Mauboussin skill manager

Perspectives

February 2012
Legg Mason Capital
Management
Seeking portfolio
manager skill

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February 24, 2012

Seeking Portfolio Manager Skill
Active Share and Tracking Error as a Means to Anticipate Alpha1

1.5%

1.0%
Annualized Four-Factor Alpha

0.5%

0.0%

-0.5%

-1.0%

-1.5%

-2.0%

-2.5%
Closet Moderately Factor Concentrated Stock
Indexers Active Bets Pickers

Source: Antti Petajisto, “Active Share and Mutual Fund Performance,” Working Paper, December 15, 2010.

• There is a logical case for active management, but the key challenge is
identifying above-average portfolio managers ahead of time.

• Most statistics in the investment industry and corporate America fail the
dual test of reliability and validity.

• Active share and tracking error are both reliable statistics, and research
shows that funds with high active share and moderate tracking error
deliver excess returns on average.

• The long-term trend has been toward lower active share, which makes it
difficult for mutual funds to generate sufficient gross returns to offset fees.

Page 1 Legg Mason Capital Management

Equity markets are generally considered to be informationally efficient, which means that all
relevant information is impounded in prices. Because it is difficult for an active manager to
generate returns in excess of that of the market after an adjustment for risk, a common
prescription is to turn to passive management in the form of index funds. This is a sensible
approach for many investors. But the case for passive management has logical limits. For
example, in economics there is an idea called the macro consistency test, which asks, “Would
this approach work if everyone pursued it?” The answer for passive investing is no. Some
percentage of investors must be active in order to ensure that information is translated into prices.
Indeed, recent research shows that active management enhances, and passive management
reduces, the informational efficiency of stock prices.2

In 1980, a pair of economists, Sanford Grossman and Joseph Stiglitz, wrote a seminal paper
called, “On the Impossibility of Informationally Efficient Markets.” 3 Their basic argument is that
there is a cost to making sure that prices properly reflect information. If there is no return for
obtaining and trading on information, there is no economic incentive to do so. They propose that
“those who do expend resources to obtain information do receive compensation” in the form of
excess returns. In-depth studies show that active managers do indeed generate gross returns in
excess of those of the market.4 However, those returns are less than the fees that managers
charge. Careful studies of active management also reveal differential skill—that is, luck alone
does not explain the results in investment management and a small percentage of managers
deliver positive excess returns after all costs.5

Of course the challenge is to identify skillful managers ex ante. There are two major approaches
to assessing manager skill.6 The first relies on an analysis of prior returns. The effectiveness of
this approach relies on extracting useful information about skill by considering a sufficiently long
time period and by controlling for various factors, including the types of risks the manager has
assumed and the systematic versus idiosyncratic risk exposure. Returns-based assessments
rarely make sufficient and appropriate adjustments to distill skill from the reported results. Further,
simulations show that even skillful managers—those endowed with an attractive ex-ante Sharpe
ratio—can deliver poor returns for years as a consequence of luck.7 In other words, even skillful
managers won’t always beat their benchmarks and unskillful managers can do well for stretches
of time as the result of randomness.

The second approach to testing manager skill is look at the portfolio holdings and characteristics
of managers. Characteristics might include a portfolio manager’s age, education, and the size of
his or her fund. The focus on portfolio construction and holdings allows for a more precise
assessment of a manager’s process. The focus of this discussion will be on active share, a
concept developed by a pair of finance professors named Martijn Cremers and Antti Petajisto, as
a means to increase the probability of identifying a skillful manager in advance.8

What Is the Characteristic of a Valuable Statistic?

The worlds of finance and investing are awash in statistics that purport to reflect what’s going on.
Statistics that are useful have two features: reliability and validity.9 Reliability means that results
are highly correlated10 from one period to the next. For example, a student who did poorly on a
test last week does poorly this week, and the student who did well last week does well this week.
High reliability and a large contribution of skill generally go together. Finance researchers use the
term “persistence,” which is the same as reliability.

The second feature is validity, which means the result is correlated with the desired outcome. For
instance, say a baseball team’s offensive goal is to score as many runs as possible. An analysis
would show that on-base percentage is better correlated with run production than batting average
is. So an enlightened manager would prefer on-base percentage to batting average as a statistic
of offensive production, all else being equal.


The returns-based approach skips the two steps of reliability and validity and goes directly to the
results. It doesn’t pause to ask: what leads to excess returns? It just measures the outcome. This
approach works in fields where skill determines results and luck is no big deal. For example, if
you have five runners of disparate ability run a 100-yard dash, the outcome of the race is a highly
reliable predictor of the next race. You don’t need to know anything about the process because
the result alone is proof of the difference in ability.

