1.
Index Investing
A cost effective approach to long term investing
Syed Zillur Rehman

2.
Table of Content
Work Cited.……………………………………………………………………………………….i
Abstract………………...………………………………………………………………………....1
Introduction……...……………………………………………………………………………….2
Burton Malkiel’s support for Index Funds….....……………………………………………....3
Allocation strategies based on market cycles……...…………………………………………...4
William Sharpe’s Arithmetic Approach…………..……………………………………………4
Bogles’ Cost Matter Hypothesis………..……………………………………………………….5
Returns in terms of Real Interest Rate and Compounding Interest………………………….6
Performance analysis of Mutual fund vs Index Fund ………………………...………………7
Portfolio Turnover……………………………………………………………...………………..8
Tax Implications………………………………………………………...……………………….9
Behavioral reasons for active investment…………………………..…………………………10
Conclusion ……………………………………………………………………………………...10

3.
Works Cited
Bogle, J. C. (1997). The First Index Mutual Fund: A History of Vanguard Index Trust and
the Vanguard Index Strategy. Retrieved 08 08, 08, from Bogle Financial Market
Research Center: http://www.vanguard.com/bogle_site/lib/sp19970401.html
Bogle, J. C. (2004). As The Index Fund Moves from Heresy to Dogma...What More Do
We Need To Know? Retrieved 08 08, 2008, from Bogle Financial Markets Research
Center: http://www.vanguard.com/bogle_site/sp20040413.html
Bogle, J. C. (2005). In Investing, You Get What You Don't Pay For. Retrieved 08 08, 2008,
from Bogle Financial Market Research Center:
http://www.vanguard.com/bogle_site/sp20050202.htm
Bogle, J. C. (2005). The Relentless Rules of Humble Arithmetic . Retrieved 08 08, 2008,
from Bogle Financial Markets Research Center:
http://www.vanguard.com/bogle_site/sp20060101.htm
Bogle, J. C. (2007). The Little Book of Common Sense Investing. Hoboken: John Wiley & Sons.
French, K. (2008). Kenneth R. French - Home Page. Retrieved 07 31, 2008, from Social
Science Research Network: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1105775
French, K. R. (2008). The Cost of Active Investing. Journal of Indexes , 50.
Malkiel, B. (2003). A Random Walk Down Wall Street. New York: W. W. Norton & Company,
Inc.
Sharpe, W. F. (1991). The Arithmetic of Active Management. Retrieved 08 08, 08, from
Stanford University: http://www.stanford.edu/~wfsharpe/art/active/active.htm
Sharpe, W. F. (2002). Indexed Investing: A Prosaic Way to Beat the Average Investor.
Retrieved 08 08, 08, from Stanford University:
http://www.standford.edu/~wfsharpe/art/talks/indexed_investing.htm

4. ‐ 1 ‐
Abstract:
In this paper, I will examine the work of some of the most notable and leading economists in
support of index based investing, also knows as passive investing. I would like to point out that
this paper is intended for average investors but, the logic is equally applicable to anyone with
long term investment objectives. I will define the meaning and the origination of index funds, its
transformation from a simple theory to an efficient investment vehicle, and its lower cost
implication in comparison to mutual funds. Subsequently, I will analyze the validity of this
strategy using arithmetic approach as presented by William Sharpe. In light of John Bogle and
Kenneth French’s research papers, where they have tracked the performance of index funds and
the effects of various costs on a portfolio, I would highlight some of the incentives reaped from
passive investing. Finally, I will discuss some of the behavioral reasons such as overconfidence
and prestige that can be attributed to active management.

5. ‐ 2 ‐
Introduction:
Index investing provides a cost effective way to earn market return by matching the
securities within a given index proportionally. This idea is based on the principle that investors
can not beat the market on a regular basis and therefore, it is futile to continuously chase higher
returns. There are number of cost elements that significantly offset gains received by higher
turnover portfolios.
In case of a mutual fund, investors not only pay explicit cost such as management fees
but also implicit costs that includes turn-over cost and realized capital gain taxes. Furthermore,
if an investor is managing their own portfolio, one has to account for the unrecognized cost for
the time spent in researching and tracking performance of companies within a portfolio. Studies
show that once the number of stocks in a given portfolio exceeds 6, it becomes very difficult to
manage their individual progress. Upon quantifying all of these factors, we find that they take up
a big chunk out of investors’ overall return. Essentially, index funds are designed to combat high
costs that investors pay without even realizing its impact on the overall return.
The discussion of return is incomplete without considering the risk factor that
accompanies it. By efficiently diversifying, we strive to build portfolios that yield maximum
return yet minimize the risk exposure. In this pursuit, fund managers pick securities that are not
optimally correlated. However, when mutual fund managers make adjustments to the portfolio,
they introduce new securities that drift away from the optimal correlation that initially existed.
Additionally, this portfolio calibration is sometimes subjected to capital gain taxes even if it
results in the net loss for the investor. In comparison, index funds’ composition does not change
as frequently, therefore investors are protected from higher turn-over cost and capital gain taxes.

