha. I too was initially confused by this notion but when I thought about it, I figured it actually makes sense for active return to not necessarily mean an alpha. In the above example, I generated an active return of -5%. Now, even though this isn’t alpha it is still considered an active return even though I failed as a fund manager. As long as am managing the fund the way I want irrespective of the return, it is considered active.

A positive active return = alpha. Example if inhad generated 15% against the 10% benchmark return, the 5% is my alpha.

Hope this helps.

You can have negative alpha as I see on morningstar reports all the time. In your example that -5% active return but is not alpha simply because it’s negative active return I think is incorrect. Alpha is measured based on a suitable benchmark via beta, I assume? It can be positive or negative. I think bannis has it right. The alpha is the risk adjusted measure while active return is not adjusted for risk, simply the return from active management.

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Yeah, I guess. Makes sense.

As has been mentioned previously, alpha is a risk adjusted active return. From a formula perspective:

Active Return = Rp - Rb

Alpha = Rp - βRb

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