The difficulty with using a returns-based approach to assessing skill is that there is not a great
deal of reliability, or persistence, in measures of excess returns. Researchers do find evidence for
modest persistence but only when returns are carefully adjusted to account for style factors.11 But
correlations over short periods, say year-to-year, for alpha based on the capital asset pricing
model (CAPM) are quite low.

This problem of low reliability applies broadly to any highly competitive field that is probabilistic.
Results, and especially short-term results, cannot distinguish between a good process and a poor
process because of the role of luck. So going directly to the results gives little indication about the
quality of the decision-making process and the skill of the participant.

In contrast, the approach that considers the holdings and characteristics of the manager allows
us to look at both reliability and validity. Now the discussion shifts a bit. The questions become:
which measures of an active manager’s portfolio reflect skill and therefore reliability? For
example, a manager may be able to control the number of holdings, risk, turnover, and fees.
Next, of the measures that are reliable, which are highly correlated with the ultimate objective of
delivering excess returns? Are there measures that are both reliable and valid?

Active Share + Tracking Error = Indicator of Skill

Let’s now take a closer look at active share. In plain language, active share is “the percentage of
the fund’s portfolio that differs from the fund’s benchmark index.”12 Assuming no leverage or
shorting, active share is 0 percent if the fund perfectly mimics the index and 100 percent if the
fund is totally different than the index.

More technically,
1 N
Active Share = ∑ ω fund ,i − ωindex,i
2 i =1
where:
ωfund,i = portfolio weight of asset i in the fund
ωindex,i = portfolio weight of asset i in the index

Here’s a really simple example. Say the index has 10 stocks, weighted as follows:

Index Holdings
Position Weight
Stock 1 20.0 %
Stock 2 15.0
Stock 3 12.0
Stock 4 11.0
Stock 5 10.0
Stock 6 9.0
Stock 7 8.0
Stock 8 7.0
Stock 9 5.0
Stock 10 3.0
Total 100.0


Now let’s say we have a fund of 10 stocks, weighted as follows:

Fund Holdings
Position Weight
Stock 1 10.0 %
Stock 2 0.0
Stock 3 5.0
Stock 4 3.0
Stock 5 20.0
Stock 11 15.0
Stock 12 12.0
Stock 13 11.0
Stock 14 9.0
Stock 15 15.0
Total 100.0

Active share is the sum of the absolute values of the difference between the weight in the index
and the weight in the fund, divided by two:

Position Index Weight Fund Weight Active Share
Stock 1 20.0% 10.0% 5.0%
Stock 2 15.0 0.0 7.5
Stock 3 12.0 5.0 3.5
Stock 4 11.0 3.0 4.0
Stock 5 10.0 20.0 5.0
Stock 6 9.0 0.0 4.5
Stock 7 8.0 0.0 4.0
Stock 8 7.0 0.0 3.5
Stock 9 5.0 0.0 2.5
Stock 10 3.0 0.0 1.5
Stock 11 0.0 15.0 7.5
Stock 12 0.0 12.0 6.0
Stock 13 0.0 11.0 5.5
Stock 14 0.0 9.0 4.5
Stock 15 0.0 15.0 7.5
Total 100.0 100.0 72.0%

In this basic example, you can see that active share is the result of not owning, or weighting
differently, the stocks in the index (see stocks 1-10) and owning stocks that are not in the index
(see stocks 11-15).

Generally, an active share of 60 percent or less is considered to be closet indexing and active
shares of 90 percent or more indicate managers who are truly picking stocks. For the past 30
years, active share has been declining steadily for the mutual fund universe in the United States.
For instance, the percentage of assets under management with active share less than 60 percent
went from 1.5 percent in 1980 to over 40 percent today.

The selection of an index as a benchmark is obviously crucial. Research by Antti Petajisto shows
that of the roughly 2,500 mutual funds he analyzed, 38.6 percent used the S&P 500 as their
benchmark. Weighted by assets, 56 percent of the funds use the S&P 500 as a benchmark.
Other popular benchmarks include the Russell 2000 (8.8 percent by number, 6.2 percent by
weight), the Russell 1000 Growth (8.4 percent by number, 5.6 percent by weight) and the Russell
1000 Value (8.2 percent by number, 8.4 percent by weight). Exhibit 1 shows the most common
benchmark indexes.


Exhibit 1: Most Common Benchmark Indexes13
60%

50%

40%
Percentage of Funds
Percentage of Assets
30%

20%

10%

0%
S&P 500 Russell Russell Russell Russell Russell Russell Russell Russell Other
2000 1000 1000 2000 2000 Midcap 3000 Midcap
Growth Value Growth Value Growth Value


There are two basic ways to raise active share.14 The first is through stock selection, as our
simple example shows. That means either buying stocks that are not represented in the index, or
owning stocks that are in the index but at a position weight that is higher or lower than what is in
the index.

