What is active risk budgeting, and how does a plan sponsor allocate tracking error across managers?

Question

AcadiFi · Accepted Answer

**Active risk budgeting** is the process of allocating a total portfolio's tracking error budget across multiple active managers (or strategies) to maximize the aggregate information ratio. It recognizes that active risk is a **scarce resource** that should be deployed where it generates the highest active return.

**Framework**

The plan sponsor sets a **total active risk budget** (e.g., 3% tracking error vs. the policy benchmark) and then distributes it across managers based on their expected information ratios and the correlations of their active returns.

**Optimal Allocation Rule**

For uncorrelated active returns, the optimal allocation of active risk to manager i is proportional to their expected IR:

**TE_i proportional to IR_i x (total risk budget)**

For correlated active returns, the optimization becomes more complex (quadratic programming).

**Worked Example**

Westfield Pension Fund has a 3.0% total tracking error budget and three active managers:

| Manager | Expected Active Return | Expected TE | Expected IR | Active Correlation |
|---|---|---|---|---|
| Kensington Growth | 2.1% | 4.0% | 0.53 | - |
| Bramley Value | 1.5% | 3.5% | 0.43 | 0.15 with Kensington |
| Oakdale Quant | 0.8% | 1.8% | 0.44 | 0.05 with others |

**Step 1: Determine optimal weights**

With low correlations, the allocation is roughly proportional to IR:

Sum of IRs = 0.53 + 0.43 + 0.44 = 1.40

| Manager | IR Weight | TE Allocation | Capital Allocation |
|---|---|---|---|
| Kensington | 0.53/1.40 = 37.9% | 37.9% x 3.0% = 1.14% | 40% |
| Bramley | 0.43/1.40 = 30.7% | 30.7% x 3.0% = 0.92% | 35% |
| Oakdale | 0.44/1.40 = 31.4% | 31.4% x 3.0% = 0.94% | 25% |

```mermaid
flowchart TD
    A["Total TE Budget: 3.0%"] --> B["Kensington: TE = 1.14%"]
    A --> C["Bramley: TE = 0.92%"]
    A --> D["Oakdale: TE = 0.94%"]
    B --> E["Diversified Portfolio TE ≈ 2.8%"]
    C --> E
    D --> E
    E --> F["Expected aggregate active return ≈ 1.6%"]
    F --> G["Portfolio IR ≈ 1.6/2.8 = 0.57"]
```

**Why Not Just Pick the Highest-IR Manager?**

Concentrating all active risk with Kensington (IR = 0.53) would give a portfolio IR of 0.53. By diversifying across three lowly-correlated managers, the aggregate IR improves to approximately 0.57 — diversification works for active risk just as it does for total risk.

**Key Principles:**
1. Managers with higher expected IR deserve more of the active risk budget
2. Managers with low active return correlations are especially valuable (diversification of active bets)
3. The capital allocation and risk allocation may differ — a low-TE quant manager may receive less capital but proportionally more active risk
4. Rebalancing the active risk budget requires ongoing monitoring of realized IR and active correlations

**Practical Considerations:**
- Ex-ante IR estimates are uncertain — consider using Bayesian shrinkage toward a prior
- Transaction costs from rebalancing between managers reduce net active return
- Manager capacity constraints limit how much risk can be allocated to a single strategy

For more on manager selection, explore our CFA Level III course.

What is active risk budgeting, and how does a plan sponsor allocate tracking error across managers?

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