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M2 T2
18 Return S.D. Beta Unsy. Risk Sharpe Treynor Jensen Appraisal
19 Millennium 0.4000 0.3300 2.5000 0.2700 1.0303 0.1360 -0.0100 0.0352 -0.0040 -0.0370
20 Omega 0.3100 0.2600 1.6200 0.0600 0.9615 0.1543 0.0232 0.0235 0.0143 0.3867
21 Momentum Watcher 0.2900 0.2400 1.4000 0.1600 0.9583 0.1643 0.0340 0.0229 0.0243 0.2125
22 S & P Index Return 0.2000 0.1700 1.0000 0.0000 0.8235 0.1400 0.0000 0.0000 0.0000 0.0000
23 Big Potential 0.1500 0.1100 0.5500 0.0150 0.8182 0.1636 0.0130 -0.0009 0.0236 0.8667
24 Alpha 0.2800 0.2700 1.7000 0.0500 0.8148 0.1294 -0.0180 -0.0015 -0.0106 -0.3600
25 Omicron 0.2200 0.2100 0.8500 0.0200 0.7619 0.1882 0.0410 -0.0105 0.0482 2.0500
26 Big Value 0.1500 0.1300 0.9000 0.0300 0.6923 0.1000 -0.0360 -0.0223 -0.0400 -1.2000
27
28 Ranking by Treynor
T2
M2
29 Return S.D. Beta Unsy. Risk Sharpe Treynor Jensen Appraisal
30 Omicron 0.2200 0.2100 0.8500 0.0200 0.7619 0.1882 0.0410 -0.0105 0.0482 2.0500
31 Momentum Watcher 0.2900 0.2400 1.4000 0.1600 0.9583 0.1643 0.0340 0.0229 0.0243 0.2125
32 Big Potential 0.1500 0.1100 0.5500 0.0150 0.8182 0.1636 0.0130 -0.0009 0.0236 0.8667
33 Omega 0.3100 0.2600 1.6200 0.0600 0.9615 0.1543 0.0232 0.0235 0.0143 0.3867
34 S & P Index Return 0.2000 0.1700 1.0000 0.0000 0.8235 0.1400 0.0000 0.0000 0.0000 0.0000
35 Millennium 0.4000 0.3300 2.5000 0.2700 1.0303 0.1360 -0.0100 0.0352 -0.0040 -0.0370
36 Alpha 0.2800 0.2700 1.7000 0.0500 0.8148 0.1294 -0.0180 -0.0015 -0.0106 -0.3600
37 Big Value 0.1500 0.1300 0.9000 0.0300 0.6923 0.1000 -0.0360 -0.0223 -0.0400 -1.2000
38




Bogey Performance and Excess Return
TA B L E 20.3
Return of Index
Performance of the
Component Benchmark Weight during Month (%)
managed portfolio

Equity (S&P 500) 0.60 5.81
Bonds (Lehman Bros. Index) 0.30 1.45
Cash (money market) 0.10 0.48
Bogey (0.60 5.81) (0.30 1.45) (0.10 0.48) 3.97%
Return of managed portfolio 5.34%
Return of bogey portfolio 3.97
Excess return of managed portfolio 1.37%



696
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Essentials of Investments, Management and Active Portfolio Companies, 2003
Fifth Edition Management




697
20 Performance Evaluation and Active Portfolio Management


Asset Allocation Decisions
The managed portfolio is actually invested in the equity, fixed-income, and money markets
with weights of 70%, 7%, and 23%, respectively. The portfolio™s performance could be due to
the departure of this weighting scheme from the benchmark 60/30/10 weights and/or to supe-
rior or inferior results within each of the three broad markets.
To isolate the effect of the manager™s asset allocation choice, we measure the performance
of a hypothetical portfolio that would have been invested in the indexes for each market with
weights 70/7/23. This return measures the effect of the shift away from the benchmark
60/30/10 weights without allowing for any effects attributable to active management of the se-
curities selected within each market.
Superior performance relative to the bogey is achieved by overweighting investments in
markets that turn out to perform better than the bogey and by underweighting those in poorly
performing markets. The contribution of asset allocation to superior performance equals the
sum over all markets of the excess weight in each market times the return of the market index.
Table 20.4A demonstrates that asset allocation contributed 31 basis points to the portfolio™s
overall excess return of 137 basis points. The major factor contributing to superior perfor-
mance in this month is the heavy weighting of the equity market in a month when the equity
market has an excellent return of 5.81%.

