Ch 8

Report
CHAPTER 8
The Efficient Market
Hypothesis
The Goals of Chapter 8
Introduce the three forms of the Efficient Market
Hypothesis (EMH) (效率市場假說)
Discuss the practicability (可行性) of technical
and fundamental analyses and the active asset
management under different forms of the EMH
Cite evidence that supports or disproves the
EMH
Examine the EMH by analyzing the
performance of stock analysts and fund
managers
※There is a lot of descriptive content in Ch. 8, so I rearrange the
lecture slides in a more logical way than that of the text book
8-2
8.1 RANDOM WALKS AND THE EFFICIENT
MARKET HYPOTHESIS
8-3
Efficient Market Hypothesis (EMH)
Kendall (1953) first found that it is almost
impossible to identify predictable patterns in
stock prices
– Stock prices seem to evolve randomly
– The past performance provided no way to predict
future price movements
Some economists treated these results from
the irrationality of the market
– Because they believe that similar to predicting the
business cycle or GDP of a nation, it is possible to
predict stock prices
– They soon realized that random price movements
indicate a well-functioning or efficient market, not
an irrational one
8-4
Efficient Market Hypothesis (EMH)
The following arguments support that the stock
prices are unpredictable in efficient markets
– Stock prices react immediately to all news (even the
mentioned events will occur in the future)
Suppose there is an accurate forecast that the stock price
of XYZ will rise by 30% in one week
– Every investor intends to buy the shares of XYZ, but no
stockholders of XYZ are willing to sell
– As a result, the stock price rises immediately to a proper
level to reflect this good news
Therefore, a forecast about future performance leads to
current stock price movement
Equivalently, we can say that the current stock price has
already reflected all information that could be used to
predict the future performance of the firm
8-5
Efficient Market Hypothesis (EMH)
– Competition as a source of efficiency
Competition among many professional, highly paid,
aggressive analysts ensures that all relevant information
can be discovered soon in the stock markets
Based on the discovered information, they can buy or sell
stocks such that stock prices ought to reflect available
information regarding their proper levels
– Stock prices change randomly
New information occurs and is discovered randomly and
unpredictably
– If it is predictable, it would be part of today’s information,
and the stock price should already reflects this information
As a result, the stock price, which reflects news
immediately, should change randomly and unpredictably
We can further conclude that the past performance is
irrelevant with future performance
8-6
Efficient Market Hypothesis (EMH)
The Efficient Market Hypothesis (EMH) (效率
市場假說)
– The notion that current stock prices fully reflect all
available information is referred to as the efficient
market hypothesis
– In other words, if the stock prices can reflect new
information immediately, then the market is
efficient
– The most important argument to support that
markets should be efficient
The pursuit for profit and the competition among
investors to discover information ensure the randomly
evolving stock prices and thus the efficiency of markets
8-7
Cumulative Abnormal Returns (CAR) (累計異常報
酬) For Takeover Attempts
※ The abnormal return (異常報酬) (or risk-adjusted return) is the difference between
the actual return and the predicted return based on the CAPM
※ In most takeover events, the acquiring firm pays a substantial premium over the
current market prices of the merged firm (synergy effect (綜效): the value of the
combined firm is higher than the sum of the values of individual firms)
※ The figure shows that the announcement of a takeover attempt should cause the
stock price of the merged firm to jump immediately
※ In addition, there is no further drift in prices after the announcement date, including
the day on which the takeover transaction is physically completed
8-8
Stock Price Reaction to CNBC Reports
※ Busse and Green (2002) show that most of the stock price responses to the
announcements of dividends or earnings occur within a very short period after
the announcements (almost immediately)
※ The time 0 is the time point at which the stocks are mentioned on the midday
show in the news program on CNBC
※ For firms with positive (negative) reports, the stock prices reflect the news in 5
minutes (12 minutes)
8-9
Different Forms of the EMH
Three forms of the EMH:
– Weak-form, semistrong-form, and strong-form EMH
– Different forms of the EMH are determined by
different information sets that security prices can
reflect
Weak-form EMH (弱式效率市場假說):
– Security prices already reflect all information
contained in the history of past trading
– If the historical data conveyed reliable signals
about future performance, all investors already
would have leaned to exploit the signal
