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