Stock prices, stock indexes and index funds

Stock prices, stock indexes and index funds
By Richard A Brealey,(1) special adviser to the Governor on financial stability issues.
In recent years, many UK investors have given up the quest for superior performance and have
instead simply sought to match the returns on some broad market index. This has led to the suggestion
that the growth in index funds has depressed the stock prices of those companies that are not
represented in the index and has thereby increased their cost of capital. This effect may have been
accentuated by the actions of fund managers, whose performance is compared with that of a market
index and so who also have an incentive to avoid those stocks that are not included in the index. This
paper argues that, in practice, these price effects are likely to be very small. In support of this view,
the paper examines the price adjustments that occur when a stock is added to, or removed from, a stock
market index.
Introduction
hold the stocks of smaller companies that are not included in
the market index and this has increased the cost of capital
The well-documented difficulty of choosing an active fund
for these companies.(3)
manager who will provide superior performance has led to a
rapid growth in index funds in the United Kingdom. These
Though index funds have an obvious reason to avoid stocks
index (or ‘tracker’) funds do not seek to provide superior
that are not included in the market index, many other funds
investment performance, but instead are designed to match
may also be reluctant to buy such stocks. This reluctance
the returns on a broad stock market index.
arises from the common practice of measuring a fund’s
performance against that of a market index. In this case, an
The distinction between index funds and funds that closely
investment in the index is effectively risk-free in the eyes of
resemble some benchmark portfolio is somewhat artificial,
the manager, while investments in excluded stocks are risky
but in 1999 explicitly indexed funds were estimated to hold
and will therefore be held by a risk-averse manager only if
about £134 billion of equities (see Table A).(2)
they offer a correspondingly higher return. So index funds
and performance benchmarking are likely to have similar
Table A
effects on required returns.
Index funds—holdings of equities; 1999
£ billions
These concerns about the effects of index funds and index
benchmarking seem to have been heightened by the
Pension funds
98.1
Insurance
11.9
relatively poor performance of small-firm stocks in recent
Retail
2.0
Overseas
22.0
years, when indexation has boomed. For example, while the
Hoare-Govett Smaller Companies (HGSC) index
Total
134.0
outperformed the FTSE All-Share index by an average of
6.1% a year during the period 1955–86, the average annual
Although about 22% of pension equity holdings are
return on the HGSC index was 6.4% below that on the
indexed, the proportion is much smaller for other categories
All-Share index during the years 1989–98. As will be
of investor, so that the total estimated investment in indexed
evident from the discussion below, it is implausible that
funds amounts to 8.6% of the capitalisation of UK-traded
index funds can account for these sharp differences in stock
equities.
returns. Nor are alternative explanations lacking, for the
underperformance of small-firm stocks during these years
One commonly expressed concern is that the growth
has been largely a consequence of their industry
of investment in these funds has pushed up the price
composition and has been matched by a lower growth in
and lowered the required return of index stocks.
dividends (see Dimson and Marsh (1999)). Moreover, the
Correspondingly, (it is argued), index funds do not
indexation argument does not sit easily with the more recent
(1) I am grateful to colleagues at the Bank of England and to Elroy Dimson of the London Business School for
providing comments on this paper. The paper has benefited from considerable assistance from
Louise Boustani and Stephen Senior.
(2) I am grateful to Lindsay Tomlinson of Barclays Global Investors for providing these estimates.
(3) For example, a CISCO survey of analysts that specialise in small companies found that more than 90%
believed that the growth of index funds is damaging the market for smaller quoted companies. See
Thunhurst (1999).
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Bank of England Quarterly Bulletin: February 2000
performance of small-cap stocks; in 1999 the HGSC index
decline depends on the magnitude of the changes that the
provided a return of 54.2%, 30% above that of the All-Share
active investors are required to make and the effect of these
index.
changes on portfolio risk. For example, if small-firm stocks
are close substitutes for large-firm stocks, these investors
The rest of this article is organised as follows. The next
will require a smaller inducement to make the portfolio
section uses a simple mean-variance portfolio model to
shift.
