Adding the active return to the table we have:
|
Period |
(1)
Portfolio Returns |
(2)
Benchmark Returns |
Active Return
(1 − 2) |
Security Selection Effect (SSE) |
Market Allocation Effect (MAE) |
|
1 |
8.90% |
6.90% |
2.00% |
40%
0.4 × 2% = 0.8% |
60%
0.6 × 2% = 1.2% |
|
2 |
14.54% |
11.30% |
3.24% |
20%
0.2 × 3.24% = 0.648% |
80%
0.8 × 3.24% = 2.592% |
The two period active return (RA,2) for each attribute can be determined using the following equation:
RA,2 = Ra,1(1 + Rb,2) + Ra,2(1 + Rp,1)
Where:
Ra,1 = active return for period 1
Rb,2 = return of the benchmark in period 2
Ra,2 = active return for period 2
Rp,1 = return on the portfolio for period 1
SSEA,2 = 0.8(1 + 0.113) + 0.648(1 + 0.089) = 1.596%
MAEA,2 = 1.2(1 + 0.113) + 2.592(1 + 0.089) = 4.158%
The overall active return is the sum of the individual attribute active returns = 1.596 + 4.158 = 5.75%
Alternatively the overall portfolio active return can be determined by compounding the periodic portfolio and benchmark returns and subtracting the compounded benchmark return from the compounded portfolio return as follows:
Compounded portfolio return = (1.089)(1.1454) − 1 = 24.73%
Compounded benchmark return = (1.069)(1.113) = 18.98%
Portfolio active return = 24.73% − 18.98% = 5.75%
