Second Investment Course – November 2005
Topic Six:
Measuring Superior Investment Performance
6-0
Estimating the Expected Returns and
Measuring Superior Investment Performance

We can use the concept of “alpha” to measure superior investment
performance:
a = (Actual Return) – (Expected Return) = “Alpha”

In an efficient market, alpha should be zero for all investments. That is,
securities should, on average, be priced so that the actual returns they
produce equal what you expect them to given their risk levels.

Superior managers are defined as those investors who can deliver
consistently positive alphas after accounting for investment costs

The challenge in measuring alpha is that we have to have a model
describing the expected return to an investment.

Researchers typically use one of two models for estimating expected
returns:
- Capital Asset Pricing Model
- Multi-Factor Models (e.g., Fama-French Three-Factor Model)
6-1
Developing the Capital Asset Pricing Model
Recall that one of the most fundamental notions in all of finance is that an
investor’s expected return can be expressed in terms of these activities:
E(R) = (Risk-Free Rate) + (Risk Premium)
Clearly, the practical challenge in measuring expected returns comes from
assessing the risk premium component properly. The Capital Market Line
(CML) offers one tractable definition of the risk premium by writing this
relationship as follows:
 E(R m )  RFR 
E(R p )  RFR   p 

m


While this is a reasonable first step, the CML expresses the risk-expected
return tradeoff that investors should expect in an efficient capital market if
they are purchasing entire portfolios of securities.
To be fully useful, financial theory must address the following question:
What is the appropriate risk-expected return relationship for individual
securities?
The problem posed by individual securities (compared to fully diversified
portfolio holdings) is that the risk of those securities contains both
systematic and unsystematic elements.
Simply put, investors cannot
expect to be compensated for risk that they could have diversified away
themselves (i.e., unsystematic risk).
6-2
Developing the Capital Asset Pricing Model (cont.)
One way to handle this problem in the context of the CML is to
adjust the number of “total risk” units that the investor assumes for
security i (i.e., i) to account for just the systematic portion of that
risk.
This can be done by multiplying i by the security’s
correlation with the market portfolio (i.e., rim):
 E(R m )  RFR 
E(R i )  RFR  (i rim ) 

m


Rearranging this expression leaves:
 i rim
E(R i )  RFR  
 

m


 [E(R m )  RFR]

or:
E(R i )  RFR  i [E(R m )  RFR]
This is the celebrated Capital Asset Pricing Model (CAPM).
Notice that the CAPM redefines risk in terms of a security’s “beta”
(i.e., i), which captures that stock’s riskiness relative to the
market as a whole.
The graphical representation of the CAPM is called the Security
Market Line (SML).
6-3
Using the SML in Performance Measurement: An Example

Two investment advisors are comparing performance. Over the last
year, one averaged a 19 percent rate of return and the other a 16
percent rate of return. However, the beta of the first investor was
1.5, whereas that of the second was 1.0.
a. Can you tell which investor was a better predictor of individual
stocks (aside from the issue of general movements in the market)?
b. If the T-bill rate were 6 percent and the market return during the
period were 14 percent, which investor should be viewed as the
superior stock selector?
c. If the T-bill rate had been 3 percent and the market return were 15
percent, would this change your conclusion about the investors?
6-4
Using the SML in Performance Measurement (cont.)
a.
To tell which investor was a better predictor of individual stocks we look at their alphas.
Alpha is the difference between their actual return an that predicted by the SML, given
the risk of their individual portfolios. Without information about the parameters of this
equation (risk-free rate and the market rate of return) we cannot tell which one is more
accurate.
b.
If RF = 0.06 and Rm = 0.14, then
Alpha1 = .19 – [.06+1.5(.14-.06)] = .19 - .18 = 0.01
Alpha2 = .16 – [.06+1(.14-.06)] = .16 - .14 = 0.02
Here, the second investor has the larger alpha and thus appears to be a more accurate
predictor. By making better predictions the second investor appears to have tilted his portfolio
toward undervalued stocks.
c.
If RF = 0.03 and Rm = 0.15, then
Alpha1 = .19 – [.03+1.5(.15 -.03)] = .19 - .21 = -0.02
Alpha2 = .16 – [.03+1(.15 -.03)] = .16 - .15 = 0.01
6-5
Using CAPM to Estimate Expected Return:
Empresa Nacional de Telecom
1. Expected Return/Cost of Equity (Assumes RF = 4.73%)
(i) RPm = 4.2%: E(R) = k = 4.73% + 0.79(4.2%) = 8.05%
(ii) RPm = 7.2%:
E(R) = k = 4.73% + 0.79(7.2%)
= 10.42%
2. Expected Price Change (Recall that E(R) = E(Capital Gain) + E(Cash Yield)):
(i) RPm = 4.2%: E(P1) = (4590)[1 + (.0805 - .0196)] = CLP 4869.53
(ii) RPm = 7.2%: E(P1) = (4590)[1 + (.1042 - .0196)] = CLP 4978.31
6-6
Estimating Mutual Fund Betas: FMAGX vs. GABAX
6-7
Estimating Mutual Fund Betas: FMAGX vs. GABAX (cont.)
6-8
Estimating Mutual Fund Betas: FMAGX vs. GABAX (cont.)
6-9
The Fama-French Three-Factor Model