examine the effect of the portfolio adjustments forced on
other investors by index funds. The discussion suggests that
We can put some approximate numbers on the price
it is improbable that the growth of index funds in the United
adjustments needed to bring about the necessary shifts in
Kingdom has had any economically significant effect on the
portfolio holdings. UK index funds hold an estimated 8.6%
cost of equity capital. The following section widens the
of the total market, and all but about 5% of these funds are
discussion to look at the possible effect on stock prices of
indexed to the FTSE All-Share index. For simplicity,
using the market index as a benchmark to assess the
therefore, we assume initially that they invest only in the
performance of active as well as passive managers. Since
All-Share index, which accounts for 93.9% of total UK
we cannot, a priori, specify managers’ reluctance to take on
market capitalisation. We use the HGSC index as a proxy
the risk of investing outside their benchmark, we can be less
for returns on non-index stocks.(1) Using index data from
dogmatic about the magnitude of the effect. The fourth
January 1990 to April 1999, we estimate the monthly
section looks at the empirical evidence of the effect of index
standard deviation of the All-Share index as 4.3% and that
composition on equity prices. Although this evidence is not
of the HGSC index as 4.6%. The correlation between the
unanimous, we place most weight on the modest price
monthly returns on the two indexes during this period
effects of adding a stock to the market index or removing it.
was 0.82.
These effects suggest that adding a stock to a market index
is likely to change required returns by only a few basis
In the absence of index funds, the representative investor
points. A puzzling finding is that the effect of index changes
would hold 93.9% of his portfolio in index stocks. If index
is not confined to the FTSE All-Share index, despite the fact
funds account for 8.6% of the market, then the
that this is the benchmark for most index funds and for
representative active investor is obliged to reduce his
measuring the performance of active portfolios. This
holdings in index stocks to 93.3% of his portfolio(2) and to
suggests that changes in index composition may have some
increase correspondingly his holding of non-index stocks.
labelling or information effect. The final section provides a
This portfolio shift causes a very small decline in the risk of
summary and conclusion.
the active investor’s portfolio as it becomes better
diversified. The ‘beta’(3) of the index stocks relative to the
The effect on stock returns of changing
portfolio of the active investor increases by a negligible
0.02%, while the comparable beta of the non-index stocks
portfolio weights
rises by a slightly greater 0.28%.(4) Since the required risk
As index funds are passive investors, their transactions do
premium should be proportional to an investment’s beta
not provide information to other investors, and these funds
relative to the mean-variance efficient portfolio,(5) the direct
take considerable care when trading to demonstrate that their
effect of an increase in the beta is to increase the required
transactions are not information-motivated. So the purchase
risk premium. If active investors continue to require the
of stocks by index funds is unlikely to have a significant
same return on their portfolio, the required returns on
direct effect on the price of index stocks.
small-firm stocks would need to rise to compensate for the
relative increase in their betas. However, even if the market
However, the activities of index funds may change the
risk premium were as high as 10%, the increase in the cost
market proportions of large and small-company stocks that
of equity for small firms would be less than 3 basis points.
are available to non-indexed (or ‘active’) investors. These
investors are therefore obliged to hold a higher proportion of
This may not be quite the end of the story, since the risk
small-company stocks than they formerly held. Since no
premium is unlikely to be constant. For example, if
single active investor is constrained to hold particular
investors have constant relative risk-aversion, the portfolio
proportions of large or small-firm stocks, the stock prices of
risk premium that they require should change
small firms would need to decline to induce the active
proportionately with the portfolio variance. In our example,
investors to increase their holdings. The extent of this
the active manager’s portfolio becomes more diversified as a
(1) Since the HGSC index contains the smallest 10% of stocks by market capitalisation, our use of this index is
likely to have somewhat underestimated the standard deviation and overestimated the correlation between
index and non-index stocks. The direction of the effect on our results is indeterminate.
(2) Calculated as (0.939 – 0.086)/(1 – 0.086) = 0.933.
(3) The ‘beta’ measures the contribution of an investment to the risk of a portfolio. It is equal to the sensitivity of
the investment’s return to changes in the value of the portfolio. If a portfolio is efficient, the expected reward
from each holding is proportional to its beta.
(4) The beta of the index stocks relative to the active investor’s portfolio increases from 1.00378 to 1.00398 and
that of the non-index stocks increases from 0.94205 to 0.94467. Since the weighting of non-index stocks in
the portfolio is increased, the weighted average of the betas remains at 1.0.
(5) A mean-variance efficient portfolio offers the highest expected return for a given level of portfolio risk (or
variance).
