Analysis of Active Portfolio Management

Active managers are paid to beat a benchmark, so investors need tools to measure whether they add value, to judge whether that value reflects skill, and to decide how much active risk to take. This module defines value added and the information ratio, contrasts it with the Sharpe ratio, and builds the fundamental law of active management, which links performance to skill, breadth and the constraints a manager faces. It then applies the law to manager selection, to setting active risk, and to comparing market timing with security selection, and closes with the law's practical limits.

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What you will learn

1. Measure value added by active management, decompose it into allocation and selection effects, and calculate ex post and ex ante information ratios, contrasting them with the Sharpe ratio.

Active return = portfolio return - benchmark return = sum of active weights x asset returns.
Value added = asset allocation effect + security selection effect.
Ex post IR = mean active return / tracking error; ex ante IR = expected active return / expected active risk.
Sharpe ratio uses total excess return and total risk and is unaffected by cash or leverage.
IR is unaffected by scaling active weights, but cash or leverage creates a beta bet that changes it.

2. Apply the fundamental law of active management, including the information coefficient, breadth and transfer coefficient.

IR = TC x IC x sqrt(BR); expected active return = IR x active risk.
IC measures forecasting skill; even small ICs can produce good IRs with enough breadth.
Breadth counts independent decisions per year; IR rises with its square root.
TC measures how much constraints (long-only, limits) dilute forecasts; TC = 1 when unconstrained.
TC squared is the share of active return variance explained by forecasts; the rest is noise.

3. Use the information ratio to select active managers, set the optimal level of active risk and combine an active fund with a benchmark portfolio.

Highest achievable Sharpe ratio: SR_P^2 = SR_B^2 + IR^2.
Choose the manager with the highest IR, not the highest active return or IC.
Optimal active risk = (IR / SR_B) x benchmark volatility.
To hit a target active risk, hold w = target active risk / fund's active risk in the active fund, the rest in an index fund.
Uncorrelated active managers combine as IR_total^2 = sum of IR_i^2.

4. Evaluate market timing and security selection strategies with the fundamental law and assess the law's practical limitations.

Market timing has low breadth (few decisions a year), so it needs a high IC to produce a good IR.
Security selection can produce a high IR from a small IC applied across many independent bets.
For binary calls, IC = 2 x (proportion correct) - 1.
Correlated bets (common factor exposures) shrink effective breadth and overstate the IR.
The law ignores transaction costs and is an ex ante relationship; realised results include noise.

Module at a glance

Active return = sum of active weights x returns; split it into asset allocation and security selection.
IR = active return / active risk; Sharpe = excess return / total risk; IR is unaffected by scaling active weights, Sharpe by cash or leverage.
Fundamental law: IR = TC x IC x sqrt(BR); expected active return = IR x active risk.
Constraints lower the transfer coefficient; TC squared is the share of active return variance explained by forecasts.
SR_P^2 = SR_B^2 + IR^2: choose the highest-IR manager and set active risk = (IR / SR_B) x benchmark volatility.
Reach a target active risk by mixing the active fund with an index fund: w = target / fund active risk.
Market timing needs high IC because breadth is low; correlated bets shrink effective breadth and overstate IR.

This free module has 4 lessons, 15 practice questions with full explanations.

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