The second way to raise active share is through systematic factor risk15, which is effectively
betting on factors by overweighting or underweighting16 industries. For example, a manager who
is bullish on an economic recovery might overweight industries that are economically sensitive, or
a manager who is bearish might overweight defensive industries. Tracking error, the standard
deviation of the difference between the returns of the fund and of the index, does an effective job
in capturing systematic factor risk. Tracking error puts more weight on correlated active bets than
active share does. You can think of active share as a complement to tracking error and a
measure that adds value in explaining fund results. A full picture of active management
incorporates both active share and tracking error.

To illustrate the difference between these measures of active management, Petajisto offers the
following illustration. Say a portfolio has 50 stocks. If all of the overweight positions are in
technology stocks that move together, then small active positions will generate high tracking
error. The portfolio has high systematic risk.

On the other hand, say the index represents 50 industries with 20 stocks in each industry and the
fund selects one stock from each industry but weights that stock at the same level as the industry.
In this case, active share will be high at about 95 percent but the tracking error will be relatively
low. As Petajisto notes, “active share is a reasonable proxy for stock selection, whereas tracking
error is a proxy for systematic factor risk.”

There is a clear relationship between active share and tracking error. When active share is low,
tracking error tends to be low and when active share is high, tracking error tends to be high. But
the data show some amount of variation. For example, funds with tracking error of 4-6 percent
can have active shares of 30 percent to 100 percent, while active shares in the 70-80 percent


range can be associated with tracking errors between 2 and 14 percent. This range of values for
each measure of active management shows why it is important to distinguish between the two.

Exhibit 2 shows a matrix that classifies 401 mutual funds based on active share and tracking error
using data from year-end 2007. The funds were sorted into quintiles based on each measure,
with one as the lowest value and five as the highest value. The cells represent the number of
funds that fall into the intersection of each pairing of quintiles. For example, if you examine the
top right corner, you can see that 47 funds, or 11.6 percent of the sample, are in the highest
quintile of both active share and tracking error. These are funds that are very different than their
benchmarks and that have results that vary quite a bit from their benchmark. In contrast, the
bottom left corner shows that nearly 15 percent of the sample—59 funds—are in the lowest
quintile of both active share and tracking error. These are index hugging funds. To be in the top
quintile, a fund must have an active share higher than 91 percent and a tracking error higher than
5.3 percent.

Exhibit 2: 401 Mutual Funds Ranked in Quintiles Based on Active Share and Tracking Error
Tracking Error
1 2 3 4 5
5 0 1 4 29 47
4 1 8 22 23 26
Active
3 7 22 25 20 6
Share
2 13 34 24 7 2
1 59 15 5 1 0

Source: Morningstar, FactSet, and LMCM analysis.

A common measure of portfolio performance is the information ratio, which is excess return
divided by tracking error. There is a fairly linear relationship between large factor bets (i.e., the
overweighting or underweighting of industries relative to the benchmark) and tracking error. So in
order to have an attractive information ratio, those factor bets have to really pay off to
compensate for the high tracking error. Broadly speaking, they don’t. So active managers are
better off maintaining high active share through stock picking than through sector bets.

The appendix provides a more sophisticated numerical example of active share and systematic
factor bets based on a fictitious index and fund.

Active Share and Fees

The downward drift in active share raises an important issue in the active versus passive debate.
If you’re going to go passive, go passive. Buy a fund that charges low fees and closely mirrors the
index. If you’re going to go active, find a manager with a good process and high active share.
Academic research shows, for example, that the best ideas of money managers generate excess
returns.17

Active managers who have crept toward closet indexing have created a losing proposition—
market-like returns accompanied by fees higher than index funds. Petajisto provides an
interesting case with Fidelity’s flagship mutual fund, Magellan. Peter Lynch made the fund famous
by delivering outstanding returns in the 1980s when he managed it, in part by sustaining high
active share. When Jeffrey Vinik ran the fund in the early 1990s, it had an active share above 70
percent. However, the fund’s next manager, Robert Stansky, who took over in 1996, took the
active share below 40 percent and kept it there for a half dozen years.

Here’s why it’s so hard to beat the market with low active share and an average expense ratio.
Say a fund has an expense ratio of 125 basis points—roughly the average of all funds in
Petajisto’s study—and the active share is 33 percent. That means that two-thirds of the portfolio


is earning the same return as the benchmark index. Therefore, the active part has to make up for
the difference with massive outperformance. For example, in order to equal the benchmark’s
returns, the active portion needs to earn an excess return of 375 basis points:

Percentage
of Portfolio Excess Return Weighted Return
Passive 67% 0.00% 0.00%
Active 33 3.75 1.25%
100%
Gross return 1.25%
Less expenses -1.25%
Net return = 0%

Petajisto did find that low active share funds tended to have lower expense ratios, but the fees
were sufficient to make outperformance extremely difficult. Generating excess returns is
challenging enough, but low active share and average fees make the task even more daunting.