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Stock prices, stock indexes and index funds
result of the increased holdings of small-firm stocks and its
These cost savings should be reflected in a decline in the
risk therefore declines slightly. The net effect is that the
cost of equity for larger firms.(1)
required return on small-firm stocks would also decline
slightly.
Finally, we should note that membership of an index is
partly within the control of the firms themselves. For
There are several reasons why the estimated effect of
example, if index membership conveyed substantial
indexing on required returns is so low. The first is simply
advantages, then firms whose stocks are included in the
that, while there has been rapid growth in the proportion of
index would have an incentive to acquire their less fortunate
pension portfolios that are indexed, the proportion of total
brethren. While this would eliminate any index effect on
market capitalisation that is indexed remains relatively
returns, the process could involve significant deadweight
modest, at 8.6%. Second, as most index funds track the
costs.
All-Share index, which accounts for a very high proportion
of market capitalisation, active investors are obliged to
make only small portfolio shifts as a result of the activities
The effect of performance benchmarks
of index funds. Third, as small-company stocks are
We have argued that the impact of index funds on the cost
relatively good substitutes for large-company stocks, active
of capital for smaller firms is likely to be negligible.
investors do not require much inducement to make these
However, index fund managers are not the only portfolio
shifts.
managers whose portfolio decisions are affected by the
composition of stock market indexes. In this section we
It is useful to check how sensitive these findings are to the
broaden the discussion of market indexes to consider the
choice of parameters. We therefore repeated the exercise
wider issue of the effect of performance benchmarks on the
assuming separately that index funds account for 20% of
cost of equity.
market capitalisation, that the index accounts for 70% of the
market (roughly the equivalent of the FTSE 100 index), and
Approximately 80% of equity funds in the United Kingdom
that the correlation between index and non-index stocks is
are managed on an agency basis by professional fund
0.4. In no case does the beta of the active investor’s
managers. The performance of these managers may affect
portfolio increase by more than 0.01.
directly the fees that they receive, or it may do so indirectly
The changes in the required returns for non-index stocks
if it influences the amount of funds under management.
stem from our assumption that investors who switch to
Sometimes the performance of a portfolio is measured
index funds increase their weighting in index stocks from
against that of a peer group; in other cases it is measured
market proportions to 100%. This is not always the case.
against a passive benchmark portfolio, which in the case of
Some funds use index portfolios simply as a way to manage
UK equity managers is typically the FTSE All-Share
their existing holdings in large-capitalisation stocks and they
index.(2) It seems highly likely that a manager’s portfolio
continue to maintain their weighting in smaller-company
decisions will be affected by the way that performance is
stocks. In addition, some institutional investors also invest
measured.
their small-firm holdings in funds that seek to track
small-firm indexes. If the shift to index funds merely
The implications of a passive benchmark for prices have
changes the way that investors manage their existing
been analysed in Brennan (1993), who showed that in such a
holdings in index stocks, then active investors would not
setting expected returns would vary linearly with the
need to make any portfolio adjustments and the growth of
expected returns on both the market portfolio and the
index funds would be unlikely to have any impact on prices
benchmark portfolio. Other things being equal, stocks that
of small-firm stocks.
are highly correlated with the benchmark would exhibit
lower expected returns. Thus Brennan’s analysis of
It is also important to note that our analysis is partial insofar
benchmarking implies that the use of market indexes to
as it focuses only on the costs of indexation. These costs
measure the performance of professional managers is likely
arise because a portfolio that is invested in an index fund
to lower the required return on shares that are represented in
which tracks only a sub-section of the market is
the index, relative to those of non-index firms.
mean-variance inefficient. Such funds oblige the
representative non-indexed investor also to hold a
Investment in the benchmark index is riskless for a manager
mean-variance inefficient portfolio and this investor has to
who is compared against that benchmark; the only risk that
be ‘bribed’ to do so. But the costs to an index fund of
matters for him is the covariance between stock returns and
omitting some stocks from the portfolio and bribing the
the portfolio of non-index stocks. How much of this risk a
active investor to buy them are likely to be far outweighed
manager is prepared to assume depends on his risk-aversion.
by the savings in management costs and transaction fees.
