Portfolio Management #54 - Analysis of Active Portfolio Management

Question 1

required qualities of a benchmark portfolio

Answer 1

LOS 54.a

1. representative - must represent the universe from which the active portfolio manager selects securities
2. inexpensively replicable
3. predictable - benchweights are known ex-ante (in the future)

Question 2

expected active return (“value added”)

Answer 2

LOS 54.a

E(R_A) = E(R_P) - E(R_B)

E(R_A) = sum_(i=1,N) d(w_i) * E(R_i), where

d(W_i) = active weight = w_Pi - w_Bi

• can be computed ex-ante (forecasted) or ex-post (historically)
• positive active returns generated by overweighting assets with higher expected returns and underweighting those with lower expected returns

Question 3

risk-adjusted active return

Answer 3

LOS 54.a

risk-adjusted: alpha →a_P = R_P - ß_PR_B

All discussion in this reading assumes that systematic risk of benchmark and managed portfolio is the same i.e. ß_P = 1, where ß_P is portfolios level of systematic risk compared the benchmark B

risk-adjusted: alpha →a_P = R_P - R_B

Question 4

Sharpe ratio, information ratio

Answer 4

LOS 54.b

Sharpe ratio: SR = (R_p - R_f) / σ_p

information ratio: IR =(R_p - R_b) / σ_(Rp-Rb) = R_A / σ_A

= active return / active risk

Question 5

qualities and differences between Sharpe and Information ratio

Answer 5

LOS 54.b

Sharpe ratio (SR):

• SR is unaffected by adding cash or leverage to the portfolio

information ratio (IR):

• is affected by adding cash or leverage
• ex-ante IR is always positive
• ex-post IR can be postive or negative
• IR of unconstrained portfolio is unaffected by agressiveness of the active weights
• combining active and benchmark portfolios into one portfolio will have same IR as the active portfolio by itself
• weights to fund with zero systematic risk (e.g. mkt neutral) that has R_f as its benchmark: SR = IR
• investor’s active risk can be reduced by combining active and benchmark portfolio weights in proportion to desired active risk

Question 6

closet index fund

Answer 6

LOS 54.b

closet index fund - fund claiming to be actively managed but closely tracks its benchmark index

• tends to have same Sharpe (SR) as benchmark
• tends to have very low info ratio (IR) as benchmark

Question 7

Fundamental Law of Active Management

3 factors that determine the information ratio (IR)

Answer 7

LOS 54.c

information coefficient (IC) - measure of mgr’s skill

• ex-ante: expected correlation between active returns and forecasted active returns
• ex-post: (IC_R) measures actual correlation between active returns and expected active returns, usually a small + value (< 0.2)

transfer coefficient (TC) - correlation between actual active weights dW_i and optimal active weights dW_i^*

• TC = for unconstrained portfolios
• TC < 1 w/ constraints: dW_i and W_i^*will differ

breadth (BR) - number od independent bets (forecasts of active return)