Sector and Security Selection Decisions
If 0.31% of the excess performance can be attributed to advantageous asset allocation across
markets, the remaining 1.06% then must be attributable to sector selection and security selec-
tion within each market. Table 20.4B details the contribution of the managed portfolio™s sec-
tor and security selection to total performance.



A. Contribution of Asset Allocation to Performance
TA B L E 20.4
(1) (2) (3) (4) (5) (3) (4)
Performance
Actual Benchmark Index Contribution to
attribution
Weight Weight Excess Return Performance
Market in Market in Market Weight (%) (%)

Equity 0.70 0.60 0.10 5.81 .5810
Fixed-income 0.07 0.30 0.23 1.45 .3335
Cash 0.23 0.10 0.13 0.48 .0624
Contribution of asset allocation 0.3099

B. Contribution of Selection to Total Performance

(1) (2) (3) (4) (5) (3) (4)
Portfolio Index Excess
Performance Performance Performance Portfolio Contribution
Market (%) (%) (%) Weight (%)

Equity 7.28 5.81 1.47 0.70 1.03
Fixed-income 1.89 1.45 0.44 0.07 0.03
Contribution of selection within markets 1.06
Bodie’Kane’Marcus: VI. Active Investment 20. Performance Evaluation © The McGraw’Hill
Essentials of Investments, Management and Active Portfolio Companies, 2003
Fifth Edition Management




698 Part SIX Active Investment Management



TA B L E 20.5
Sector selection within the equity market

(1) (2) (3) (4) (5) (6) (3) (5)
Beginning of Month Sector
Weights (%) Allocation
Sector
Difference Sector Over/Under- Contribution
Sector Portfolio S&P 500 in Weights Return Performance* (basis points)

Basic materials 1.96 8.3 6.34 6.4 0.9 5.7
Business services 7.84 4.1 3.74 6.5 1.0 3.7
Capital goods 1.87 7.8 5.93 3.7 1.8 10.7
Consumer cyclical 8.47 12.5 4.03 8.4 2.9 11.7
Consumer noncyclical 40.37 20.4 19.97 9.4 3.9 77.9
Credit sensitive 24.01 21.8 2.21 4.6 0.9 2.0
Energy 13.53 14.2 0.67 2.1 3.4 2.3
Technology 1.95 10.9 8.95 0.1 5.6 50.1
Total 129.3

*S&P 500 performance net of dividends was 5.344%. Returns were compared net of dividends.


Panel B shows that the equity component of the managed portfolio has a return of 7.28%
versus a return of 5.81% for the S&P 500. The fixed-income return is 1.89% versus 1.45% for
the Lehman Brothers Index. The superior performance in both equity and fixed-income mar-
kets weighted by the portfolio proportions invested in each market sums to the 1.06% contri-
bution to performance attributable to sector and security selection.
Table 20.5 documents the sources of the equity market performance by each sector within
the market. The first three columns detail the allocation of funds within the equity market
compared to their representation in the S&P 500. Column (4) shows the rate of return of each
sector, and column (5) documents the performance of each sector relative to the return of the
S&P 500. The contribution of each sector™s allocation presented in column (6) equals the prod-
uct of the difference in the sector weight and the sector™s relative performance.
Note that good performance (a positive contribution) derives from overweighting well-
performing sectors such as consumer nondurables, as well as underweighting poorly perform-
ing sectors such as capital goods. The excess return of the equity component of the portfolio
attributable to sector allocation alone is 129 basis points, or 1.29%. As the equity component
of the portfolio outperformed the S&P 500 by 1.47%, we conclude that the effect of security
selection within sectors must have contributed an additional 1.47 1.29, or 0.18%, to the per-
formance of the equity component of the portfolio.
A similar sector analysis can be applied to the fixed-income portion of the portfolio, but we
do not show those results here.