6. ‐ 3 ‐
There are number of well known economists who have done significant amount of
research in support of index investing, including Paul Samuelson, Charles Ellis, and Al Ehrbar.
In addition, Burton Malkiel who is the one of the pioneer and strong advocate of index investing
considers it as the most successful investing vehicle, particularly on the basis of Efficient Market
Hypothesis. John Bogle gave practical meaning to the earlier ideologies by creating first index
fund, which tracked S&P’s 500 index. He has done extensive research in the field by analyzing
various cost effects on active versus passive portfolios within a certain time period. In essence,
all of the above mentioned scholars agree that in the long run, an index fund will create less
expensive and optimally diversified portfolios.
Burton Malkiel support for Index Funds:
The logic behind the index fund is supported by the Efficient Market Hypothesis, which
implies that it is impossible to out-perform the market due to its continuously changing
information. Burton Malkiel describes this phenomenon as, “markets can be efficient even if
they sometimes make egregious errors in valuation, as was certainly true during the 1999-2000
Internet bubble. Markets can be efficient even if many market participants are quite irrational.
Markets can be efficient even if stock prices exhibit greater volatility than can apparently be
explained by fundamentals such as earnings and dividends (Malkiel, 2003, p. 244).” What this
means is that investors may be able to beat market on occasional basis, but in the long run it is
not possible as markets are fundamentally efficient. By the time any critical information about a
security becomes available to investors, it is already too late to jump on the ‘profit bandwagon’
as the new price quickly reflects that. Most of the time, fluctuations in prices is only a temporary
phenomenon and once the dust settles, it simply reflects the true underlying value of the security.

7. ‐ 4 ‐
Allocation strategies based on market cycles:
One of the skills marketed by fund managers is their ability to efficiently move between
cash and equities position based on market cycles. In ideal situation, they would like to have
most of their assets in stocks at the trough of the market cycle, whereas their allocation should
consist of more of cash and fixed income assets at the peak just before the downward
momentum. However, John Bogle’s research in comparing equity mutual fund’s cash to total
assets ratio and S&P 500 shows a contradictory behavior; the peaks in mutual funds’ cash
position coincided with market troughs during 1970, 1974, 1982, end of 1987, and late 1990
(Malkiel, 2003, p. 194). Similarly, during the peak periods in the market, they maintained low
cash position. Thus, there is little evidence to support that fund managers can successfully
predict different market cycles and move funds between fixed income and equities position
accordingly.
According to Mr. Malkiel, “over the past fifty-four years the market has risen in thirty-
five years, been even in three years, and declined in only fifteen. Thus, the odds of being
successful when you are in cash rather than stocks are almost three to one against you (Malkiel,
2003, p. 194).” John Bogle quantified the cost incurred by comparing the dollar-weighted
returns earned by a fund’s shareholders with the time-weighted returns by the fund itself. He
found that the dollar-weighted returns of the 200 largest equity mutual funds, the returns enjoyed
by the shareholders lagged the time-weighted returns by fully 3.3 percentage points per year
(Bogle, 2005, p. 8).
William Sharpie’s Arithmetic Approach:
William Sharpe proposed that a simple arithmetic can be used to justify that a passive
investor will always outperform an active investor. His reasoning is based on the fact that over

