active beta definition
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Hi asja,
Can you see this for help: http://forum.bionicturtle.com/viewthread/598/
Image copied here:
http://learn.bionicturtle.com/images/forum/activeReturns.png
Ch 17 Grinold is tough standalone assigment (as i mentioned in the video), frankly, because it is the culmination of the entire book; you almost need to read 1-16 to follow 17!
the active return is the portfolio return - benchmark (not the alpha/residual, right?)
active systemic return = active beta * (excess) benchmark return; active systemic return is what gets decomposed into three pieces in Ch 17
active beta is the exposure to the benchmark that contributes to the active return
analogy: CAPM beta is exposure to ERP that contributes to expected return
another (better, I think) way to view this formula is:
active return = factor*exposure + active residual
(note resemblence to APT: the universal factor model is: E(r) = exposure*factor + exposure*factor + etc)
that's how i prefer to view this formula: as a version of the generic factor model (focused on *active* return) where the factor exposure are divided into two sets. Then, as usual, a residual too.
...okay, but here we break the factor*exposure into two sets:
1. active beta; i.e., exposure to benchmark
2. exposures to non-benchmark but still common factors
Re: "Up(t) equal to Upar(t)?"
The Up(t), i think, is just a generic factor model reference; in fact, i think it could apply to APT (i am short on time, sorry, or i'd research it)
Upar(t) is more specifically about active returns: the factor model (think APT) is very generic and can be used with various metrics. In this case, it's about the decomposition of the *active* return
David
Can you see this for help: http://forum.bionicturtle.com/viewthread/598/
Image copied here:
http://learn.bionicturtle.com/images/forum/activeReturns.png
Ch 17 Grinold is tough standalone assigment (as i mentioned in the video), frankly, because it is the culmination of the entire book; you almost need to read 1-16 to follow 17!
the active return is the portfolio return - benchmark (not the alpha/residual, right?)
active systemic return = active beta * (excess) benchmark return; active systemic return is what gets decomposed into three pieces in Ch 17
active beta is the exposure to the benchmark that contributes to the active return
analogy: CAPM beta is exposure to ERP that contributes to expected return
another (better, I think) way to view this formula is:
active return = factor*exposure + active residual
(note resemblence to APT: the universal factor model is: E(r) = exposure*factor + exposure*factor + etc)
that's how i prefer to view this formula: as a version of the generic factor model (focused on *active* return) where the factor exposure are divided into two sets. Then, as usual, a residual too.
...okay, but here we break the factor*exposure into two sets:
1. active beta; i.e., exposure to benchmark
2. exposures to non-benchmark but still common factors
Re: "Up(t) equal to Upar(t)?"
The Up(t), i think, is just a generic factor model reference; in fact, i think it could apply to APT (i am short on time, sorry, or i'd research it)
Upar(t) is more specifically about active returns: the factor model (think APT) is very generic and can be used with various metrics. In this case, it's about the decomposition of the *active* return
David
Hi David,
"active systemic return = active beta * (excess) benchmark return;"
Are you saying that Rb(t) is actually not benchmark return, but benchmark return - RFR? Why do we care about excess return or RFR here? Is it because they are from CAPM?
so Rb(t) is benchmark return - RFR, which is consistent with CAPM, but Bj(t) is not excess return, which is consistent with APT. so the whole thing is a mixture of CAPM and APT?
Thanks.
"active systemic return = active beta * (excess) benchmark return;"
Are you saying that Rb(t) is actually not benchmark return, but benchmark return - RFR? Why do we care about excess return or RFR here? Is it because they are from CAPM?
so Rb(t) is benchmark return - RFR, which is consistent with CAPM, but Bj(t) is not excess return, which is consistent with APT. so the whole thing is a mixture of CAPM and APT?
Thanks.
Hi asja,
No, the APT is excess return, also. Grinold is pretty much excess returns (returns over riskfree) throughout.
Grinold sets that up early, it applies to the APT example in Ch 7:
http://www.bionicturtle.com/premium/spreadsheet/1.a.5._grinold_apt_7.1_7.2/
those are excess returns, both APT and CAPM...David
No, the APT is excess return, also. Grinold is pretty much excess returns (returns over riskfree) throughout.
Grinold sets that up early, it applies to the APT example in Ch 7:
http://www.bionicturtle.com/premium/spreadsheet/1.a.5._grinold_apt_7.1_7.2/
those are excess returns, both APT and CAPM...David
Hi David,
There is one more point that I am confused about. Performance analysis is to test the significance of the attributed returns. but i could not find an example. Is it basically to test BETAi is significant with t-stat (beta(i) / (standard error(i)). Does each factor have an "info ratio"? I am asking because Schweser says "the active systematic returns and residual retunrs (from common and specific factors) can be tested for statistical signicance using t-stat for info ratios"
Thanks.
There is one more point that I am confused about. Performance analysis is to test the significance of the attributed returns. but i could not find an example. Is it basically to test BETAi is significant with t-stat (beta(i) / (standard error(i)). Does each factor have an "info ratio"? I am asking because Schweser says "the active systematic returns and residual retunrs (from common and specific factors) can be tested for statistical signicance using t-stat for info ratios"
Thanks.
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