Two Equity Managers, a Correlation Regime Shift, and an Active-Risk Budget
A $900 million foundation allocates 60% to equities through two managers: Manager A (active risk 4.0%, expected alpha 3.0%) and Manager B (active risk 6.5%, expected alpha 2.9%). The split is 50/50. B's trailing three-year alpha is 5.2% versus A's 1.4%, and the committee proposes shifting to 70/30 in favor of B to 'capture more alpha.' Active-return correlation between the managers was 0.15 over ten years but has been 0.55 for the last 18 months, as both built overweight positions in the same six mega-cap technology names. The foundation's investment policy limits total-fund active risk to 3.0%. The remaining 40% of assets are indexed.
1. Compute expected alpha and active risk for the 50/50 and 70/30 splits under both correlation assumptions, and evaluate whether the proposed shift achieves the committee's objective.
Read the worked answer
Expected alpha (weighted average; correlation irrelevant):
- 50/50: 0.5(3.0) + 0.5(2.9) = 2.95%
- 70/30 toward B: 0.3(3.0) + 0.7(2.9) = 2.93%
The shift reduces expected alpha. It raises risk. B is not a higher-alpha manager; it is a higher-tracking-error manager with a lower information ratio (0.45 vs 0.75). The committee has confused trailing alpha with skill.
Active risk of the equity sleeve = √(wₐ²σₐ² + w_b²σ_b² + 2wₐw_bσₐσ_bρ), with σₐσ_b = 26.0:
| Split | ρ = 0.15 | ρ = 0.55 |
|---|---|---|
| 50/50 | √(4.00+10.56+1.95) = 4.06% | √(4.00+10.56+7.15) = 4.66% |
| 70/30 (B) | √(1.44+20.70+1.64) = 4.88% | √(1.44+20.70+6.01) = 5.31% |
Total-fund active risk = 0.60 × sleeve: 50/50 gives 2.44% or 2.80%; 70/30 gives 2.93% or 3.19%.
The proposal breaches the 3.0% limit under the current correlation regime - the firm would be passing the policy limit using a ten-year correlation that no longer describes the portfolio.
2. Recommend an allocation and justify it relative to the active-risk budget.
Read the worked answer
Allocate by alpha per unit of active variance, w ∝ αᵢ/σᵢ² (the unconstrained alpha-maximizing solution when correlation is modest):
- A: 3.0 / 16.0 = 0.1875
- B: 2.9 / 42.25 = 0.0686
Normalized: approximately 73% A / 27% B - the mirror image of the proposal. This is the direction the committee should move, not the reverse.
Risk check. At 70/30 toward A, with ρ = 0.55: √(0.49×16.0 + 0.09×42.25 + 0.2856×26.0) = √(7.84 + 3.80 + 7.43) = 4.37%, or 2.62% at total-fund level - comfortably inside 3.0% even in the stressed regime, with expected alpha of 0.7(3.0) + 0.3(2.9) = 2.97%, higher than either alternative.
Caveats to state explicitly:
- The α/σ² rule assumes alphas are unbiased estimates; B's 5.2% trailing alpha should be decomposed before use - if it came from a passive mega-cap growth tilt rather than stock selection, it is not repeatable alpha.
- The correlation is not a fixed input. Size the position so the policy limit holds at ρ = 0.55, not at ρ = 0.15.
- Correlation of active returns rises precisely when active risk is realized, so the stressed value is the planning value.
3. What monitoring and governance actions should accompany the decision?
Read the worked answer
- Overlap analysis quarterly. Identify common holdings and common factor exposures (the six mega-cap names). Set a formal cap - for example, no more than 15% of the equity sleeve's active risk from any single stock or from the shared names - and treat a breach as a risk event requiring a report to the committee.
- Factor and style attribution. Require B to show how much of the 5.2% trailing alpha is selection versus a growth/momentum factor loading and a benchmark mismatch. Three years is a short sample; the IR of 0.45 is not evidence of skill.
- Correlation assumption in the risk model. Use a short-window stressed correlation as the binding constraint; document why the ten-year figure is not used for limit monitoring.
- Hire/terminate discipline. State in advance what would trigger a review of either manager (for example, rolling three-year IR below 0.30, or active risk outside a stated band), so that the decision is not relitigated on trailing returns.
- Committee education. The 70/30 proposal should be minuted, with the arithmetic showing it lowers expected alpha and raises risk. Governance quality is judged on whether bad reasoning was recorded and rejected, not just on the outcome.