8. ‐ 5 ‐
any specified time period, the market return will be a weighted average of the securities within
the market, using beginning market value as weights. He presented two assertions to support his
claim:
1. Before cost, the return on active and passive investment will be equal.
2. After cost, the return on passive fund will be greater than active investment.
In order to prove the first point, he reasoned that if the market returns 10% before costs,
then a passive investor will also receive the same return. Furthermore, the market return must
equal a weighted average of the returns on active and passive funds, therefore the return on
active investment should be the same as well. The second assertion is justified by the fact that it
is more expensive to maintain an active portfolio as it would require research work, payment to
security analysts, etc. The cost of managing an index fund is between 0.15% to 0.50% as
compared to active investment where the minimum cost is 1.0% (Sharpe, 2002, p. 3). So, when
we see fund managers driving luxurious cars and living out loud, it would be fair to assume that
those are all paid by the courtesy of naïve investors. After accounting for cost, an active
portfolio would result in a lower return than a passive portfolio.
Bogle’s Cost Matter Hypothesis:
John Bogle explained that even if people disagree with Efficient Market Hypothesis,
there are still some strong reasons to believe in index investing. He calls it the Cost Matters
Hypothesis and explains, “No matter how efficient or inefficient markets may be, the returns
earned by investors as a group must fall short of the market returns by precisely the amount of
the aggregate costs they incur. It is the central fact of investing.... Intermediation costs in the
U.S. equity market may well total as much as $250 billion a year or more. If today’s $13 trillion
stock market were to provide, say, a 7% annual return ($910 billion), costs would consume more

9. ‐ 6 ‐
than a quarter of it, leaving less than three-quarters of the return for the investors—those who put
up 100% of the capital (Bogle, 2004, p. 4).”
According to Mr. Bogle, today’s investors undermine the importance of costs because of
the three reasons. First, costs such as portfolio transaction costs, the un-recognized impact of
front-end sales changes, and taxes incurred on realized gains are not clearly defined. For
instance, when a mutual fund manager presents brochure highlighting their year-to-year market-
beating accomplishments, most of the times those graphs do not reflect the effects of cost.
Second, during bear market of 1980’s and 1990’s when the stock market returns have been high
as compared to average fund, investors tend not to take cost into equation. There have been
numerous studies that prove that the psychological effects of 1-2% become almost negligible in
light of 15-20% return. Third, focus on short-term returns in contrast to long-term opportunities.
Most of the average investors get carried away with short-term profits and fail to realize long-
term effects of cost in term of real and compounding interest (Bogle, 2007, p. 40).
Returns in terms of Real Interest Rate and Compounding Interest:
Bogle has found that the nominal long-term returns of about 10 percent on stocks turned
out to be about 6½ percent in real terms. Then, there are effects of compounding costs that can
significantly widen the difference between index funds versus managed fund returns. “If we
assume that mutual fund costs continue at their present level of at least 2½% a year, an average
mutual fund might return 5½%. Extending this tax-deferred compounding out in time on your
investment of $3,000 each year over 40 years, and investment in the stock market itself would
grow to $840,000, with the market index fund not far behind. Your actively managed mutual
fund would produce $430,000—only a little more than one-half as much (Bogle, 2004, p. 20).”
Performance analysis of Mutual fund vs Index Fund:

10. ‐ 7 ‐
Bogle conducted research on the last 20 years of S&P 500 index versus Average Equity
Fund. After finding out the gross return, he subtracted several cost factors such as taxes,
inflation, and transaction costs to determine net return. Before taxes, Standard & Poor’s 500
Index returned 12.8% where as average equity mutual fund returned 10.0%, a difference of 2.8
percentage points a year. After taxes, this difference further extended to 4.1 percentage points a
year. By taking inflation into the equation, the real annual return for the index fund drops to
8.9% and the equity fund to 4.8% (Bogle, 2005, p. 5).
According to a study conducted by John Bogle over a sixteen-year period, investors get
to keep only 47% of the cumulative return of the average actively managed mutual fund, but they
keep 87% in a market index fund. This means $10,000 invested in the index fund grew to
$90,000 vs. $49,000 in the average actively managed stock mutual fund. That is a 40% gain from
the reduction of silent partners (Bogle, 2005, p. 6).
Kenneth French found that the average difference between the actual standardized cost of
investing and the passive cost for the 1980 to 2006 period is 67 basis point. If the expected real
return on the US stock market is a constant 6.7%, the capitalized cost is 10% of the current value
of the market (French, 2008, p. 21). “Furthermore, the actual cost of investing – the fees and
expenses paid for mutual funds, the investment management costs paid by institutions, the fees
paid to hedge funds and the transaction costs paid by all traders – is 0.82% of the value of all
NYSE, Amex, and NASDAQ stocks in 1980 and 0.75% is 2006. In the passive scenario,
investors pay passive fees, annual turnover is 10%, and there are no hedge funds. As a result, the
cost of investing is only 0.18% of the aggregate market cap in 1980 and 0.09% in 2006 (French,
2008, p. 23).”
Portfolio Turnover:

11. ‐ 8 ‐
Turnover refers to the selling and buying of securities by fund managers in order to
outperform the market. Selling securities in some circumstances may result in capital gains tax
charges, which are sometimes passed on to fund investors. A passive investor trade for two
reasons, to accommodate cashflows and to maintain target risk return trade offs. Because index
funds are passive investments, the turnovers are lower than actively managed funds. Based on
the Kenneth French’s finding, turnover has risen steadily from 20% in 1975 and 59% in 1990 to
an impressive 173% in 2006 and 215% in 2007 (French, 2008, p. 16). There are several reasons
for this extraordinary growth in trading, but some of the most notable are, reduction in cost,
negotiated brokerage commission, the development of electronic trading networks, and the
decimalization of stock prices.
Tax Implications:
Another important advantage of index investing is its tax efficiency, which is the crucial
financial factor because of its substantial effect on net returns. Index funds do not trade from
security to security thus; they tend to avoid capital gain taxes. Joel Dickson and John Shoven
used 62 mutual funds with long-term records; they found that, pre-tax, $1 invested in 1962
would have grown to $21.89 in 1992. After paying taxes on income dividends and capital gains
distributions, however, that same $1 invested in mutual funds by a high-income investor would
have grown to only $9.87 (Malkiel, 2003, p. 195). Recently, Exchange–traded index funds
(ETF’s) have been designed to lessen the impact of taxes. S&P 500 tends to be more tax-
efficient because of their ability to bear in-kind redemption which delivers low-cost shares
against redemption request.
In order to prove the tax efficiency of index funds, Bogle compared ICA mutual fund
with S&P 500 index fund. He found that during the past 25 years, for example, federal taxes

12. ‐ 9 ‐
consumed an estimated 2.5 percentage points of its annual return, reducing it from 13.7% to
11.2% for taxable investors. While an S&P 500 index fund is hardly exempt from taxes, its
passive market-matching strategy is highly tax-efficient. During the same period, taxes on an
index fund would have cost an estimated 0.9 percentage points, reducing its 13.8% pre-tax return
to 12.9%, a net after-tax advantage over ICA of 1.7 percentage points per year. Not only do
taxable investors pay high costs in fund advisory fees, operating expenses, and sales
commissions when they buy active fund management, they also pay a remarkably high tax cost
(Bogle, 2004, p. 13).
Reasons for active investment:
After looking at all the above reasons, the question that comes in mind is why investors
select active management over passive. There are number of reasons that can be attributed to
this irrational behavior. According to Kenneth French, “the dominant reason is a general
misperception about investment opportunities. Many are unaware that the average active
investor would increase his return if he switched to a passive strategy. Financial firms certainly
contribute to this confusion. Although a few occasionally promote index funds as a better
alternative, the general message from Wall Street is that active investing is easy and profitable.
This message is reinforced by the financial press, which offers a steady flow of stories about
undervalued stocks and successful fund managers.
Overconfidence is probably the other major reason investors are willing to incur the extra
fees, expenses, and transaction costs of active strategies. There is evidence that overconfidence
leads to active trading. Investors who are overconfident about their ability to produce superior
returns are unlikely to be discouraged by the knowledge that the average active trader must lose.

13. ‐ 10 ‐
There is another behavioral explanation for active investing. He suggests that, in addition
to expected return and risk, investors are concerned with what he calls the expressive
characteristics of their portfolios. Thus, some investors may accept a lower expected return in
exchange for the bragging rights that come with a fund that has performed well. Others may
give up the low cost and diversification of a passive mutual fund for the prestige of their own
separate account (French, 2008, p. 25).”
Conclusion:
In conclusion, index investing offers a great way to earn market return without incurring
enormous cost that accompanies with active management. By choosing passive funds, investors
pay absolute minimal fees, which are at least 50% lower than what is charged by mutual funds.
Over the long run, this cost reduction can substantially increase the value of a portfolio because
of the compounding interest. Furthermore, it has been proven that fund managers can not predict
market cycles and they have demonstrated poor judgment when moving funds from fixed income
to equities position. Because index funds have lower turn over, investors are protected from
transaction cost and capital gain taxes. Also, this stability will be in the interest of stock market
as a whole because investors would focus on long term objectives. Fund managers’ quest to beat
the market results in a greater volatility and causes portfolios to drift away from optimal
correlation. Based on the above facts, it is astounding to comprehend the existence of mutual
funds, especially when the added benefits offered by index funds are unparallel. Recently, there
has been an upsurge in ETF sector as investors have started to switch away from cost intensive
sub-par active funds.