Reliability and Validity

We noted before that the returns-based approach to assessing skill skips the steps of reliability
and validity. Now we apply the features of a useful statistic to active share and tracking error. The
way to test reliability in this case is to examine the coefficient of correlation, r, between the active
share for the same fund over two different time periods. Using a sample of approximately 400
mutual funds, the r between active share for 2007 and 2010 is 86 percent. (See exhibit 3, left
side.) Cremers and Petajisto also found active share to be reliable. This makes sense, because
active share is within the control of a portfolio manager.

Tracking error, too, appears to have good reliability. For the same funds and same time period,
the coefficient of correlation, r, is 76 percent. (See exhibit 3, right side.) To put these figures in
context, three-year alphas based on the CAPM have a coefficient of correlation of close to zero.

Exhibit 3: Reliability of Active Share and Tracking Error

r = 0.86 r = 0.76
1.00 25.00
2010 Tracking Error
2010 Active Share

0.80 20.00

0.60 15.00

0.40 10.00

0.20 5.00

0.00 0.00
0.00 0.20 0.40 0.60 0.80 1.00 0.00 5.00 10.00 15.00 20.00 25.00
2007 Active Share 2007 Tracking Error

Source: Morningstar, FactSet, and LMCM analysis.

The second feature of a useful statistic is validity—it leads you to the outcomes that you seek.
The research suggests that high active share is desirable if it is the result of stock picking, but
less desirable if it is the result of factor bets that show up as high tracking error. Petajisto sorts
1,124 funds into five categories based on results from 1990 through 2009 (see exhibit 4). Stock
pickers are in the highest quintile of active share, but in the bottom 80 percent of tracking error


within that active share quintile. He labels “concentrated” the funds in the highest quintile of active
share that have the highest tracking error. These funds have high systematic factor risk. Funds in
the stock pickers category have an average active share of 97 percent with an average tracking
error of 8.5 percent. The concentrated funds have similar active share, at 98 percent, but have a
tracking error of 15.8 percent, which is almost double that of the stock pickers.

Exhibit 4: Fund Categories and Their Statistics (5 = Top, 1 = Bottom)
Average Average Portfolio Number Average
Label Description Active Share Tracking Error Turnover of stocks Expense Ratio
Stock pickers Top quintile AS, quintiles 1-4 TE 97% 8.5% 83% 66 1.41%
Concentrated Top quintile AS, top quintile TE 98% 15.8% 122% 59 1.60%
Factor bets Quintiles 2-4 AS, top quintile TE 79% 10.4% 104% 107 1.34%
Moderately active Quintiles 2-4 AS, quintiles 1-4 TE 83% 5.9% 84% 100 1.25%
Closet indexers Bottom quintile AS, quintiles 1-4 TE 59% 3.5% 69% 161 1.05%


Funds that make relatively large factor bets are in the bottom four quintiles for active share but
have among the highest tracking error within those quintiles. Moderately active funds are in the
middle quintiles for active share but have tracking error that is much lower than the funds making
factor bets. Finally, the closet indexers have low active share and low tracking error.

The test of validity is whether these categories correlate with excess returns. Exhibit 5 shows the
results from Petajisto’s research. Importantly, these results include a period when large
capitalization stocks did well (the 1990s), small capitalization stocks outperformed (the 2000s),
and the financial crisis. Petajisto shows that stock pickers generate annual alpha of 1.39 percent,
whereas all of the other categories have negative alpha. The funds that rely on factor bets are the
worst performing category. However, funds with high tracking error and high active share perform
less poorly.

Exhibit 5: Four-Factor Alpha for 1,124 Funds from 1990-2009 Based on Fund Category
1.5%

1.0%
Annualized Four-Factor Alpha

0.5%

0.0%

-0.5%

-1.0%

-1.5%

-2.0%

-2.5%
Closet Moderately Factor Concentrated Stock
Indexers Active Bets Pickers


Petajisto’s large sample over 20 years provides a solid basis to establish validity. The smaller
sample we used to establish reliability provided similar results. The funds that were in the highest
quintile for active share and the bottom 80 percent of tracking error—64 funds altogether—
generated annualized alpha of 3.8 percentage points from 2008-2010, well in excess of the
results of the sample of all 400 funds.


