Portfolio Management: Information Ratio

Question 1

Ex-post Information Ratio

Answer 1

IR = (α / standard error of α) / √n

• √n: The number of periods covered by the past α
• α: Estimated coefficient of alpha
• α / Standard error of α: the t-statistic of α
• Standard error of α = SDα / √n

Question 2

Annualized Value Added for Portfolio

Answer 2

Anualized VA = α - (ƛ X ω²)

Step 1: Annualized α = α(n)

Step 2: Annualized ω = ω(√n)

• • ω: Residual risk*
• • α: Residual return*

Question 3

Optimal Annual Residual Risk (for portfolio)

Answer 3

ω* = IR/2ƛ

• • ω*: Optimal annual residual risk*
• • IR: Information ratio*

Question 4

Information Coefficient for Market Timing

Answer 4

IC = (2 X Winning%) - 1

Question 5

Information Ratio for Market Timing

Answer 5

IR = IC X √BR

• • BR = Breadth (number of trades, which is like n-periods for managers)*
• • IC = Information coefficient*

Question 6

Combined Information Ratio

Answer 6

Step 1: IRcom² = IRx² + IRy²

Step 2: IRcom = √IRcom²

- IRcom: Information ratio for both strategies