– Implies that the trend or technical analysis (技術分
析) is fruitless (discussed in the next section)
8-10
Different Forms of the EMH
Semistrong-form EMH (半強式效率市場假說):
– Stock prices already reflect all publicly available
information, including past prices, fundamental
data on the firm’s product line, balance sheets,
earning forecasts, etc
– Implies that fundamental analyses (基本分析) to
study earnings and growth forecasts do not work
(discussed in the next section)
8-11
Different Forms of the EMH
Strong-form EMH (強式效率市場假說):
– Stock prices reflect all relevant information,
including public information and private
information available only to company insiders
– Implies that even for investors with private
information, they cannot earn abnormal returns
– SEC limits the trading by corporate officers,
directors, and large stockholders and requires
these insiders to report trades to prevents them
from profiting by exploiting their privileged situation
Degree of efficiency differs in various markets
or different securities
– Emerging markets, markets with less rigorous
disclosure requirement, and small stocks with less
notice by stock analysts are less efficient
8-12
Information Sets for Different Forms of
the EMH
※ The above figure shows the information set of different
EMH forms (strong-form > semistrong-form > weak-form)
※ Semistrong-form efficiency implies that weak-form
efficiency holds (but NOT vice versa)
※ Strong-form efficiency implies that both semistrong-form
and weak-form efficiency hold (but NOT vice versa)
8-13
8.2 IMPLICATIONS OF THE EMH
(For Technical and Fundamental
Analyses and Active vs. Passive
Management )
8-14
Types of Stock Analysis
Technical Analysis (技術分析)
– Using past information of prices and trading
volumes to search for recurrent and predictable
patterns in future stock prices (introduced in Ch 9)
– Buying winners or shorting losers (追高殺低) are
typical examples:
Buy (short) stock performing relatively well (poor) recently
because such trend may continue for a long enough
period of time to offer profit opportunities
– For markets in any form of efficiency, the technical
analysis based on past information is worthless
since the market prices already reflect all past
information
8-15
Types of Stock Analysis
Fundamental Analysis (基本分析)
– Using publicly economic and accounting
information to predict stock prices (Ch. 12 to Ch. 14)
– In a semistrong-form or strong-form efficient market,
fundamental analyses do not work
Because many individual and institutional investors
conduct fundamental analyses based on public information
to design their investment strategies, the stock prices
already reflect all public information
– In contrast, fundamental analyses are feasible in
weak-form efficient and inefficient markets
Due to the competition among investors, you can make
money only if your analysis is better than that of your
competitors, i.e., you can predict the performance of firms
more accurately than the prediction of other investors
8-16
Implications of EMH for Active or
Passive Management
Three reasons to suggest that the active
management is not preferred in efficient markets
1. Huge efforts to find securities with minor mispricing by
technical or fundamental analyses in efficient markets
An example for a fund adopting active management:
– Consider a fund with a $5 billion portfolio, and the fund
manager plan to organize a research to pursue the increase of
the rate of return by 0.1% per year
– That means the fund manager would be willing to spend up to
$5 million (= 0.1% × $5 billion) on research
– The active portfolio management is economically feasible only
for managers of large portfolios but not appropriate for
individual investors  magnitude issue (規模問題)
– For institutional investors, is it worthy to spend those huge
efforts? Is there any alternative to improve the performance? 8-17
Implications of EMH for Active or
Passive Management
2. Difficult to distinguish the change of the
performance coming from the researches or the
fluctuations of the market
Because of that, it is doubtful that whether mutual funds
have the ability to discover mispriced stocks
3. Difficult to judge the degree of mispricing and
whether it is sufficiently large to repay the costs in
the active portfolio management
Proponents of the EMH believe the active
management is largely wasted in an efficient
market and they advocate a passive
management that makes no attempt to
outperform the market
8-18
Implications of EMH for Active or
Passive Management
Passive investment strategy is to buy a welldiversified portfolio without attempting to
search out mispriced securities
One common strategy for the passive
management is to invest in an index fund,
which is designed to replicate the performance
of the market portfolio underlying the index
– The fees is relatively lower because an index fund
does not need to pay analysts to assess stock
prospects and incurs less tax and transaction costs
due to its low turnover rate
8-19