Thus an index fund can be viewed as an extreme case of a
(1) Some impression of the potential impact of these cost savings can be gained from Cuoco and Kaniel (1999),
who consider the case of proportional management fees on required returns. They conclude that with
proportional fees over five years equal to 12% of the terminal value of the portfolio, the equilibrium ratio of
reward to risk (the Sharpe ratio) would be between 40% and 60% higher than it would be in an economy in
which all investors managed their portfolios directly and costlessly.
(2) Foreign investors in UK shares are more likely to be measured against an index of large-cap stocks such as the MSCI index.
63

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Bank of England Quarterly Bulletin: February 2000
benchmarked portfolio, where the manager has infinite
Table B
risk-aversion and so totally avoids non-index stocks.
Estimated excess return to membership of the
S&P Composite index
Since we do not know the degree of risk-aversion of active
Per cent
fund managers, we cannot predict the magnitude of the
Year
Excess return
Year
Excess return
effect on prices of the use of indexes to benchmark their
1977
-3.99
1985
-0.08
performance. Brennan undertook an empirical test of his
1978
-4.85
1986
2.21
model using US data. However, such tests of asset-pricing
1979
5.33
1987
5.92
1980
2.39
1988
3.45
models are notoriously subject to noise and, perhaps not
1981
3.17
1989
4.87
1982
6.94
1990
-2.94
surprisingly, Brennan’s results were indeterminate. For the
1983
1.58
1991
4.15
1984
4.69
entire 1931–91 period, the estimated expected return
declined significantly as a stock’s sensitivity to the index
Mean
2.19 (t = 2.33)
increased, but in recent years this effect largely disappeared
Source: Chan and Lakonishok (1993).
or was even reversed. When Brennan controlled for a
variety of factors, the more recent data were consistent with
15 years is 36.0%. It is difficult to know how to interpret
the hypothesis that a high correlation with a market index
these findings. It is possible that the estimated returns to
reduced expected returns.
index membership are spurious and that the index dummy is
simply proxying for errors in (say) the size variable. If,
however, the index composition is the true reason for the
More recently, Cuoco and Kaniel (1999) have employed a
excess returns, then one interpretation is that the coefficient
general equilibrium model to examine the effect of
on the index dummy is measuring the effect on the
alternative compensation schemes for portfolio managers.
equilibrium expected returns. In this case, required returns
They show that with symmetric performance fees, managers
are substantially higher for index stocks. Alternatively, the
will have an incentive to overweight the benchmark
succession of positive returns on index stocks may reflect
portfolio, and this increases the required return on
successive unanticipated changes in required returns,
non-benchmark stocks. They estimate that with very high
perhaps as a result of the growth of index funds. However,
levels of performance fees, the price differential between
it is difficult to reconcile such a large and prolonged
benchmark and non-benchmark stocks is around 4% if the
excess return with the far smaller price movements that
returns on the two portfolios are uncorrelated, and less than
occur when individual stocks are included for the first time
1% if the correlation is 0.9. As we shall see, these effects
in the index.
are similar in magnitude to the price changes that are
observed at the time of changes to index composition.
The view that the growth of index funds has had a major
effect on market prices is supported by Goetzmann and
Empirical evidence on the effect of membership
Massa (1999), who find a strong contemporaneous
of stock market indexes
correlation since 1993 between daily inflows into three
Fidelity indexed mutual funds and changes in the S&P
We now consider the empirical evidence on the effect of
index. The authors argue that the market is reacting to daily
index membership on required returns. Such effects may be
demand and that the effects on price are permanent. They
due to the role of index funds, to the use of indexes as
estimate the index level, net of any flows effect, and
performance benchmarks, or, more speculatively, to some
conclude that ‘the important role played by the index funds
form of information effect.
is shown not only by the huge difference (-36%) between
the two indexes that can be explained in terms of funds’
Most studies of the effect of membership of a market index
flows’. Unfortunately for our purposes, the Goetzmann and
have focused on abnormal returns at the time of changes to
Massa paper does not examine whether flows into the
index composition. Before reviewing these studies, we
indexed mutual funds are correlated with similar flows into
discuss briefly two other relevant papers: Chan and
actively managed funds or whether the price movements are
Lakonishok (1993) and Goetzmann and Massa (1999).
limited to the S&P index. So it is possible that they are
Chan and Lakonishok’s analysis was based on a sample of
simply picking up an example of the impact of mutual fund
returns on all NYSE, AMEX, and Nasdaq stocks with a
flows on overall market levels.
