Translate information coefficient into feasible active risk

Learning goals

• Calculate the simplified expected information ratio.
• Explain why 1.6% applies to this case.
• Identify the case-specific assumption or failure mode before taking action.

Draft · approximately 30 minutes, excluding further revision.

Shared case and decision context

A manager has forecast information coefficient 0.05, 100 genuinely independent decisions per year and transfer coefficient 0.8 under a simplified fundamental-law model. Expected active risk is 4%. The decisions may in practice share a common macro exposure.

Economic or professional mechanism

The information ratio links expected active return to tracking risk, while the fundamental law connects forecasting skill, independent breadth and implementation efficiency under restrictive assumptions. Counting trades is not the same as counting independent investment decisions. Constraints and costs reduce the translation from paper forecasts to implemented active positions.

Apply, challenge and communicate

The model IR is 0.4 and expected active return 1.6%. Correlated bets reduce effective breadth and the realized result is uncertain. Separate forecast quality from portfolio construction, execution and fees when evaluating a manager; a high turnover count is not evidence of genuine diversification.

Select active risk within constraints, not from a ratio alone

An information ratio compares expected active return with tracking risk under the chosen benchmark. Higher estimated IR can justify more active risk only after estimation uncertainty, liquidity, capacity, fees and investor limits. In a mean–variance active overlay with risk aversionλ, expected active return IR×σA gives utility IR×σA−λσA²/2 and unconstrained optimumσA=IR/λ. With IR 0.4 andλ10, the illustrative optimum is 4%; a 2% policy cap still binds.

Market timing often concentrates decisions in a few correlated bets; security selection can offer breadth only when signals and residual outcomes are sufficiently independent. A strategy change raising nominal decision count from 100 to 400 doubles modeled IR only if IC and transfer coefficient remain unchanged and breadth is genuinely independent. Correlated trades or constraints can make this apparent improvement disappear.

Formula and assumptions

IR≈IC*sqrt(independent breadth)*TC; expected active return=IR*active risk

Case analysis with explicit assumptions

1. A manager has forecast information coefficient 0.05, 100 genuinely independent decisions per year and transfer coefficient 0.8 under a simplified fundamental-law model. Expected active risk is 4%. The decisions may in practice share a common macro exposure.
2. Method: IR≈IC*sqrt(independent breadth)*TC; expected active return=IR*active risk
3. Case result: 0.40. The model IR is 0.4 and expected active return 1.6%. Correlated bets reduce effective breadth and the realized result is uncertain. Separate forecast quality from portfolio construction, execution and fees when evaluating a manager; a high turnover count is not evidence of genuine diversification.

Errors to catch

• Do not replace the stated assumptions with an unstated shortcut. Reconcile units, timing and the claim being valued or duty being assessed.
• A guaranteed realized return is not a defensible conclusion for these case facts.

Original knowledge check

Answer every question before checking. Review explanations after submitting; retry starts a new attempt.

Sources and coverage status

These original lessons are drafts. Public outlines are used to check scope; the official learning-outcome text and proprietary question banks are not reproduced here. Follow the source for exam-year requirements and updates.

• Reference · www.cfainstitute.org
• Reference · www.investor.gov