Implications of EMH for Active or
Passive Management
Markets are weak-form efficient or worse 
Active management
– Conduct security analyses, like fundamental and/or
technical analyses, to pick securities
For weak-form efficient or worse markets, it is valuable
that stock analysts generate reports and send them to
investors based on the results of fundamental analyses
For inefficient markets, it is also possible to timing the
market based on the technical analyses
Markets are semistrong-form efficient or better
 Passive management
– Buy and hold well-diversified portfolios, like index
funds
8-20
The Role of Portfolio Management in
an Efficient Market
Although all securities are fairly priced (because
the market is efficient), the most important
function of portfolio managers is to construct
portfolio to eliminate firm-specific risk by
diversification
– Moreover, the portfolio manager in an efficient
market is to tailor the portfolio for the needs of
investors, rather than to outperform the market
Investors’ optimal positions vary according to many factors,
like age, tax bracket, risk aversion, or employment status
For example, for retired persons, they may prefer funds
providing high and stable dividend yields such that they
can receive regular incomes from the funds
8-21
8.3 ARE MARKETS EFFICIENT
8-22
Empirical Tests of Market Efficiency
Three issues imply the debate of whether
markets are efficient will never stop
– Roles and performance of professional investors
The proponents of the EMH believe that the existence of
professional investors can result in efficient markets
This is because stock prices are not far from fair values
and that only managers of larger portfolios can exploit
minor mispricing to earn enough trading profits
However, the effort of professional investors is difficult to
be identified (0.1% improvement vs. 20% volatility)
Thus, we can conclude neither the effort of professional
investors is valuable nor their existence results in an
efficient market, although their actions are indeed the
driving force to let market prices move to fair levels
8-23
Empirical Tests of Market Efficiency
– Selection bias issue (選擇性偏誤)
Another method to examine the EMH is to test all trading
strategies in the market. If they can not provide abnormally
higher returns, we can conclude the market is efficient
Assuming that you discover an investment strategy that
really makes money, what will you do?
Hence, the trading strategies we observe in the market
have been preselected in favor of failed attempts, so we
cannot evaluate the true ability of portfolio managers to
invent profitable strategies
You cannot deny the possible existence of profitable
strategies that are not released and therefore the possibility
that the market is not efficient
8-24
Empirical Tests of Market Efficiency
– Lucky event issue (純屬好運)
Some studies examine the EMH according to the
performance of fund managers. If they cannot beat the
market, then we can conclude that the market is efficient
However, if many professional investors use a variety of
schemes to make fair bets, statistically speaking, some will
be lucky and win a great majority of bets (e.g., Peter Lynch
or Warren Buffett), and some will be unlucky and lose a lot
– So, we cannot conclude that the superior record of few
winners disprove the efficient market hypothesis although
what we heard are all about the feats of winners
Proper tests (discussed in Section 8.4) may include:
– To study the distribution or the average of the performance of
fund mangers
– To test whether the winners can repeat their performance in
another periods, i.e., to examine the consistency of the
performance of fund managers
8-25
Weak-Form Tests: Patterns in Stock Returns
Patterns from the past information can be found
 Markets are not weak-form efficient
Returns over short horizons (< 1 year)
– For weekly returns of NYSE individual stocks,
fairly small magnitude of positive serial correlation
is found
– For 3- to 12-month periods, there is some evidence
of positive serial correlation in both the aggregate
market and portfolios of best- and worstperforming stocks (the latter is known as the
momentum effect (動能效果))
Returns over long horizons (3 to 5 years)
– Pronounced negative serial correlation in the
performance of the aggregate market
8-26
Weak-Form Tests: Patterns in Stock Returns
– The reversal effect (反轉效果) for extremely
performing individual stocks
Many studies suggest that over long horizons, the
performance of extreme-performing stocks tends to reverse,
i.e., losers rebound and winners fade back
De Bondt and Thaler (1985) find that the worst-performing
portfolio (according to 5-year historical returns) outperform
the best-performing portfolio in the following three years
The reversal effect implies a contrarian (反向操作)
investment strategy–investing in recent losers and
avoiding recent winners–should be profitable
※Possible explanation for the short-term momentum
and long-term reversal effects
