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PORTFOLIO PERFORMANCE MEASUREMENT
If we are paying an active manager to provide superior performance, how can we be sure we are getting what we pay for?
Techniques:Risk-adjusted measuresMarket-timing measuresPerformance attribution and “style” analysis
RISK-ADJUSTED MEASURES
What return should we have expected, for the same level of risk, from a manager with no particular skill?
Did our manager do better than this?What’s the relevant measure of risk?What’s the relevant benchmark portfolio?
SHARPE MEASURE
• Compare portfolio risk premium to total risk
• Equal to slope of Capital Allocation Line
• Need a benchmark: market portfolio?
)r(
r)r(E
p
fp
MODIGLIANI MEASURE
• Portfolio risk may be different from benchmark risk
• What would managed portfolio risk premium have been if we had levered or unlevered to benchmark risk?
)r()r(
r)r(Em
p
fp
ADJUSTING TO MARKET RISK
E(rp) Modigliani
rf
p
m
TREYNOR MEASURE
• Compare portfolio risk premium to systematic risk
• Potentially misleading for a portfolio with substantial unsystematic risk
p
fp r)r(E
JENSEN’S ALPHA
• Alpha is a measure of excess return relative to CAPM standard
• Again, watch for unsystematic risk
• Ease of regression application
fmpfpp r)r(Er)r(E
APPRAISAL RATIO
• Compare alpha to residual risk
• Watch out for differences in systematic risk
• Could be useful for comparing active portfolios
)e( p
p
BEFORE- OR AFTER-THE-FACT MEASUREMENT?
The theory behind risk-adjusted performance measures calls for before-the-fact measurementWhat are the data-gathering problems in
before-the-fact measurement?
In practice, we’re stuck with after-the fact dataLuck vs. skill: problem of statistical power
A PROBLEM WITH AFTER-THE-FACT MEASUREMENT
According to our estimate of alpha, the manager in the example looks good. But why?Good stock picker?Good market timer?Market-timing ability is hard to detect with
Jensen’s alpha
SUCCESSFUL MARKET TIMINGAND MISLEADING ALPHA
rp-rf
High beta portfolio
B
Estimated regression line
Low beta portfolio A
rm-rf
negative estimated alpha
TESTING FOR MARKET TIMING:TREYNOR-MAZUY
ct significan positive,for Look
e)rr(c)rr(barr p2
fmfmfp
TESTING FOR MARKET TIMING:HENRIKSSON-MERTON
ct significan positive,for Look
otherwise 0
rr if 1D
e)rr(cD)rr(barr
fm
pfmfmfp
PERFORMANCE ATTRIBUTIONANALYSIS
• For each asset class i:
– Benchmark weights
– Benchmark returns
– Portfolio weights
– Portfolio weights pi
pi
Bi
Bi
r
w
r
w
DECOMPOSING PERFORMANCE
iBipiBipi
iBipiBiBi
iBipi
iBiBi
ipipi
)rr)(ww(
)rr(wr)ww(
rwrw
PERFORMANCE ATTRIBUTIONCOMPONENTS
• Asset allocation contribution
• Security selection contribution
• Interaction
i
iBi
iBi
rw
r)w(
)r(w
“STYLE” ANALYSIS
Define the manager’s “style” in terms of benchmark portfolios (e.g., asset classes)Regress managed portfolio returns against
benchmark returnsFitted values from the regression are the
manager’s style-adjusted expected returnsResidual (“tracking error”) is the measure of
superior performance
EXAMPLE OF STYLE ANALYSIS
selection toleattributab %return
iancevar residualR-1
style toleattributab %return
variationlainedexpR
erbrbrbr
2
2
Tbond3cap small2cap eargl1p
THE PORTFOLIO MANAGEMENT PROCESS
Security Index Fund Money MarketAnalysis Management Fund Management
Active PassivePortfolio Portfolio
Market-Timing Information
Overall Risky Risk-Free Portfolio Portfolio
Client Preferences
Optimal OverallPortfolio
Performance Measurement