The conclusion is that a thoughtful combination of active share and tracking error reflects the
essential features of a good statistic: they are reliable and valid. Still, active share needs additional
testing before it can be declared sufficient to indicate ex ante skill. One specific concern is
benchmark selection. Small capitalization funds, for instance, tend to have higher active share than
large capitalization funds. This is because small capitalization indexes have more stocks, with a
lower average weight, than large capitalization indexes do. So the favorable results from the
analysis of active share may stem in part from the fact that small capitalization funds beat their
indexes more often than large capitalization funds do.18

Summary

Investment management is a very competitive business, in part because there are so many bright
and motivated people seeking to beat their benchmarks. As a result, randomness plays a large role
in determining results in the short term and it is difficult to deliver excess returns over time. Still,
academic research shows that some funds do better than chance would suggest, and that active
managers beat their benchmarks before fees. The fundamental question is whether funds with a
good chance of outperforming their benchmark can be identified in advance.

There are two approaches to assessing managers. The first examines past results. This approach
can reveal information if the track record is sufficiently long and enough controls are put into place
so as to ensure that the results are not the consequence of risk. But relying on results in any domain
that is based on probability is inherently troublesome, because the challenge of sorting skill and
randomness is daunting.

The second approach studies the characteristics and behavior of the manager in order to assess
whether he or she has a good process. To be useful, any measure of performance must have two
features: reliability and validity. Most manager assessments use statistics that are neither reliable
nor valid. We argue that a combination of active share and tracking error provides a glimpse into
process. Taken together, these statistics are also reliable and valid. Based on this discussion, we
can arrive at four conclusions:

• There is a role for active management. Having some active managers is a logical necessity.
Research shows that active management increases the informational efficiency of stock
prices and that passive management makes prices less efficient. The key challenge is
identifying above-average managers ahead of time.
• Reliability and validity. Most statistics in the investment industry fail the dual test of reliability
and validity. This is true in corporate America as well. As a consequence, it’s important to
break down investment results further in order to get a better handle on potential skill.
• The combination of active share and tracking error provides insight. Active share and
tracking error are both reliable statistics. For example, for 400 mutual funds (2007 to 2010)
the coefficient of correlation for active share was 86 percent while tracking error was 76
percent. In seeking validity, the goal is to identify funds with high active share (top quintile)
that are not in the highest quintile for tracking error. High tracking error indicates sizeable
factor bets, which tend to deliver poor returns. Research by Cremers and Petajisto,
confirmed by our own smaller sample, shows that funds with high active share and
moderate tracking error deliver excess returns.
• There is a long-term trend toward lower active share. The percentage of assets under
management with active share below 60 percent—considered to be closet indexing—has
risen from 1.5 percent 30 years ago to more than 40 percent today. Passive management
makes sense for a great deal of investors. But the essential message is this: If you’re going
to be active, go active. Don’t own a fund with low active share, because the chances are
good that the fund’s gross returns will be insufficient to leave you with attractive returns after
fees.

I’d like to acknowledge the intellectual contribution of Arturo Rodriguez, CFA. As always, Dan Callahan, CFA,
added great value in all aspects of preparing this piece.