market capitalisation in excess of $50 million during the
period 1977–91. For each year the authors estimated a
We now turn to the effect of changes in index composition.
cross-sectional regression of return on beta, market
If required returns are dependent upon a stock’s inclusion in
capitalisation, the book-to-market ratio, an industry dummy,
the market index, then any unanticipated additions or
and a dummy for membership of the Standard and Poor
deletions of a stock from the market index should be
(S&P) Composite.
associated with an abnormal change in price, and this should
allow a more direct assessment of the effect on required
The regression coefficients for the S&P dummy are reported
returns of index membership. There have been a number of
in Table B and show the excess realised return to
studies in the United States of the effect of changes in index
membership of the index. The mean excess return is 2.2%
composition, the results of which are summarised in
per annum and the excess compound return over the
Table C. Notice that most deletions from the S&P index are
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Stock prices, stock indexes and index funds
Table C
contaminated by other news. As the principal criterion for
Announcement effect of additions to and deletions from
inclusion in an index is the stock’s market capitalisation,
the S&P Composite index
these changes in the index may be partly anticipated and
therefore the impact on prices may be underestimated.
Abnormal return (per cent)
Years
Additions
Deletions
Our data samples consist of: (a) all quarterly additions and
Shleifer (1986)
1966–75
-0.2
n.a.
Shleifer (1986)
1976–83
+2.8
n.a.
deletions to the All-Share index between March 1994 and
Goetzmann and Garry (1986)
1983
n.a.
-2.0
Harris and Gurel (1986)
1973–83
+1.5
-1.4
June 1999, and (b) all transfers into or out of the FTSE 100
Woolridge and Ghosh (1986)
1977–83
+2.9
n.a.
index from other sections of the All-Share index. So there is
Jain (1987)
1977–83
+3.1
n.a.
Lamoureux and Wansley (1987)
1966–75
+0.5
n.a.
no overlap between the two samples. After allowing for
Lamoureux and Wansley (1987)
1976–85
+2.3
n.a.
Dhillon and Johnson (1991)
1984–88
+3.3
n.a.
missing price data, the sample consisted of 120 additions to
Edmister and Graham (1994)
1983–89
+3.3
n.a.
and 110 deletions from the All-Share index and 36 additions
Beneish and Whaley (1996)
1986–94
+4.4
n.a.
Lynch and Mendenhall (1997)
1990–95
+3.2
-6.3
to and 40 deletions from the FTSE 100 index.
n.a. = not available.
We define the abnormal return as the difference between the
the result of mergers or bankruptcy and so the number of
return on the stock and the return on the All-Share index.
useful observations for deletions is much smaller than for
We measure the daily abnormal returns on stocks entering or
additions.
leaving the index during the days surrounding the
announcement date. Since the announcement takes place
Table C indicates that most researchers find a positive return
after market close, we define day 0 as the day following the
of about 3% when a stock is included in the index and a
announcement. The effective day is then typically day six
negative return for deletions. There is less agreement as to
or seven. We calculate the mean abnormal return for each
whether these abnormal returns reflect temporary price
day and, to provide a rough measure of significance, we
pressure or are consistent with a permanent change in the
standardise the mean abnormal returns by the standard
cost of capital. For example, Harris and Gurel (1986) find
deviation of the abnormal returns over a period of 76 days
that prices tend to revert to their pre-announcement levels
surrounding the eleven-day event period (defined below).
after about three weeks. Lynch and Mendenhall (1997) find
Given the small price effects that we observe and the
further positive abnormal returns between the announcement
considerable noise in the data, we do not attempt to measure
date and the effective date, which is partially reversed after
whether any abnormal returns are permanent.
the effective date. Edmister and Graham (1994) observe a
permanent shift in price.