Stock market might overreact to relevant news, and such
overreaction leads to momentum effect over short horizons
Subsequent correction of the overreaction leads to
negative serial correlation (the reversal effect) over longer
8-27
horizons
Semistrong Form Tests: Market Anomalies
Efficient market anomalies (效率市場異常現象):
The phenomenon difficult to reconcile with the
semistrong-form EMH that several easily
accessible quantity, e.g., the P/E ratio or the
firm size, seem to predict risk-adjusted returns
P/E (price/earning) ratio (本益比) effect
– Basu (1977, 1983) found that the portfolios with low
P/E have higher returns than those with high P/E
– The P/E ratio effect holds even for returns adjusted
for portfolio beta, i.e., the return in excess of the
return predicted by CAPM
– A possible explanation is that the CAPM beta cannot
fully adjusts for risk, and P/E can act as a useful
indicator of another source of risk
8-28
Semi-Strong Form Tests: Market Anomalies
Small-Firm Effect (小公司效應)
– Banz (1981) examined the small-firm effect
The smaller-firm portfolios tend to be riskier (with higher
betas), so it is not surprised that they should provide
higher expected rates of return
Even when returns are adjusted for risk using the CAPM,
there is still a consistent premium of the smaller-sized
portfolios
See the figure on the next slide
– Keim (1983), Reinganum (1983), and Blume and
Stambaugh (1983) showed that the small-firm effect
occurs virtually entirely in January, particularly in the
first 2 weeks of January. Thus the size effect is also
called the “small-firm-in-January” effect
8-29
Returns in Excess of Risk-Free Rate and in
Excess of the SML
※ This figure shows the historical performance of portfolios formed by classifying
the NYSE stocks into 10 portfolios according to the firm size each year
※ Returns in excess of CAPM, also known as abnormal returns (異常報酬), means
to calculate the results of ri – [rf + βi(rM – rf)]
※ It is obvious that “invest in low-capitalization stocks” could earn more abnormal
returns, i.e., earn higher returns for bearing the same level of the systematic risk 8-30
Semi-Strong Form Tests: Market Anomalies
Neglected-firm and liquidity effects (流動性效應)
– Neglected-firm effect
Small firms tend to be neglected by large institutional
traders, so information about smaller firms is less available
(see Arbel and Strebel (1983) and Arbel (1985))
This information deficiency makes smaller firms riskier
investments that command higher returns (another way to
explain the small-firm effect)
– Since small and less-analyzed stocks are in general
less liquid and less-liquid stocks usually provide
higher returns, Amihud and Mendelson (1986, 1991)
intend to use the liquidity risk on stock returns to
explain both the small- and neglected-firm effects
However, their theory cannot explain why the abnormal
returns of small firms concentrate in January
8-31
Semi-Strong Form Tests: Market Anomalies
Book-to-market ratio (帳面市值比)
– Fama and French (1992) showed that B/M ratio can
be a powerful predictor of stock returns, i.e., high
B/M ratio stocks offer higher expected return (see
the figure on the next slide)
– In addition, they also found that the dramatic
dependence of returns on book-to-market ratio is
independent of beta (betas for these ten groups are
almost indistinguishable), so the same pattern can
be derived by comparing the risk-adjusted returns
for the ten groups
8-32
Average Annual Return
as a Function of Book-to-Market
※ The decile with the highest B/M ratio has an average annual return of
18.7%, while the lowest B/M ratio decile has an average of only 10.64%
8-33
Semi-Strong Form Tests: Market Anomalies
Post-Earnings Announcement Price Drift
– Although the EMH suggests the stock price
should jump immediately when good or bad news
is made public, stock prices response to firm’s
earnings announcements in a sluggish way (see
the figure on the next slide)
– Therefore, it is possible to earn abnormal profits
by simply purchasing a stock portfolio of positiveearnings-surprise companies
– Since predictable continuing trends ought to be
impossible in an efficient market, so this
phenomenon is still a anomaly
8-34
Cumulative Abnormal Returns (CAR) in
Response to Earnings Announcements
※ Rendleman, Jones, and Latane (1982) classified stocks into 10 deciles based
on the magnitude of the “surprise” of the earnings, and calculated CARs for each
decile for the following 3 months
※ Earnings surprise is the difference between the actual announced earnings and
the expected earnings from market participants
※ There are indeed jumps on the announcement day to reflect the earnings
surprise, but the stock price continues to move in the same direction of the jump
for the following 3 months
8-35
Strong-Form Tests: Inside Information
It is not surprising if insiders are able to make
superior profits in their trading firm’s stock
(see Jaffe (1974), Seyhun (1986), Givoly and
Palmon (1985), etc.)