The most popular multi-factor model currently used in practice was
suggested by economists Eugene Fama and Ken French. Their model
starts with the single market portfolio-based risk factor of the CAPM and
supplements it with two additional risk influences known to affect security
prices:
- A firm size factor
- A book-to-market factor

Specifically, the Fama-French three-factor model for estimating expected
excess returns takes the following form:
(Rit – RFRt) = ai + bi1(Rmt – RFRt) + bi2SMBt + bi3HMLt + eit
where, in addition to the excess return on a stock market portfolio, two other risk factors are
defined:
SMB (i.e., “Small Minus Big”) is the return to a portfolio of small capitalization stocks less
the return to a portfolio of large capitalization stocks
HML (i.e., “High Minus Low”) is the return to a portfolio of stocks with high ratios of
book-to-market values (i.e., “value” stocks) less the return to a portfolio of low bookto-market value (i.e., “growth”) stocks
6 - 10
Estimating the Fama-French Three-Factor Return Model:
FMAGX vs. GABAX
6 - 11
Fama-French Three-Factor Return Model: FMAGX vs. GABAX (cont.)
6 - 12
Fama-French Three-Factor Return Model: FMAGX vs. GABAX (cont.)
6 - 13
Style Classification Implied by the Factor Model
Growth
Value
FMAGX *
Large
* GABAX
Small
6 - 14
Fund Style Classification by Morningstar

FMAGX

GABAX
6 - 15
Active vs. Passive Equity Portfolio Management

The “conventional wisdom” held by many investment analysts is that
there is no benefit to active portfolio management because:
- The average active manager does not produce returns that exceed those
of the benchmark
- Active managers have trouble outperforming their peers on a consistent
basis

However, others feel that this is the wrong way to look at the Active
vs. Passive management debate. Instead, investors should focus
on ways to:
- Identifying those active managers who are most likely to produce
superior risk-adjusted return performance over time

This discussion is based on research authored jointly with Van
Harlow of Fidelity Investments titled:
“The Right Answer to the Wrong Question:
Identifying Superior Active Portfolio Management”
6 - 16
The Wrong Question
Stylized Fact:
Most active mutual fund managers cannot outperform the S&P 500
index on a consistent basis
Beat %
90%
70%
50%
30%
10%
JAN80
JAN82
JAN84
JAN86
JAN88
JAN90
JAN92
JAN94
JAN96
JAN98
JAN00
JAN02
JAN04
DATE
6 - 17
Fund Performance versus Style Rotation (Rolling 12 Month Returns)
Beat %
90%
Small-Large
40%
Higher Small-Cap Returns
R2000-R1000
70%
20%
50%
0%
30%
Percent Beating
S&P 500
(
20%)
(
40%)
Higher Large-Cap Returns
10%
JAN80
JAN85
JAN90
JAN95
JAN00
JAN05
DATE
6 - 18
The Wrong Question (cont.)
Stylized Fact:
Most active mutual fund managers compete against
the “wrong” benchmark
100
90
80
70
60
50
40
30
20
10
0
S&P 500
Diversified Equity
Mutual Funds
0 10 20 30 40 50 60 70 80 90100
6 - 19
Defining Superior Investment Performance

Over time, the “value added” by a portfolio manager
can be measured by the difference between the
portfolio’s actual return and the return that the portfolio
was expected to produce.