Stocks entering or leaving the All-Share index typically
have very low market capitalisations. They are therefore
A number of commentators attribute the abnormal returns to
thinly traded, and the effect of the announcement may be
the influence of index funds, and there is some evidence that
delayed. Given the fact that the events cluster in time,
a change in index composition does lead to portfolio shifts
mismatches between the returns on the stocks and those of
(though this need not be a result of the activities of index
the market index may be common across the different
funds). For example, several studies indicate that stocks
stocks, and this is liable to show up in spuriously large
that are being added to the index experience an abnormal
absolute abnormal returns. It therefore suggests that our
rise in trading volume. Pruitt and Wei (1989) also find that
measures of statistical significance, particularly for changes
stocks that are added to the S&P index experience an
to the All-Share index, should be treated with considerable
increase in institutional ownership, and that the abnormal
caution. As a check that our results are not materially
return is positively related to this change in institutional
affected by such mismatches, we also examine and report
ownership.
raw returns. The choice between abnormal and raw returns
does not materially affect the pattern of the results, though
To see whether changes in index composition have a similar
for individual days the two measures sometimes differ
impact on returns in the United Kingdom, we collected data
markedly.
on all additions to and deletions from the FTSE All-Share
and FTSE 100 indexes. The FTSE index committee meets
Table D reports the abnormal returns for a period of eleven
each quarter to consider possible additions and deletions.
days surrounding the announcement date. The first column
The proposed changes are announced after market close and,
shows that on the day of the announcement of additions to
on average, become effective six to seven trading days
the All-Share index there is a positive, but not significant,
later.(1) These changes largely result from earlier new
abnormal return and this is followed by a significant rise on
listings or changes in market capitalisation. Between the
the following day. Thereafter, the returns are predominantly
regular quarterly reviews, changes are made to the index as
negative and over the entire eleven-day period additions to
a result of changes in corporate structure, such as a merger.
the index are associated with a cumulative abnormal return
We focus here only on changes made at the quarterly
of just 0.3%. In the case of deletions from the All-Share
review, as the stock returns are less likely to be
index, returns are fairly consistently and sometimes
(1) The mean number of days from announcement date to effective date varies from 5.5 for FTSE 100 additions to
7.1 for both additions and deletions to the FTSE All-Share.
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Bank of England Quarterly Bulletin: February 2000
Table D
associated with a somewhat larger negative cumulative
Abnormal returns during the period surrounding the
return.(3)
announcement of additions and deletions to the market
index, March 1994 to June 1999
If the price movements stemming from a change in index
Mean abnormal return (mean raw return)
composition are indeed permanent and unanticipated, then
we can estimate roughly the implied change in the cost of
Day relative to
FTSE All-Share
FTSE 100
announcement
Additions
Deletions
Additions
Deletions
capital. The Gordon growth model states that the dividend
-2
+0.2
+0.1
-0.1
-0.1
+1.4 (a) +1.4 (b) -0.6
-0.6
yield is equal to (r - g), where r is the required return and g
-1
+0.1
-0.1
-0.4
-0.7
+1.4 (a) +1.4 (b) -0.9
-1.0 (b)
the expected dividend growth rate. It is unlikely that the
0
+0.5
+0.4
-0.3
-0.7
-0.4
-1.1 (b) +0.1
-0.7
1
+0.8 (b) -0.1
-0.4
-1.1 (b) -0.4
-0.8
+0.6
+0.1
announcement of a change in index composition affects
2
+0.2
-0.1
+0.2
+0.3
-0.9 (b) -0.5
-0.1
+0.3
3
-0.1
+0.1
-1.2 (b) -0.8
-0.1
+0.2
-0.8
-0.4
either the prospective dividend or the expected dividend
4
-0.5
+0.2
-1.2 (b) -0.6
-0.2
+0.1
+0.0
+0.3
growth, so the change in the cost of equity is simply equal
5
-0.2
+0.0
-0.3
-0.1
+1.1 (b) +0.8
-0.8 (b) -1.0 (b)
6
-0.2
+0.3
-0.7
-0.8
+1.8 (a) +1.3 (b) -1.7 (a) -2.1 (a)
to the product of the abnormal announcement return and the
7
-0.3
+0.2
-0.4
+0.1
-1.1 (b) -1.2 (b) +1.4 (a)+1.3 (b)
8
-0.2
-0.1
+0.2
+0.3
-1.4 (a) -1.3 (b) +0.7
+0.7
dividend yield. For example, a permanent 3% rise in price
N
120
110
36
40
and a 3% dividend yield would imply a 9 basis point decline
(a) Significant at the 1% level.
in the cost of equity. If part or all of the abnormal return is
(b) Significant at the 5% level.
temporary, then the fall in the cost of equity is less than
9 basis points. If the much larger price movements
significantly negative for the entire eleven-day period. The
estimated by Chan and Lakonishok and Goetzmann and
cumulative abnormal return over the eleven days is
Massa reflect adjustments to the required returns on index
-4.5%.(1)
stocks, then the fall in the cost of equity for index stocks is
The remaining columns of Table D show the effects of
of the order of one percentage point.
