70 THEORY AND EVIDENCE ON SHORT SELLING
problem, bad luck that has temporarily depressed earnings, and so on).
Virtually never will a firm publicize facts like the obsolescence of their
products, the products’ lack of durability, or the stupidity (or senility) of
their management. Just imagine what the sales reps for the competition
could do with statements such as “Competitor X has a better product,”
“Our product is obsolete,” or “We have found unexpected durability
problems with our product.” A plaintiff’s lawyer would love to have a
statement on record saying, “Our product is unsafe.”
If analysts or brokers identify a stock that is underpriced, they can be
expected to publicize the information that make them believe it is under-
valued. They, and their firm, could get an order to purchase the stock by
informing investors of the information. Just as an example, a recent news
story states, “Keane’s nod carries some punch as his advice reaches
12,000 retail stock brokers at Wachovia Securities.”
11
If each broker
keeps only nine investors informed, the word has reached 108,000 inves-
tors, more than the 100,000 investors discussed above.
In contrast, even when short selling is allowed, few investors will
place short sale orders. Only a few investors will own any given stock,
so phone calls saying the stock is over valued will typically be greeted
with “That’s interesting, but I don’t own any.” In many cases, if the
stock is actually owned, it is because the broker making the call sold it
to the investor. There are real problems in calling a client up and
explaining why the stock you previously urged him to buy should now
be sold. Even those who own a stock are unhappy at brokers and ana-
lysts who draw attention to a stock’s problems, since this forces its price
down, making current owners poorer. The current owner usually has an
ego investment in the stocks he owns, and telling him that these stocks
are overvalued is to question his good judgment.

to themselves, their spouses, or their bosses that they have made a bad
investment. Selling a stock means admitting to a mistake. A much better
psychological strategy (even if a bad investment strategy) is to find reasons
why the stock that has gone down is still a good investment and will come
back. One study found that stocks above their purchase price are 50% more
likely to be sold than stocks that are below their purchase prices.
13
Because
of this bias, more analytic attention to stocks where there is not obvious
bad news may unearth publicly available information that can be acted on
profitably. The information may have been disseminating slowly enough so
that prices have not fully adjusted yet. A stock that has fallen without an
obvious explanation may be one that should be looked into further.
When we combine the obstacles to short selling with the asymmetry
in the ease with which positive versus negative information is dissemi-
nated, we discover that there will be very few grossly underpriced secu-
rities that can be discovered from publicly available information, while
there will be some overpriced securities that can be identified. As will be
seen below, this observation has strong implications for investment
strategy and for how a firm should allocate its analytical resources.
Accounting Implications
The above argument shows how in the absence of short selling, mistakes
on the high side (those which cause investors to raise their estimate of the
value of a stock) tend to raise stock prices, while those on the negative side
do not. Thus there is an important asymmetry here. Accounting conven-
12
Harrison Hong, Terence Lim, and Jeremy Stein, “Bad News Travels Slowly: Size,
Analyst Coverage, and the Profitability of Momentum Strategies,” Journal of Fi-
nance (February 2000), pp. 265–295.
13

accounting methods should be biased towards the conservative side.
As an example, consider whether to expense an item such as research
or to permit it to be capitalized. Although it is recognized that most
research will be valuable over a number of years, it is difficult to know
how many years. This difficulty has kept research from being capitalized
and then amortized. Suppose a firm was free to amortize research expen-
ditures over a number of years, even if the research had yielded very lit-
tle. This would make the reported profits higher. Some investors might
realize the research had yielded little, and value the company at a lower
price. However, there would probably be enough investors who took the
company’s accounting at face value for the stock price to reflect their
higher valuations. However, if the research is expensed when done (the
current procedure), there will probably be some investors who do not
realize the research expenditures have long-term value. However, there
14
Edward M. Miller, “Why Overstated Earnings Affect Stock Prices But not the Re-
verse,” Journal of Accounting, Auditing, and Finance (Fall 1980), pp. 6–19.
15
See a standard text such as Anthony F. Herbst, Capital Asset Investment (New
York: John Wiley & Sons, 2002).
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Restrictions on Short Selling and Exploitable Opportunities for Investors 73
are likely to be enough investors who recognize the value of the research
(or at least intelligently estimate it), to raise the firm’s stock price. These
investors will be the optimists who set prices.
An example can be provided by convertible bonds. The drug com-
pany, Cephalon, issued convertible bonds with a zero interest rate. Why
would anyone buy bonds that do not yield anything? The answer is that
the conversion option is valuable. Cephalon’s stock price could go up a
lot, especially if its antidrowsiness drug, Provigil, is approved for new

A more complex example is provided by the current controversy over
contingent convertible bonds.
16
These are convertible bonds that provide
16
David Henry, “The Latest Magic in Corporate Finance,” Business Week (Septem-
ber 8, 2003), pp. 88–89.
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74 THEORY AND EVIDENCE ON SHORT SELLING
for conversion only if a contingency has occurred, such as the price reach-
ing a considerably higher value than the conversion value. Under stan-
dard accounting rules, the earnings per share are adjusted for full
conversion of convertible securities that could be converted. However,
with a high contingent price that must first be reached, this conversion
need not be reflected in the accounts until the higher price is reached.
With contingent convertible bonds, the conversion adjustment is
avoided until the contingency occurs, which is usually further in the future.
For recent Cephalon contingent convertible bonds, there was a potential
15% dilution. Failure to make allowance for dilution makes a stock appear
more attractive. The investors who fail to make the adjustments will be the
optimistic investors that tend to set the price. This applied to the original
question of whether to make any adjustments for potential dilution and to
the current issue of whether firms should be allowed to avoid adjusting for
dilution when a contingency provision is involved.
Another example is the current controversy over whether and how to
expense employee options. Clearly these options are of value to employees
and frequently are used in recruiting and retaining valued employees.
Employees consider them part of the compensation package. It is also clear
that they typically cost the shareholders something through potential dilu-
tion. If they could be easily valued, there would be no dispute about the

