Interaction effect

A portfolio beats its benchmark. Attribution analysis asks why, and splits the answer into three parts.

The allocation effect credits the manager for weighting sectors differently from the benchmark. The selection effect credits the manager for picking better securities within each sector. What is left over — the part that arises only because the manager did both at once in the same sector — is the interaction effect.

The workbook describes it as the combined impact of asset allocation and security selection. It captures the performance impact when a manager both overweights a sector and selects superior stocks within that sector — and, just as much, when those two decisions work against each other.

Three components (Chapter 10, section 10.5).

Total excess return = Asset allocation effect + Security selection effect + Interaction effect

Wp and Wb are the portfolio's and benchmark's weights in a sector; Rp and Rb are the portfolio's and benchmark's returns in that sector.

Reading the sign in each sector.

Why it exists. The selection effect is measured at benchmark weights. If the manager held more (or less) of a sector than the benchmark, the extra (or missing) weight also earned the return difference. That piece belongs to neither pure effect — it is the interaction.

Why it matters. Attribution evaluates manager skill, diagnoses whether excess return came from stock-picking or allocation, and informs future strategy.

Interaction effect = Σ (Wp − Wb) × (Rp − Rb)

The workbook's example (Chapter 10, section 10.5):

Excess return = 8.70% − 7.80% = 0.90%.

Interaction effect, sector by sector:

Healthcare: the manager picked better healthcare stocks but held less of them than the benchmark. Financials: held more financials but picked worse ones. Both cost a little.

Putting it together: allocation +0.10% + selection +0.85% + interaction −0.05% = 0.90%, exactly the excess return.

In rupees (illustrative): on a ₹1,00,00,000 portfolio, 0.90% excess is ₹90,000 over the benchmark, of which ₹85,000 is attributable to selection, ₹10,000 to allocation, and −₹5,000 to interaction.

Interaction effect is one of the three components of performance attribution analysis in Chapter 10 (Performance Measurement and Evaluation of Portfolio Managers, 10% weightage), section 10.5, with a full worked example. A calculation question can ask for any one effect given the other two and the total excess return, or ask for the interaction figure directly from weights and returns.

• Interaction uses both differences: (Wp − Wb) × (Rp − Rb). Allocation uses Rb; selection uses Wb.
• The three effects add up to the total excess return — use that to check or back out a missing figure.
• Underweight × worse return is positive. Two negatives multiply to a positive.
• A negative interaction does not mean both decisions were bad — in the example, overall selection and allocation were both positive.
• Watch the percentages: 5% × 2% = 0.10%, not 10%.
• The workbook's interpretation says the interaction was slightly negative because allocation and selection "did not reinforce each other optimally".