In other words, it is not expected that markets
are strong-form efficient
In order to prevent the inside trading hurts the
interests of investing public, SEC requires all
insiders to register their trading activities and
release this information to the investing public
8-36
Interpreting the Evidence
The P/E, small-firm, B/M, short-term momentum,
and long-term reversal effects are currently the
most puzzling phenomena in empirical finance
Two kinds of explanations: Risk Premiums (風險
溢酬) vs. Market Inefficiencies (市場無效率)
– Fama and French (1993) argue that these effects
can be explained as manifestations of risk premiums
(that is, in their three-factor model, size or B/M ratios
act as proxies for some other fundamental risks)
– Indeed, not only rM can reflect the business cycle,
rSMB and rHML seem to predict the business cycles in
many countries as well (see the next slide)
8-37
Return to Style Portfolio as a Predictor of
GDP Growth
※ This figure shows the difference between the average rSMB (rHML) before a good
GDP growth and the average rSMB (rHML) before a poor GDP growth
※ The differences are significantly different from zero for many countries, which
indicates there must be some relationship between the rSMB (rHML) and the
business cycle and thus rSMB (rHML) can act as proxies for other fundamental risks8-38
Interpreting the Evidence
– On the other hand, Lakonishok, Shleifer, and Vishny
(1994) argue that these effects are evidences of
inefficient markets
– They believe that investors extrapolate (外插) past
performance too far into the future, and therefore
overprice (underprice) firms with recent good (poor)
performance. Ultimately, when investors recognize
their errors, prices move reversely
– This argument can explain the short-term
momentum, the long-term reversal, and partial P/E,
small-firm, B/M effects
Prices decrease (increase)  P/Es decrease (increase), tend to
be small (large) firms, and B/Ms increase (decrease)
Investors seem too pessimistic (optimistic) about the future
according to recent poor (well) performance. When these tooextreme expectations are corrected, firms with recent poor
performance will outperform firms with recent well performance
8-39
Interpreting the Evidence
Anomalies (異常現象) or Data Mining (數據挖掘)
– Some academics wonder whether these anomalies
are really unexplained puzzles in financial markets,
or whether they instead are an artifact of data mining
– Data mining: Rerun the computer to analyze past
returns over and over and examine stock returns
along enough dimensions  simple chance may
cause some criteria to appear to predict returns
– One way to address the problem of data mining is to
find a data set that has not already been researched
and see whether the relationship in question shows
up in the new data set (in-sample vs. out-of-sample
tests)
8-40
8.4 MUTUAL FUND AND ANALYST
PERFORMANCE
(Another Indicators for the Degree of
Efficiency of Markets)
8-41
Stock Market Analysts
Markets are efficient  Almost all securities
reflect news quickly and are at their fair prices
 Stock analysts’ reports are worthless, and
fund managers cannot earn abnormal returns
and show persistent performance
Do stock analysts add value – mixed evidence
– Womack (1996)
Positive (negative) changes of stock analysts’
recommendations are associated with the changes of stock
prices by 5% (–11%)
Are price changes due to stock analysts’ superior information
or pressure brought by the recommendations themselves?