Endnotes:
1
Alpha is a measure of performance versus a benchmark on a risk-adjusted basis. An alpha of
+1.0 means the portfolio has outperformed its benchmark index by 1%. An alpha of -1.0 means it
has underperformed its benchmark by 1%.
2
Russ Wermers and Tong Yao, “Active vs. Passive Investing and the Efficiency of Individual
Stock Prices,” Working Paper, February 2010; Rodney N. Sullivan and James X. Xiong, CFA,
“How Index Trading Increases Market Vulnerability,” Financial Analysts Journal, forthcoming (see
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1908227; and Jeffrey Wurgler, “On the
Economic Consequences of Index-Linked Investing,” Challenges to Business in the Twenty-First
Century: The Way Forward, W.T. Allen, R. Khurana, J. Lorsch, and G. Rosenfeld, eds.,
forthcoming (see http://archive.nyu.edu/bitstream/2451/31353/2/4_essay_Wurgler.pdf.)
3
Sanford J. Grossman and Joseph E. Stiglitz, “On the Impossibility of Informationally Efficient
Markets,” American Economic Review, Vol. 70, No. 3, June 1980, 393-408.
4
Russ Wermers, “Mutual Fund Performance: An Empirical Decomposition into Stock-Picking
Talent, Style, Transaction Costs, and Expenses,” Journal of Finance, Vol. 55, No. 4, August
2000, 1655-1695.
5
Robert Kosowski, Allan G. Timmerman, Russ Wermers, and Hal White, “Can Mutual Fund
‘Stars’ Really Pick Stocks?” Journal of Finance, Vol. 61, No. 6, December 2006, 2551-2595;
Laurent Barras, Olivier Scaillet, and Russ Wermers, “False Discoveries in Mutual Fund
Performance: Measuring Luck in Estimated Alphas,” Journal of Finance, Vol. 65, No. 1, February
2010, 179-216.
6
Russ Wermers, “Performance Measurement of Mutual Funds, Hedge Funds, and Institutional
Accounts,” Annual Review of Financial Economics, Vol. 3, 2011, 537-574.
7
David L. Donoho, Robert A. Crenian, and Matthew H. Scanlan, “Is Patience a Virtue? The
Unsentimental Case for the Long View in Evaluating Returns,” The Journal of Portfolio
Management, Fall 2010, 105-120.
8
K. J. Martijn Cremers and Antti Petajisto, “How Active is Your Fund Manager? A New Measure
That Predicts Performance,” Review of Financial Studies, Vol. 22, No. 9, September 2009, 3329-
3365.
9
William M.K. Trochim and James P. Donnelly, The Research Methods Knowledge Base, Third
Edition (Mason, OH: Atomic Dog, 2008), 80-95.
10
Correlation refers to the relationship between two sets of data. When asset prices move
together, they are described as positively correlated; when they move opposite to each other, the
correlation is described as negative. If price movements have no relationship to each other, they
are described as uncorrelated.
11
The most widely used are Carhart’s four-factor model (CAPM, size, valuation, momentum) and
the Fama-French three-factor model (CAPM, size, valuation). See Mark M. Carhart, “On
Persistence in Mutual Fund Performance,” Journal of Finance, Vol. 52, No. 1, March 1997, 57-82
and Eugene F. Fama and Kenneth R. French, “Common Risk Factors in the Returns of Stocks
and Bonds,” Journal of Financial Economics, Vol. 33, No. 1, February 1993, 3-56.
12
Antti Petajisto, “Active Share and Mutual Fund Performance,” Working Paper, December 15,
2010.
13
S&P 500 Index is an unmanaged index of common stock performance. Russell 2000 Index is
an unmanaged list of common stocks that is frequently used as a general performance measure
of U.S. stocks of small and/or midsize companies. Russell 1000 Growth Index is an unmanaged
index of those companies in the large-cap Russell 1000 Index chosen for their growth orientation.
Russell 1000 Value Index is an unmanaged index of those companies in the large-cap Russell
1000 Index chosen for their value orientation. Russell 2000 Growth Index is an unmanaged index
of those companies in the small-cap Russell 2000 Index chosen for their growth orientation.
Russell 2000 Value Index is an unmanaged index of those companies in the small-cap Russell
2000 Index chosen for their value orientation. Russell Midcap Growth Index is an unmanaged
index of those companies in the Russell Midcap Index chosen for their growth orientation. Russell
3000 Index is an unmanaged index of the 3,000 largest U.S. companies. Russell Midcap Value
Index is an unmanaged index of those companies in the Russell Midcap Index chosen for their
value orientation.


14
Eugene F. Fama, “Components of Investment Performance,” Journal of Finance, Vol. 27, No.
3, June 1972, 551-567.
15
Systematic risk is the risk inherent to the entire market or the entire market segment.
16
Overweighting refers to having a greater allocation to a holding, sector, etc than the index;
underweighting refers to having a smaller allocation to a holding, sector, etc than the index.
17
Randy Cohen, Christopher Polk, and Bernhard Silli, “Best Ideas,” Working Paper, March 2009.
Also, Klaas P. Baks, Jeffrey A. Busse, and T. Clifton Green, “Fund Managers Who Take Big Bets:
Skilled or Overconfident,” Working Paper, March 2006.
18
Robert C. Jones, CFA, and Russ Wermers, “Active Management in a Mostly Efficient Market,”
Financial Analysts Journal, Vol. 67, No. 6, November/December 2011, 29-45.


Appendix: Decomposing Active Share

On the left is a fictitious index. The list shows the 50 stocks in the index, which industry each
company is in, and the weight within the index. On the right is our fictitious fund, which has 25
stocks. Note that the stocks in the fund do not overlap completely with the stocks in the index. In
other words, the fund holds some stocks that are not in the index.