This difference is usually referred to as the portfolio’s
alpha.
Alpha = (Actual Return) – (Expected Return)
6 - 20
Measuring Expected Portfolio Performance

In practice, there are three ways commonly used to measure the return
that was expected from a portfolio investment:
- Benchmark Portfolio Return



Example: S&P 500 or Russell 1000 indexes for a U.S. Large-Cap Blend fund
manager, IPSA index for Chilean equity manager
Pros: Easy to identify; Easy to observe
Cons: Hypothetical return ignoring taxes, transaction costs, etc.; May not be
representative of actual investment universe; No explicit risk adjustment
- Peer Group Comparison Return



Example: Median Return to all U.S. Small-Cap Growth funds for a U.S. Small-Cap
Growth fund manager, Sistema fondo averages for Chilean AFP managers
Pros: Measures performance relative to manager’s actual competition
Cons: Difficult to identify precise peer group; “Median manager” may ignore large
dispersion in peer group universe; Universe size disparities across time and fund
categories
- Return-Generating Model



Example: Single Risk-Factor Model (CAPM); Multiple Risk-Factor Model (FamaFrench Three-Factor, Carhart Four-Factor)
Pros: Calculates expected fund returns based on an explicit estimate of fund risk;
Avoids arbitrary investment style classifications
Cons: No direct investment typically; Subject to model misspecification and factor
measurement problems; Model estimation error
6 - 21
The Wrong Question (Revisited)
Stylized Fact:
Across all investment styles, the “median manager” cannot produce
positive risk-adjusted returns (i.e., PALPHA using return model)

Monthly Mean PALPHA Value at Percentile (%):
Fund Style
# of Obs.
5th
25th
Median
75th
95th
% Pos.
Alphas
Overall
LV
LB
LG
MV
MB
MG
SV
SB
SG
S&P 500
Index Fund
19551
2,387
3,377
3,351
1,413
1,691
3,169
929
1,222
2,012
-1.56
-2.11
-1.44
-1.08
-2.61
-1.86
-1.48
-2.02
-1.42
-1.37
-0.55
-0.57
-0.55
-0.38
-0.67
-0.79
-0.63
-0.65
-0.59
-0.45
-0.18
-0.21
-0.22
-0.07
-0.23
-0.32
-0.21
-0.25
-0.19
-0.02
0.04
0.12
0.07
-0.01
0.17
0.11
0.07
0.19
0.01
0.12
0.39
0.79
0.66
0.38
0.80
0.69
0.64
1.04
0.57
0.77
1.24
33.77
23.51
42.02
30.21
29.10
35.31
32.77
32.16
48.46
25.62
6 - 22
The Right Answer

When judging the quality of active fund managers, the important
question is not whether:

The average fund manager beats the benchmark
 The median manager in a given peer group produces a positive
alpha

The proper question to ask is whether you can select in advance
those managers who can consistently add value on a risk-adjusted
basis

Does superior investment performance persist from one period to the
next and, if so, how can we identify superior managers?
6 - 23
Lessons from Prior Research

Fund performance appears to persist over time

Original View:
Managers with superior performance in one period are equally likely to produce superior or inferior performance in
the next period

Current View:
Some evidence does support the notion that investment performance persists from one period to the next
The evidence is particularly strong that it is poor performance that tends to persist (i.e., “icy” hands vs. “hot” hands)
Security
characteristics, return momentum, and fund style appear to influence fund
performance

Security Characteristics:
After controlling for risk, portfolios containing stocks with different market capitalizations, price-earnings ratios, and
price-book ratios produce different returns
Funds with lower portfolio turnover and expense ratios produce superior returns

Return Momentum:
Funds following return momentum strategies generate short-term performance persistence
When used as a separate risk factor, return momentum “explains” fund performance persistence
6 - 24
Lessons from Prior Research (cont.)
Security characteristics, return momentum, and fund style appear to influence fund
performance (cont.)


