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ANALYSIS OF ACTIVE PORTFOLIO MANAGEMENT - Coggle Diagram
ANALYSIS OF ACTIVE PORTFOLIO MANAGEMENT
Active return
Ra=Rp-Rb
alpha=Rp - beta(RB)
Asset allocation return
Security selection return
Sharpe ratio
no change khi add cash and leverage
Information ratio
Active return/ active risk
giảm khi add cash and leverage
A closet index fund will have a SR similar to that of the benchmark index, a very low IR, and little active risk. After fees, the IR of that fund is often negative.
A fund with zero systematic risk that uses the risk-free rate as its benchmark would have an IR that is equal to its SR.
The IR will change with the addition of cash or the use of leverage.
The IR of an unconstrained portfolio is unaffected by the aggressiveness of the active weights.
Investors can select an appropriate amount of active risk by investing a portion of their assets in the active portfolio and the remaining portion in the benchmark.
If we combine an actively managed portfolio with an allocation to the benchmark portfolio, the resulting blended portfolio will have the same IR as the original actively managed portfolio.
Active risk
optimal Active risk= IR/Sharpe ben * risk B
optimal sharpe= căn( sharpe B bình + IR bình)
total risk bình = rish benmark bình + risk optimal bình
Component of IR
IC
management skill
• Ex-ante IC is the risk-weighted correlation between active returns and forecasted active returns.
• Ex-post IC measures actual correlation between active returns and expected active returns.
TC
the correlation between actual active weights and optimal active weights
BR
the number of independent active bets taken per year
The Fundamental Law of active portfolio management
The Grinold rule allows us to compute the expected active return based on the information coefficient, active risk, and a standardized score.
IC: skill của management
risk: độ liều
S: lợi nhuận được chuẩn hóa
The expected active portfolio return, is the sum product of active security weights and forecasted active security returns
IC: độ giỏi của quản lý
Độ active của quản lý
risk: độ liều
Nếu có constrant thì nhân thêm TC vào
Ex-post perfomamnce
active return trong điều kiện là quản lý đó = IC + TC
căn (BR)
risk
R actual = expected + noise
Market timing
IC = 2(% correct) - 1
Market timing is simply a bet on the direction of the market (or a segment of the market).
Market timing can also be used to make sector rotation decisions
(allocating assets into sectors that are expected to outperform).
Market timing can also be used to make sector rotation decisions (allocating assets into sectors that are expected to outperform).
Công thức annualized ac tive risk: +risk A= risk c x căn BR
xích ma C bằng căn (xích ma X - xích ma Y) bình, vì là standard deviation nên phải use correlation
Strengths
The fundamental law can be used to evaluate a range of active strategies, including security selection, market timing, and sector rotation.
Limitations
Garbage in, garbage out problem: Poor input estimates lead to incorrect evaluations.
Ex-ante measurement of skill
that managers tend to overestimate their ability to outperform the market
Independence of investment decisions
Problem: Two or more decisions rely on same (or similar) information → They are not independent.