Summing Up Component Contributions
In this particular month, all facets of the portfolio selection process were successful. Table
20.6 details the contribution of each aspect of performance. Asset allocation across the major
security markets contributes 31 basis points. Sector and security allocation within those mar-
kets contributes 106 basis points, for total excess portfolio performance of 137 basis points.
The sector and security allocation of 106 basis points can be partitioned further. Sector allo-
cation within the equity market results in excess performance of 129.3 basis points, and secu-
rity selection within sectors contributes 18 basis points. (The total equity excess performance
Bodie’Kane’Marcus: VI. Active Investment 20. Performance Evaluation © The McGraw’Hill
Essentials of Investments, Management and Active Portfolio Companies, 2003
Fifth Edition Management




699
20 Performance Evaluation and Active Portfolio Management


Contribution
TA B L E 20.6 (basis points)
Portfolio attribution:
1. Asset allocation 31.0
summary
2. Selection
a. Equity excess return
i. Sector allocation 129
ii. Security allocation 18
147 0.70 (portfolio weight) 102.9
b. Fixed-income excess return 44 0.07 (portfolio weight) 3.1
Total excess return of portfolio 137.0



of 147 basis points is multiplied by the 70% weight in equity to obtain contribution to port-
folio performance.) Similar partitioning could be done for the fixed-income sector.


<
2. a. Suppose the benchmark weights had been set at 70% equity, 25% fixed-income, Concept
and 5% cash equivalents. What then would be the contributions of the man-
CHECK
ager™s asset allocation choices?
b. Suppose the S&P 500 return had been 5%. Recompute the contribution of the
manager™s security selection choices.


20.3 THE LURE OF ACTIVE MANAGEMENT
Now that we know how to measure the success of active portfolio managers, we reconsider
the rationale for active management. How can a theory of active portfolio management make
sense if we accept the notion that markets are in equilibrium? Chapter 8 on market efficiency
gives a thorough analysis of efficient market theory; here we summarize how the theory fits
with active management strategy.
Market efficiency prevails when many investors are willing to depart from a passive strat-
egy of efficient diversification, so that they can add mispriced securities to their portfolios.
Their objective is to realize “abnormal” returns.
The competition for such returns ensures that prices will be near their “fair” values. This
means most managers will not beat the passive strategy if we take risk into account with
reward. Exceptional managers, however, might beat the average forecasts that are built into
market prices and consequently construct portfolios that will earn abnormal returns.
How can this happen? There is economic logic behind the result, as well as some empirical
evidence indicating that exceptional portfolio managers can beat the average forecast. First the
economic logic. If no analyst can beat the passive strategy, investors eventually will not be
willing to pay for expensive analysis; they will adopt less-expensive, passive strategies. In that
case, funds under active management will dry up, and prices will no longer reflect sophisti-
cated forecasts. The resulting profit opportunities will lure back active managers who once
again will become successful.2 The critical assumption here is that investors make wise deci-
sions on how to manage their money. Direct evidence on that has yet to be produced.
As for empirical evidence, consider the following: (1) some portfolio managers experience
streaks of abnormal returns that are hard to label as lucky outcomes; (2) the “noise” in realized
rates of return is enough that we cannot reject outright the hypothesis that some investment
managers can beat the passive strategy by a statistically small, yet economically significant,

2
This point is worked out fully in Sanford J. Grossman and Joseph E. Stiglitz, “On the Impossibility of Information-
ally Efficient Markets,” American Economic Review 70 (June 1980), pp. 393“408.
Bodie’Kane’Marcus: VI. Active Investment 20. Performance Evaluation © The McGraw’Hill
Essentials of Investments, Management and Active Portfolio Companies, 2003
Fifth Edition Management




E XC E L Applications www.mhhe.com/bkm


> Excel Applications
Performance Attribution


The Excel model “Performance Attribution” that is available on the book™s website is built on the
example that appears in section 20.2. The model allows you to specify different allocations and to
analyze the contribution sectors and weightings for different performances.
You can learn more about this spreadsheet model by using the interactive version available on
our website at www.mhhe.com/bkm.

A B C D E F
1 Chapter 20 Performance Attribution
2 Solution to Question
3 Bogey Portfolio Weight Return on Portfolio
4 Component Index Benchmark Index Return
5 Equity S&P500 0.6 5.8100% 3.4860%
6 Bonds Lehman Index 0.3 1.4500% 0.4350%
7 Cash Money Market 0.1 0.4800% 0.0480%
8
9 Return on Bogey 3.9690%

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