Rp pfcXRfrSp

k where:

Rp = the total portfolio return

]TXPk x Rfk = the common factor return k

Sp = the specific return

Performance attribution can be applied not only to total returns, but also to active returns, and even active residual returns. Next we'll describe the process of applying attribution to active portfolio returns. Active portfolio returns are defined as:


Where, much like total returns, the active returns are decomposed into returns that are attributed to factors and specific (or residual) returns. Unlike total returns, however, all of the active returns are credited to the manager. Active returns are defined as the portfolio returns less the benchmark returns. Active returns are thus the result of the manager's skill. An analysis of active returns can help determine the source of these returns that are over and above the benchmark. Also, analysis of factor contributions can reveal whether or not a particular strategy worked. For example, if an analyst adds value, the contribution of that factor would be positive.

Using the mathematical definitions and relationships of the components of active returns, they can further be decomposed into three components: Active systematic returns, active residual returns attributed to common factors, and active residual returns attributed to portfolio specific factors. Using these components, active portfolio returns can also be defined as:

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