transfer into or out of the FTSE 100 index. The puzzle here
is the behaviour of the additions to the index, as the returns
Summary and conclusion
are large in absolute terms and appear often to be highly
significant. However, there is little consistency in the sign
Accumulating evidence that active portfolio managers do
of the returns and the total change over the eleven-day
not achieve consistently superior performance has led to a
period is an insignificant +1.2%. By contrast, the deletions
rapid growth in index funds with low turnover and reduced
from the FTSE 100 index are predominantly negative and on
management costs. For the most part, these funds track the
three days significantly so. The cumulative abnormal return
performance of major market indexes and therefore tend not
over the eleven-day period for index deletions is -2.0%.(2)
to be invested in the stocks of very small firms. This growth
Since few funds either track the FTSE 100 or are
in index funds has forced active managers to hold a higher
benchmarked to it, the apparent abnormal returns on
proportion of small-firm stocks than they otherwise would
changes to the FTSE 100 suggest that the effects of index
and, since they need to be induced to do this voluntarily, the
composition may be more complex than a simple tracking or
expected return on these stocks must rise. We have argued
benchmarking effect.
that the portfolio adjustments forced on active managers are
in practice very small and, since small-firm stocks are fairly
We repeated the exercise with day 0 redefined as the date
good substitutes for large-firm stocks, the effect of index
that the index change became effective. There is no
funds on required returns is likely to be no more than
evidence of any effective-day effect for the All-Share index,
several basis points.
but there are some quite large changes in the price of stocks
entering and leaving the FTSE 100 index. For stocks
If market indexes are used as benchmarks for measuring the
entering the index there is a mean abnormal return of 2.9%
performance of professional active managers, then index
on the preceding day, which is fully reversed on days 0 and
stocks become effectively riskless for these managers and
+1. For deletions there is an abnormal decline of 2.0% on
they need to be induced to hold the remaining stocks.
day -1, which is again reversed on days 0 and +1. This
Unlike index-fund managers, these active managers are not
behaviour is suggestive of some anticipatory price
totally averse to holding non-index stocks, and so the
pressure.
incremental effect on prices of benchmarking is likely to be
less than if these funds were formally indexed.
In summary, stocks that are added to both the FTSE
All-Share and the FTSE 100 indexes experience, on average,
Most empirical studies of the effect on prices of index
a positive abnormal return over the eleven-day period
composition cannot distinguish the effect of index funds
immediately preceding and following the announcement.
from that of benchmarking or possible information effects.
However, this abnormal return is both statistically and
Chan and Lakonishok suggest that membership of the S&P
economically insignificant. Deletions from the index are
index has had a substantial effect on prices in recent years,
(1) For the All-Share index, the cumulative raw returns are +0.9% for index additions and -4.2% for deletions.
(2) For the FTSE 100 index, the cumulative raw returns are +0.4% for index additions and -3.1% for deletions.
(3) One possible explanation is that stocks that are deleted from the index are likely to be smaller than additions.
If an index is weighted by market value, then the returns on the index are more heavily influenced by larger
companies, so that the abnormal returns on the smaller-cap stocks are likely to be larger in absolute terms than
those of the larger-cap stocks. I am grateful to Elroy Dimson for this observation.
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Stock prices, stock indexes and index funds
while Goetzmann and Massa find that flows into index
in a negligible rise in price. Deletions, however, were
funds have also had a marked cumulative price effect.
associated with an eleven-day cumulative abnormal return
However, it is difficult to reconcile these results with studies
of -4.5% for All-Share stocks and -2.0% for the FTSE 100
of the effect of additions or deletions to the index. In the
index. If permanent, these returns suggest that index
United States these have typically found a price impact of
deletions result in a small increase in the required return on
around 3%, which would imply a shift in required returns
equity for the affected firms. However, the fact that
of a few basis points. Our sample of changes to the
abnormal returns are observed for both indexes suggests that
FTSE All-Share and FTSE 100 indexes from 1994 to 1999
the effect is not simply due to the growth of index funds or
indicated that in both cases an addition to the index resulted
performance benchmarking.
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Bank of England Quarterly Bulletin: February 2000
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