Fund Style Definitions:
After controlling for risk, funds with different objectives and style mandates produce different returns
Value funds generally outperform growth funds on a risk-adjusted basis

Style Investing:
Fund managers make decisions as if they participate in style-oriented return performance “tournaments”
The consistency with which a fund manager executes the portfolio’s investment style mandate affects fund
performance, in both up and down markets
Active
fund managers appear to possess genuine investment skills

Stock-Picking Skills:
Some fund managers have security selection abilities that add value to investors, even after accounting for fund
expenses
A sizeable minority of managers pick stocks well enough to generate superior alphas that persist over time

Investment Discipline:
Fund managers who control tracking error generate superior performance relative to traditional active managers
and passive portfolios
 Manager Characteristics:
The educational backgrounds of managers systematically influence the risk-adjusted returns of the funds they
manage
6 - 25
Data and Methodology for Performance Analysis

CRSP (Center for Research in Security Prices) US Mutual Fund
Database


Survivor-Bias Free database of monthly returns for mutual funds for the period 1962-2003
Screens
Diversified domestic equity funds only
Eliminate index funds
Require 30 prior months of returns to be included in the analysis on any given date
Assets greater than $1 million
Period 1979 – 2003 in order to analyze performance versus an index fund and have sufficient
number of mutual funds

Return-generating model:
Fama-French
E(Rp) = RF + {m[E(Rm) – RF] + sml[SML] + hml[HML]}

Style classification

Map funds to Morningstar-type style categories based on Fama-French SML and HML
factor exposures (LV, LB, LG, MV, MB, MG, SV, SB, SG)
6 - 26
Methodology: Fund Mapped by Style Group
Mutual Fund Style Category:
Year
LV
LB
LG
MV
MB
MG
SV
SB
SG
Total
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
9
7
5
13
14
8
7
5
6
9
12
19
25
32
38
49
57
86
160
355
469
771
812
907
836
23
26
20
23
27
26
23
18
22
29
30
42
63
163
202
269
210
405
535
636
456
604
680
962
1250
70
59
32
38
60
55
74
95
80
89
92
92
97
176
166
198
224
421
478
601
827
992
1181
840
1078
0
2
1
1
1
1
3
3
3
3
2
1
3
7
8
4
20
20
52
160
157
316
302
345
226
3
7
6
5
7
1
1
5
2
8
3
3
3
10
5
16
67
45
111
130
107
82
129
193
375
21
36
39
43
31
37
37
41
51
50
54
46
44
77
92
148
234
279
357
256
641
587
699
835
764
0
2
0
0
0
0
7
12
14
10
0
1
0
3
2
3
24
47
83
133
261
215
155
99
242
3
3
3
1
2
4
1
0
5
7
11
3
2
11
19
24
97
83
106
172
119
142
110
194
263
27
30
25
34
42
35
30
18
16
31
43
53
48
90
103
162
264
262
324
356
412
459
457
647
580
156
172
131
158
184
167
183
197
199
236
247
260
285
569
635
873
1197
1648
2206
2799
3449
4168
4525
5022
5614
6 - 27
Methodology (cont.)
Estimate Model
Evaluate
Performance
Time
36 Months

Use past 36 months of data to estimate model parameters


Standardized data within each peer group on a given date to allow for timeseries and cross-sectional pooling [Brown, Harlow, and Starks (JF, 1996)]
Evaluate performance


