To calculate allocation effect. We sum up the contribution to allocation for each sector the contribution to allocation in each sector is equal to the portfolio's sector weight minus the Benchmark sector weight times The Benchmark sector return minus the return for the entire Benchmark portfolio in consumer staples the portfolio manager chose to underweight versus The Benchmark 20% versus 30 percent. But because Consumer Staples outperformed the aggregate Benchmark, 13% versus 8.8 percent the decision to underway consumer stapleso lower the overall excess return the contribution to allocation is negative 0.4 percent the portfolio weight in the tech sector is equal to the Benchmark weight. Therefore there is no contribution to allocation effect in materials the portfolio manager held a higher weight than the Benchmark 35% versus 25 Sent but the sector underperformed the aggregate Benchmark negative 2% versus 8.8 percent therefore the decision to overweight materials lowered the overall excess return the contribution to allocation is negative 1.1 percent overall the combined allocation effect, which is the sum of each sector's allocation effect for this portfolio was negative 1.5 percent demonstrating that the sector waiting decisions negatively contributed to the performance of the portfolio.

The contribution to selection in each sector is equal to the portfolios sector return minus the Benchmark sector return multiplied by The Benchmark sector weight the security selected in the portfolios Consumer Staples sector underperformed the benchmarks consumer staple sector by six percent five percent times The Benchmark weight of 30% to this sector results in a contribution of negative 1.8% The portfolio manager did not do a good job in picking consumer security.

However, the PM did have success in choosing Tech Securities the portfolios selected Securities in the tech sector outperformed The Benchmark Tech sector by 13% 13% multiplied by The Benchmark weight of 45% for this sector results in a 5.9% contribution to selection.

The portfolio's materials Securities underperformed the benchmarks materials creating a selection contribution of negative 1% Overall. The combined selection effect for this portfolio was positive 3.1% Therefore active decisions in security selection was beneficial to Performance. But notice in this case, it is positive only because of the strong success in picking Tech securities.

Selection in allocation do not completely explain the difference between the portfolio and The Benchmark. The difference is the interaction effect in our example, the combined allocation effect negative 1.5 percent and combined selection effect, 3.1% together represent. Just one point six percent of the difference between the portfolios return and The Benchmark return but the total difference we noted earlier was 1.8% 0.2% is missing the interaction effect explains this remaining difference.

The contribution to interaction in each sector is equal to the portfolio sector weight minus the Benchmark sector weight multiplied by the portfolio sector return minus the Benchmark sector return in the consumer sector, the manager was underweight by 10% and selection was negative the effect of being underweight in a sector in which the manager underperforms leads to a positive contribution from interaction of 0.6 percent for the tech sector the portfolio weight equals The Benchmark weight and thus there is no contribution to interaction because the manager had an overweighting to a sector in which selection was negative the contribution from interaction in materials was negative.

Therefore the total contribution from interaction is 0.2% the missing amount after the allocation and selection calculations in many cases. You won't see any interaction effect some analyzes will Eliminate the interaction effect by replacing the benchmark's weight with the portfolio weight in the selection formula when this is done. They are essentially combining the interaction with selection effects.

In our prior example, we limited our analysis to sector allocations and security selections, but similar analysis can be performed with factors by comparing exposures to certain factors versus a benchmark and their returns factors are not limited to traditional exposures like the one shown here. They could include ESG as we discussed in the alpha indexing and factors module.

To calculate the return from each factor tilt we use a similar formula as we did for allocation effect, but instead of portfolio weights. We are comparing portfolio exposures to each factor here. Our total generated returns from Factor tilts is 5.73% with the portfolio's return. We could also add security selection to this analysis to determine the total active return for the portfolio, which is the active return from Factor tilts and from security selection.