Womack argues that the price impact seems to be permanent,
which supports that stock analysts do reveal new information 8-42
Stock Market Analysts
– Jegadeesh, Kim, Krische, and Lee (2004)
Changes in consensus recommendations are associated
with price changes, but the level of consensus
recommendations is an inconsistent predictor of future stock
performance
(Consensus recommendations are the mean of all outstanding
recommendations for a given firm)
– Barber, Lehavy, McNichols, and Trueman (2001)
Firms with the most-favorable recommendations outperform
those with the least-favorable recommendations (level of
consensus recommendations does matter)
8-43
Mutual Fund Managers
Persistent well or poor performance for fund
managers – mixed evidence
– The phenomenon may be caused from potential
measurement error for benchmark returns
Maybe some funds bear more (less) systematic risk
such that can provide consistently higher (lower) rate of
return
Therefore, we should examine the abnormal (or riskadjusted) return (i.e., the difference between the actual
returns and the returns predicted by the CAPM or said
the α in the CAPM)
Malkiel (1995) computed these abnormal returns (α) for
a large sample of mutual funds between 1972 and
1991 (see the figure on the next slide)
8-44
Estimates of Individual Mutual Fund Alphas
Based on CAPM
※ The distribution of α is near a normal distribution, with a mean that is slightly
negative but statistically indistinguishable from zero
※ Therefore, it suggests that these funds, on average, does not outperform the
market index on a risk-adjusted basis
8-45
Mutual Fund Managers
– Another measurement error:
Since mutual funds tend to hold in equity of smaller
firms, whereas the S&P 500 is comprised of large firms,
mutual funds tend to outperform the S&P 500 market
portfolio due to the small-firm effect
– The abnormal (or risk-adjusted) return of the FamaFrench three-factor model should be examined
Some mutual funds exploit the momentum or reversal
effects to earn abnormal returns
– The abnormal (or risk-adjusted) return of the Carhart
four-factor model (introduced next) should be examined
8-46
Mutual Fund Managers
Carhart (1997) proposed a four-factor model to
study the performance of mutual funds
– Four factors include the rS&P 500, rSMB, rHML, and prioryear stock market return (PR1YR)
Ri  i  iM RM  iHML rHML  iSMBrSMB  iPR1YR PR1YR  ei
– PR1YR, like rSMB and rHML, is the return of a zeroinvestment, factor-mimicking portfolio to capture the
intermediate-term momentum effect
– PR1YR is defined as the difference of the this-year
average returns between the best 30% performing
stocks and the worst 30% performing stocks on NYSE,
Amex, and Nasdaq in the prior year
– A positive (negative) coefficient for PR1YR indicates
that the mutual funds tend to invest and hold the
current winner (losers) in the next period
8-47
Estimates of Individual Mutual Fund Alphas
Based on the Four-Factor Model
※ Since α’s are distributed normally around 0, the evidence is consistent with
market efficiency based on the 4-factor model
※ By examining the α of the 4-factor model, Carhart finds that there are no
consistently superior performers, i.e., the consistent better (unadjusted)
performance observed in the market is not due to the better skill of fund
managers, but due to the consistent investment in smaller firms, higher B/M firms,
or the past winners
※ On the contrary, there could be consistently inferior performers, but Carhart
attributes the repeated weak performance to the structure of the expenses and
transaction costs of mutual funds rather than to pick wrong stocks consistently 8-48
Persistence of Mutual Fund Performance
※ To analyze the persistence of mutual fund performance, Carhart classifies stocks
into ten groups according to the excess returns of the formation year and
examines their excess returns in the subsequent 5 years
※ The above figure shows that except for the best and worst performing groups,
performances of the rest are independent of the formation-year returns, and in
fact, the superiority of the best groups is very minor
8-49
Mutual Fund Managers
Berk and Green (2004)
– Skill should show up not in superior returns but
rather in the amount of funds under management
Skilled fund managers with abnormal performance will
attract new funds until the additional costs and complexity
of managing those extra funds drive alphas down to zero
Thus, even if managers are skilled, positive alpha will be
short-lived (see the figure on the next slide)
Black, Elton, and Gruber (1993)
– On average, bond funds underperform fixed-income
indexes by an amount roughly equal to the expense
costs
– For bond funds, there is no evidence that past
performance can predict future performance
8-50
Alphas in Ranking Quarter and Following
Quarter
※ Bollen and Busse (2004) rank mutual performance into 10 deciles, using the
alpha of the 4-factor model over a base quarter
※ The solid (dashed) line is the average alpha of funds within each decile in the
ranking quarter (in the following quarter)
※ Both lines are downward-sloping  There exists some performance
consistency
※ However, the consistency is weak due to the minor downward slope for the
dashed line
8-51
Mutual Fund Managers
Chen, Ferson, and Peters (2010)
– On average, bond (equity) mutual funds outperform
passive bond (equity) index in terms of gross returns
but underperform once the fees are subtracts
Kosowski, Timmerman, Wermers, and White
(2006) (existence of stars of mutual funds)
– There may be a minority of managers with exceptional
stock-picking ability, which is sufficient to cover their costs
such that their superior performance tends to persist over
time
– Peter Lynch (of Fidelity’s Magellan Fund), Warren Buffett
(of Berkshire Hathaway), John Templeton (of Templeton
Funds), Bill Miller (of Legg Mason), and John Neff (of
Vanguard’s Windsor Fund)
8-52

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