3 Months (1 Month)
Use estimated model parameters to calculate out-of-sample alphas based on
factor returns from the evaluation period
Roll the process forward one quarter (one month) and
estimate all parameters again, etc.
6 - 28
Performance Analysis
Distributions of Out-of-Sample Future Alphas (FALPHA)
Quarterly – Equally Weighted 1979-2003
Quarterly FALPHA Value at Percentile (%):
Fund Style
# of Obs.
5th
25th
Median
75th
95th
% Pos.
Alphas
Overall
LV
LB
LG
MV
MB
MG
SV
SB
SG
S&P 500
Index Fund
126,613
17,195
23,566
30,642
6,214
4,251
19,172
4,963
4,475
16,135
295
-8.85
-7.53
-7.07
-7.95
-10.82
-8.21
-9.71
-12.37
-9.95
-11.07
-1.41
-3.12
-2.98
-2.43
-2.66
-3.13
-3.23
-3.79
-4.39
-3.96
-4.03
-0.37
-0.49
-0.66
-0.48
-0.25
-0.09
-0.24
-0.56
-1.30
-1.12
-0.59
0.08
2.06
1.82
1.28
1.89
2.93
2.88
2.67
1.99
1.89
3.10
0.51
8.55
6.80
6.10
7.99
9.41
9.06
10.32
10.81
8.47
10.89
1.22
44.50
42.28
42.37
46.59
49.10
47.49
45.34
38.32
40.20
45.53
54.58
6 - 29
Time Series Analysis
Pooled Regressions – Fund Characteristics versus Future Alpha
1979-2003
Variable
1 Month Alpha
Parameter
Prob
Estimate
3 Month Alpha
Parameter
Prob
Estimate
Intercept
0.000
1.000
0.000
1.000
Past Alpha
0.071
0.000
0.072
0.000
Expense Ratio
(0.012)
0.000
(0.023)
0.000
Diversify (R-Sq)
(0.036)
0.000
(0.055)
0.000
Volatility
(0.012)
0.000
(0.006)
0.043
Turnover
0.016
0.000
0.019
0.000
Assets
0.007
0.000
0.008
0.009
6 - 30
Cross-Sectional Analysis

Use past 36 months of data to estimate model parameters

Run a sequence of Fama-MacBeth cross-sectional regressions of
future performance against fund characteristics and model
parameters (alpha and R2 )

Average the coefficient estimates from regressions across the
entire sample period