Index Holdings Weight Fund Holdings Weight
Energy Company 6 7.7% Consumer Discretionary Company 1 7.7%
Information Technology Company 1 7.2% Consumer Staples Company 1 7.1%
Information Technology Company 4 4.1% Information Technology Company 5 7.0%
Energy Company 3 4.0% Energy Company 4 6.2%
Information Technology Company 6 3.7% Consumer Staples Company 3 6.0%
Industrials Company 3 3.6% Information Technology Company 7 5.2%
Consumer Staples Company 4 3.5% Consumer Discretionary Company 4 5.0%
Telecommunication Services Company 4 3.4% Health Care Company 6 5.0%
Health Care Company 3 3.4% Financials Company 6 4.9%
Health Care Company 5 3.2% Financials Company 5 4.7%
Information Technology Company 3 3.1% Energy Company 1 4.7%
Consumer Staples Company 2 3.0% Telecommunication Services Company 2 4.1%
Financials Company 7 2.8% Industrials Company 4 4.0%
Consumer Staples Company 5 2.6% Financials Company 1 4.0%
Financials Company 2 2.6% Industrials Company 1 3.8%
Financials Company 4 2.4% Information Technology Company 8 3.4%
Information Technology Company 5 2.3% Materials Company 7 2.4%
Health Care Company 4 2.2% Materials Company 6 2.3%
Telecommunication Services Company 5 2.2% Information Technology Company 2 2.2%
Consumer Staples Company 6 2.0% Health Care Company 2 2.2%
Consumer Staples Company 3 2.0% Materials Company 5 2.1%
Consumer Discretionary Company 7 2.0% Utilities Company 5 1.8%
Energy Company 2 1.8% Consumer Discretionary Company 6 1.5%
Energy Company 5 1.7% Utilities Company 1 1.4%
Health Care Company 1 1.7% Telecommunication Services Company 6 1.3%
Financials Company 3 1.5% Total 100.0%
Energy Company 4 1.4%
Industrials Company 5 1.3%
Consumer Discretionary Company 3 1.3%
Health Care Company 2 1.1%
Financials Company 1 1.1%
Materials Company 1 0.8%
Utilities Company 6 0.8%
Telecommunication Services Company 1 0.4%
Total 100.0%


The table below shows the calculation of active share by placing the index and the fund next to
one another. This fund has an active share of 88.5 percent. On the left you can see how active
share rises as the result of stock picking. The fund doesn’t hold some of the stocks that are the
index’s largest weighting and does hold stocks that are not in the index.

On the right is the active share as the result of sector weights (tracking error captures this well).
Naturally, active share is a blend of stock picking and sector bets. These amounts are related. In
general, high active share via stock picking and relatively low active share via sector bets does
best.
Total Active Share Sector Active Share
Weight in Weight in Active Weight in Weight in Active
Holdings Index Fund Share Sectors Index Fund Share
Energy Company 6 7.7% 0.0% 3.9% Energy 16.8% 10.9% 3.0%
Information Technology Company 1 7.2% 0.0% 3.6% Materials 3.4% 6.7% 1.7%
Information Technology Company 4 4.1% 0.0% 2.1% Industrials 8.4% 7.9% 0.3%
Energy Company 3 4.0% 0.0% 2.0% Consumer Discretionary 6.9% 14.3% 3.7%
Information Technology Company 6 3.7% 0.0% 1.8% Consumer Staples 13.1% 13.1% 0.0%
Industrials Company 3 3.6% 0.0% 1.8% Health Care 11.6% 7.2% 2.2%
Consumer Staples Company 4 3.5% 0.0% 1.7% Financials 10.3% 13.6% 1.7%
Telecommunication Services Company 4 3.4% 0.0% 1.7% Information Technology 20.4% 17.8% 1.3%
Health Care Company 3 3.4% 0.0% 1.7% Telecommunication Services 6.3% 5.4% 0.4%
Health Care Company 5 3.2% 0.0% 1.6% Utilities 2.9% 3.2% 0.1%
Information Technology Company 3 3.1% 0.0% 1.6% Total 100.0% 100.0% 14.3%
Consumer Staples Company 2 3.0% 0.0% 1.5%
Financials Company 7 2.8% 0.0% 1.4%
Information Technology Company 5 2.3% 7.0% 2.3%
Health Care Company 4 2.2% 0.0% 1.1%
Telecommunication Services Company 5 2.2% 0.0% 1.1%
Consumer Discretionary Company 7 2.0% 0.0% 1.0%
Energy Company 2 1.8% 0.0% 0.9%
Industrials Company 5 1.3% 0.0% 0.7%
Materials Company 1 0.8% 0.0% 0.4%
Utilities Company 6 0.8% 0.0% 0.4%
Total 100.0% 100.0% 88.5%


The views expressed in this commentary reflect those of Legg Mason Capital Management
(LMCM) as of the date of this commentary. These views are subject to change at any time based
on market or other conditions, and LMCM disclaims any responsibility to update such views.
These views may not be relied upon as investment advice and, because investment decisions for
clients of LMCM are based on numerous factors, may not be relied upon as an indication of
trading intent on behalf of the firm. The information provided in this commentary should not be
considered a recommendation by LMCM or any of its affiliates to purchase or sell any security. To
the extent specific securities are mentioned in the commentary, they have been selected by the
author on an objective basis to illustrate views expressed in the commentary. If specific securities
are mentioned, they do not represent all of the securities purchased, sold or recommended for
clients of LMCM and it should not be assumed that investments in such securities have been or
will be profitable. There is no assurance that any security mentioned in the commentary has ever
been, or will in the future be, recommended to clients of LMCM. Employees of LMCM and its
affiliates may own securities referenced herein. Predictions are inherently limited and should not
be relied upon as an indication of actual or future performance. Legg Mason Capital
Management, LLC consists of two legal entities, Legg Mason Capital Management and LMM
LLC.


