R.50 Analysis of Active Portfolio Management

Question 1

Information Ratio

Sharpe Ratio

Answer 1

Question 2

Independance of investment decisions and measuring BR

Answer 2

Question 3

Full and Basic Fundamental Law (expected return of active portfolio)

• differences and formulas

Answer 3

• Each gives expected returns of an active portfolio
• Full is constrained with a TC value
• TC (transfer coefficient) = correlation b/w optimal active weights and actual active weights
• Basic is unconstained and can remove TC from equitation (b/c value always 1)

Question 4

Optimal Active Risk

Optimal Sharpe Ratio

Total Risk

Answer 4

Optimal Active Risk= ( ^IR/ SR_B )( STD_B)

​Optimal Portfolio Sharpe Ratio= ( SR_B² + IR²) ^{(<span>1/2)</span>}

Total Risk of Active Portfolio= s²_B + s²_A

Question 5

Ex-post measurement

Decomposition of

• Active Return variance
• Active Risk
• Value Added

Answer 5

Ex-post: Ex Post Performance Measurement (actual performance is function of relative weights and realized relative returns)

Active Return

• realized IC = (TC)²
• Constraint-induced noise (1-TC)²

Active Risk squared

• Variance of active returns, or active risk squared, is used to decompose active risk.
• = σ²(R_p - R_B)
• = active factor risk + active specific risk (sum of securities’ weights² x σ²_E)

Value Added

• see pic

Question 6

Ex Ante skill measurement

Answer 6

Question 7

Information Ratio

Expected active return

“Full” fundamental law of active management

Answer 7