T-statistics based on the time-series means of the coefficients
6 - 31
Cross-Sectional Performance Results
Fama-MacBeth Regressions – Fund Characteristics versus Future Alpha
1979-2003
Variable
Past Alpha
1 Month Alpha
Parameter
Prob
Estimate
3 Month Alpha
Parameter
Prob
Estimate
0.047
0.000
0.061
0.000
Expense Ratio
(0.012)
0.033
(0.019)
0.063
Diversify (R-Sq)
(0.021)
0.091
(0.023)
0.333
Volatility
(0.011)
0.377
(0.022)
0.306
Turnover
0.015
0.034
0.022
0.072
Assets
0.008
0.034
0.009
0.190
6 - 32
Logit Performance Analysis
Fund Characteristics versus a Positive Future Alpha
1979-2003
Variable
1 Month Alpha
Parameter
Prob
Estimate
3 Month Alpha
Parameter
Prob
Estimate
Intercept
(0.159)
0.000
(0.228)
0.000
Past Alpha
0.082
0.000
0.093
0.000
Expense Ratio
(0.021)
0.000
(0.033)
0.000
Diversify (R-Sq)
(0.085)
0.000
(0.117)
0.000
Volatility
(0.003)
0.419
(0.022)
0.000
Turnover
0.028
0.000
0.022
0.000
Assets
0.015
0.000
0.023
0.000
6 - 33
Probability of Finding a Superior Active Manager
Probability of Future Positive 3-month Alpha
Median Manager Controls for Turnover, Assets, Diversify, and Volatility
EXPR:
-2 (Low)
-1
0
+1
+2 (High)
(High –
Low)
-2 (Low)
0.4143
0.4062
0.3982
0.3903
0.3824
(0.0319)
-1
0.4369
0.4288
0.4206
0.4125
0.4045
(0.0324)
0
0.4599
0.4516
0.4434
0.4352
0.4270
(0.0329)
+1
0.4830
0.4746
0.4664
0.4581
0.4498
(0.0331)
+2 (High)
0.5061
0.4978
0.4895
0.4812
0.4729
(0.0333)
(High –
Low)
0.0918
0.0916
0.0913
0.0909
0.0905
Std. Dev.
Group
PALPHA:
6 - 34
Probability of Finding a Superior Active Manager (cont.)
Probability of Future Positive 3-month Alpha
“Best” Manager Controls for Turnover, Assets, Diversify, and Volatility
EXPR:
-2 (Low)
-1
0
+1
+2 (High)
(High – Low)
-2 (Low)
0.5051
0.4968
0.4884
0.4801
0.4718
(0.0333)
-1
0.5282
0.5199
0.5116
0.5033
0.4950
(0.0333)
0
0.5512
0.5430
0.5347
0.5264
0.5181
(0.0331)
+1
0.5741
0.5659
0.5577
0.5495
0.5412
(0.0328)
+2 (High)
0.5965
0.5885
0.5804
0.5723
0.5641
(0.0324)
(High – Low)
0.0915
0.0918
0.0920
0.0922
0.0923
Std. Dev.
Group
PALPHA:
6 - 35
Portfolio Strategies Based on Active Manager Search
Asset Weighted Alpha Deciles - Quarterly Rebalance
1979-2003
2.00%
Average Annualized Alpha
1.50%
1.00%
0.50%
0.00%
1
2
3
4
5
6
7
8
9
10
-0.50%
-1.00%
-1.50%
-2.00%
-2.50%
6 - 36
Portfolio Strategies (cont.)
Asset Weighted - Quarterly Rebalance
Formation Variables Separated by Upper and Lower Quartile Values
1979-2003
Portfolio Formation Variables
Expense
Alpha
Overall Sample
Lo
Hi
Lo
Hi
Hi
Lo
Hi
Lo
S&P 500 Index Fund
Cumulative Value Average Alpha
of $1 Invested
(%)
Alpha Volatility
(%)
1.046
0.181
2.153
1.009
1.005
1.515
0.738
1.446
0.673
0.037
0.018
1.691
(1.221)
1.502
(1.585)
2.142
4.025
3.371
3.469
3.596
4.712
1.022
0.088
1.700
Return
Differential
(bp)
2
291
309
6 - 37
The Benefit of Selecting Good Managers and
Avoiding Bad Managers
Positive
Alpha
Probability
Above Median
Bottom
Top
Peer
Peer Quartile Peer Quartile
No Information
44.3%
50.0%
24.4%
24.6%
Alpha
Expense Ratio
Alpha, Expense Ratio
Alpha, Expense Ratio, Risk, Turnover, Assets
49.0%
46.0%
50.6%
60.0%
54.2%
52.8%
58.8%
62.9%
27.4%
27.1%
28.8%
34.2%
27.7%
24.8%
28.3%
48.7%
Overall Incremental Probability
15.7%
12.9%
9.8%
24.2%
6 - 38
Implementing a “Fund of Funds” Strategy: An Example
Methodology
Estimate Model
Evaluate
Performance
Time
9 Months
3 Months (1 Month)

Use past 9 months of daily data to estimate model and insample alpha

Optimize portfolio based on an assumption of risk aversion,
i.e., risk-return tradeoff preference