Important risks
All investments are subject to risks, including loss of principal. Small-cap stocks involve greater risks and volatility
than large-cap stocks.

This document is for information only and does not constitute an invitation to the public to invest. You should be aware that the investment
opportunities described should normally be regarded as longer term investments and they may not be suitable for everyone. The value of
investments and the income from them can go down as well as up and investors may not get back the amounts originally invested, and can
be affected by changes in interest rates, in exchange rates, general market conditions, political, social and economic developments and
other variable factors. Past performance is no guide to future returns and may not be repeated. Investment involves risks including but not
limited to, possible delays in payments and loss of income or capital. Neither Legg Mason nor any of its affiliates guarantees any rate of return
or the return of capital invested. Please note that an investor cannot invest directly in an index. Forward-looking statements are subject to
uncertainties that could cause actual developments and results to differ materially from the expectations expressed. This information has
been prepared from sources believed reliable but the accuracy and completeness of the information cannot be guaranteed and is not a
complete summary or statement of all available data. Individual securities mentioned are intended as examples of portfolio holdings and are
not intended as buy or sell recommendations. Information and opinions expressed by either Legg Mason or its affiliates are current as of the
date indicated, are subject to change without notice, and do not take into account the particular investment objectives, financial situation or
needs of individual investors. The information in this document is confidential and proprietary and may not be used other than by the intended
user. Neither Legg Mason nor any officer or employee of Legg Mason accepts any liability whatsoever for any loss arising from any use of this
document or its contents. This document may not be reproduced, distributed or published without prior written permission from Legg Mason.
Distribution of this document may be restricted in certain jurisdictions. Any persons coming into possession of this document should seek
advice for details of, and observe such restrictions (if any).

This document may have been prepared by an advisor or entity affiliated with an entity mentioned below through common control and ownership by
Legg Mason, Inc.

This material is only for distribution in the jurisdictions listed.

Investors in Europe:

Issued and approved by Legg Mason Investments (Europe) Limited, registered office 201 Bishopsgate, London EC2M 3AB. Registered in England and
Wales, Company No. 1732037. Authorized and regulated by the Financial Services Authority. Client Services +44 (0)207 070 7444. This document is for
use by Professional Clients and Eligible Counterparties in EU and EEA countries. In Switzerland this document is only for use by Qualified Investors. It is
not aimed at, or for use by, Retail Clients in any European jurisdictions.

Investors in Hong Kong, Korea, Taiwan and Singapore:
This document is provided by Legg Mason Asset Management Hong Kong Limited in Hong Kong and Korea, Legg Mason Asset Management
Singapore Pte. Limited (Registration Number (UEN): 200007942R) in Singapore and Legg Mason Investments (Taiwan) Limited (Registration Number:
(98) Jin Guan Tou Gu Xin Zi Di 001; Address: Suite E, 55F, Taipei 101 Tower, 7, Xin Yi Road, Section 5, Taipei 110, Taiwan, R.O.C.; Tel: (886) 2-8722 1666) in
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Korea, Singapore and Taiwan.

Investors in the Americas:
This document is provided by Legg Mason Investor Services LLC, a U.S. registered Broker-Dealer, which may include Legg Mason International -
Americas Offshore. Legg Mason Investor Services, LLC, Member FINRA/SIPC, and all entities mentioned are subsidiaries of Legg Mason, Inc.

Investors in Canada:
This document is provided by Legg Mason Canada Inc. Address: 220 Bay Street, 4th Floor, Toronto, ON M5J 2W4. Legg Mason Canada Inc. is affiliated
with the Legg Mason companies mentioned above through common control and ownership by Legg Mason, Inc.

Investors in Australia:
This document is issued by Legg Mason Asset Management Australia Limited (ABN 76 004 835 839, AFSL 204827) (“Legg Mason”). The contents are
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This material is not for public distribution outside the United States of America.
Materials were prepared by Brandywine Global Investment Management, LLC and distributed by Legg Mason Investor Services, LLC.

Legg Mason Perspectives® is a registered trademark of Legg Mason Investor Services, LLC.

© 2012 Legg Mason Investor Services, LLC. Member FINRA, SIPC. Legg Mason Capital Management of Legg Mason, LLC. and Legg Mason Investor
Services, LLC and all entities mentioned above are subsidiaries of Legg Mason, Inc. 406921 MIPX013439 3/12 FN1210649

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