Performance Evaluation
- performance measurement - rate of return
- performance attribution - sources of return
- performance appraisal - luck vs skill
TWRR
time weighted rate of return; geometric rate of return
not impacted by external cash flows
Return CF at Beginning
Return CF at End
MWRR
money weighted rate of return
FV = PV( 1 + r )n + CF( 1 + r )n
impacted by CFs; used when manager controls timing of CFs
Portfolio Return
P = Manager + Style + Active Return
Style (TAA, client) = Benchmark - Index Return
Act Return (manager) = Portfolio - Benchmark Return
Benchmark Characteristics
- specified in advance
- appropriate
- measurable
- unambiguous
- relective of manager’s style
- accountable
- investable
Benchmark Types
- absolute return
- manager universe
- market index
- style index
- factor-model-based
- returns based
- custom security-based
Tests of Benchmark Quality
- min systematic bias
- low tracking error
- high coverage ratio
- low turnover
- positive active positions
- similar risk characteristics
Micro Performance Attribution
- pure sector allocation
- within sector selection
- allocation/ selection interaction
Pure Sector Allocation
over/under weight sectors
Σ (wp - wb) (rb - roverall benchmark)
Within Sector Selection
security selection
Σ wb (rp - rb)
Allocation/ Selection Interaction
Σ (wp - wb) (rp - rb)
Macro Performance Attribution
- policy allocations
- benchmarks returns
- fund returns, valuations, external CF
Macro Attribution Analysis
break down portfolio return by
- net contributions
- rf
- asset categories (SAA)
- benchmarks (TAA)
- inv manager
- allocation effects (error term)
Fundamental Factor Model
Micro Attribution
- identify factors
- determine beginning exposure to factors (BM)
- active exposure
- active impact
FI Attribution Analysis
- int rate effect (BM return)
- int rate management (duration, convexity, yeild curve)
- sector/ quality management
- security selection
- traing effect (error)
Alpha
risk adj return; systematic risk (β)
α = Rp - [rf + β ( RM - rf )]
Treynor Measure
return on risk; systematic risk (β)
T = ( Rp - rf ) / β
Sharpe Ratio
return on risk; total risk (SD)
SR = ( Rp - rf ) / σp
M2
return on risk; total risk (SD)
M2 = rf + [( Rp - rf ) / σp] σm
IR
information ratio
IR = active return/ active risk = ( Rp - Rb ) / ( σp - σb )