Compute the performance of the portfolio over the next three
(one) months

Roll the process forward each quarter and estimate all
parameters again, etc.
6 - 39
“Fund of Funds” Strategy
Fidelity Advisor Diversified Equity Fund Styles (6/04)
100
FAIVX
IVV
90
FGIOXFDGIX
FHCIX
EQPIX
FFSIX
FAGCX
FUGIX
Cap: Small to Large
FALIX
80
70
FTQIX
FCNIX
FCLIX
FATIX
EQPGX
FTIMX
FHEIX
60
FFYIX
50
FMCCX
FRVIX
40
FASOX
FSCIX
30
FBTIX
FDCIX
20
10
0
FVLIX
FVIFX
0
10
20
30
40
50
60
Value to Grow th
70
80
90
100
6 - 40
“Fund of Funds” Portfolio Strategy
Portfolio Weights Over Time
Name
Fidelity Advisor Equity Growth Instl
Fidelity Advisor Equity Income Instl
Fidelity Advisor Growth Opport Instl
Fidelity Advisor Equity Value I
Fidelity Advisor Large Cap Instl
Fidelity Advisor Value Strat Instl
Fidelity Advisor Technology Instl
Fidelity Advisor Cyclical Indst Instl
Fidelity Advisor Consumer Indst Instl
Fidelity Advisor Dynamic Cap App Inst
Fidelity Advisor Dividend Growth Inst
Fidelity Advisor Financial Svc Instl
Fidelity Advisor Growth & Income Inst
Fidelity Advisor Health Care Instl
Fidelity Advisor Mid Cap Instl
Fidelity Advisor Telecomm&Util Gr Ins
iShares S&P 500 Index
200103 200106 200109 200112 200203 200206 200209 200212 200303 200306 200309 200312 200403
7.1%
5.3%
9.9%
9.6%
20.0% 20.0% 20.0% 19.5% 20.0% 20.0% 12.0%
9.0%
5.3% 20.0%
13.4%
10.0%
2.6%
2.6% 10.8% 10.6% 14.5% 14.6%
6.1%
2.9%
18.2% 18.6% 18.5% 18.8% 18.5% 10.4% 10.6% 10.6%
7.0%
7.0%
0.3%
4.5%
4.6%
4.9%
8.0%
8.1%
7.5%
6.1%
5.6%
4.8%
4.2%
6.2%
5.0%
6.0%
7.3%
7.3%
5.6%
6.0%
7.4%
0.7%
4.9%
3.9%
4.1%
0.7%
1.2%
1.2%
10.9% 11.1%
2.5%
1.4%
1.5%
2.5%
1.7%
6.1%
9.3%
0.5%
20.0% 20.0% 20.0% 20.0% 20.0%
2.1%
2.1%
7.6% 15.8% 15.9%
4.3%
4.2%
4.2%
9.3%
8.6%
7.8%
7.1%
1.2%
1.8% 11.8% 11.7% 11.5%
4.7% 12.3% 12.4% 15.1%
12.1% 16.7% 20.0% 17.1% 15.6%
7.4%
7.3% 11.1% 17.5% 17.4%
5.8%
5.7%
3.2%
2.2%
4.7%
4.5%
4.0%
8.8% 10.8%
9.7%
6.0%
5.7%
5.5%
5.5%
2.3%
9.6% 10.1%
8.6%
0.9%
0.9%
5.0%
1.9%
5.0%
4.7%
4.7%
1.4%
11.7% 15.2% 20.0%
7.8%
8.2%
8.1% 12.8% 14.9%
8.6%
8.5%
8.5% 12.3% 15.0%
Portfolio Characteristics
Avg Annual
Active
Portfolio
Return
S&P 500
0.68%
Periods
% Beat
Bench in
Up Market
84
60%
% Beat
Bench in
Best Active
Down Market
Return
67%
5.20%
Worst
Active
Return
Longest
Winning
Streak
Longest
Losing
Streak
Annual
Tracking
Error
(3.7%)
7
4
3.3%
6 - 41
Cumulative Returns versus S&P 500
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
-0.1
JAN97
JAN98
JAN99
JAN00
JAN01
JAN02
JAN03
JAN04
JAN05
6 - 42
Active vs. Passive Management: Conclusions

Both passive and active management can play a
role in an investor’s portfolio

Strong evidence for both positive and negative
performance persistence (i.e., alpha persistence)


Prior alpha is the most significant variable for forecasting future alpha

Expense ratio, risk measures, turnover and assets are also useful in
forecasting future alpha
The existence of performance persistence provides
a reasonable opportunity to construct portfolios
that add value on a risk-adjusted basis
6 - 43