XMb 2PPA XRb MB 26f3pAtx6RBt t t t t

The following example illustrates the calculation of expected active beta return, active beta surprise, and benchmark timing return given portfolio return information. Data for the active portfolio beta and the benchmark returns for one year over 12 consecutive months is given in Figure 3. Long-term expected excess benchmark returns are selected to be 6%. All other values are calculated, as described as follows.

Performance Analysis: Examining Active Systematic Returns (Figure 3) Column 1: t

12 individual periods are examined. . Column 2: ¡3pA(t)

Gives the active portfolio beta for each period t

Ppa M = average active beta over the entire examination period Column 3: RB(t)

Gives the benchmark excess return over each period t

Rb(í) = average benchmark return over the entire examination period Column 4: ¡3pA(t) x R0(t)

Active systematic returns for each period t are calculated in this column. This is only to ensure that the breakdown of active systematic returns into active beta return, active beta surprise, and active benchmark timing return yields the same total as calculating active systematic returns with the decomposition.

In this example, total active systematic returns are found to be 1.5234% Column 5: S(3pA(t)

The deviation of the active portfolio beta is the difference between the beta in period t and the overall average.

The deviation from the average benchmark excess return is the difference between the benchmark excess return in period t and the overall average excess return.

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