there are many markets where short selling is forbidden). Although in
the United States short selling is possible, it is not nearly as simple as
many mathematical models would make it. In these models, short posi-
tions are equivalent to long positions with a negative sign. Someone
who sells short can just take the money and invest it elsewhere (just as
someone with a long position can sell it and invest the funds elsewhere).
This, of course, is not what really happens in a short sale.
The lender of the stock which is sold short needs assurance that the
stock will be returned. This is traditionally done by providing a cash
deposit equal to the value of the stock sold short (and marked to market
as its price changes). For most individuals, no interest is paid on these
proceeds (the cases where interest is paid will be discussed later). Con-
sidering this case provides some useful insights.
The simplest case can be shown with the aid of Exhibit 5.3. Suppose
there is a nondividend paying company that is going to liquidate at a
EXHIBIT 5.3 Price Limits when Short Sellers Receive No Interest on the Proceeds
5-Miller-Restrictions Page 75 Thursday, August 5, 2004 11:10 AM
76 THEORY AND EVIDENCE ON SHORT SELLING
future date, say 2010. One might imagine it as a mining company that
will liquidate when the deposit is exhausted (or when it’s right to mine
the deposit lapses). The well-informed investors analyze the company
and estimate the liquidating dividend, C, in the exhibit. To decide how
much to pay for the security, the informed investors discount this liqui-
dating dividend at the appropriate risk-adjusted rate, and arrive at a
value for each earlier date. Curve BC shows this price as a function of
time. An informed investor should follow a simple rule: Buy the stock if
its price is less than the value on line BC. The logic is simple. When the
security can be bought at a price below BC, it is priced to yield more
than other securities of equivalent risk.
It is easy to argue that in a market with many well-informed inves-

be held since the investor can do better with other assets.
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Restrictions on Short Selling and Exploitable Opportunities for Investors 77
With reason this stock can be said to be overpriced. Although many
defenders of the efficient market hypothesis assert overpriced stocks are
short sales candidates, this stock is not a short sale candidate. Because
stock E will rise in price, it is not a short sale candidate. Investors lose
money by shorting stocks that subsequently rise in price. The advice,
“buy low, sell high,” applies to short sales.
The example points out that an overpriced stock is not necessarily a
short sale candidate. This is a mistake frequently made by efficient mar-
ket proponents who casually assert that overpriced stocks will be sold
short. (The usual definition of an overpriced stock is one that is
expected to have a return below that on securities of comparable risk.)
Sometimes short selling is plausible. If the price is above line AC,
informed investors could potentially short the stock and make a profit.
Since line AC is the liquidation price, a stock sold now and bought back
just before the company is liquidated would be profitable (if there are
no carrying costs for the short sale). Of course, there could be a wild
ride before the profit was realized.
Notice is that the upper limit (set by short selling) and the lower
limit (set by buying) can be quite far apart. The lines are far apart when
there will be several years before the uncertainty about the true value is
resolved (which happens here when the company is liquidated). Between
the two lines, the rule for informed investors is “sell, if owned.” Since
line BC shows the price increase required for the stock to show a normal
return, if the price is above this line, the appreciation will be below that
needed to justify holding it. Thus, the stock should be sold if owned.
Admittedly, whether or not short sales of overpriced stocks are
made is not critical as long as investors are considered to all have the

ceeds of the shorts sale as a security deposit on which they do not earn
interest, a situation that is true for most individual investors.
Investors Who Can Receive Use of the Proceeds
Up to this point, the theory has been developed on the assumption that
investors can never receive use of the proceeds of a short sale. This is the
situation for most individual investors. However, in the United States this
rests on custom, not legal prohibition. Institutions and brokerage houses
can frequently borrow certificates using procedures that give them some
return on the proceeds. As a practical matter, the ability of the institutions
to borrow shares under circumstances where they receive part of the pro-
ceeds is of only limited importance, since most institutions are operating
under constraints that prevent short selling. However, some institutions
(such as hedge funds, long–short investment companies, certain mutual
funds, and other investment companies) may sell short and other large
players (brokerage houses) may arrange to receive a return on the pro-
ceeds of a short sale. Thus this case should be considered.
There are several procedures that permit receiving some return on the
security provided against loan of the certificates Hanson and Kopprasch
once reported 75% of brokers’ call is standard.
18
In other cases, borrow-
ers of the shares deposit either other securities as security (in which case
the return on these securities is still available to the short seller), or a
bank letter of credit. They pay the lender an explicit fee for each day the
shares are loaned. This fee offsets the earnings from the proceeds, in
18
See H. Nicholas Hanson and Robert W. Kopprasch, “Pricing of Stock Index Fu-
tures,” in Frank J. Fabozzi and Gregory M. Kipnis (eds.), Stock Index Futures
(Homewood, IL: Dow Jones-Irwin, 1984) pp. 72–73.
5-Miller-Restrictions Page 78 Thursday, August 5, 2004 11:10 AM

weighted mean fee was only 17 basis points per year. The vast majority
of the dollar value of stocks appeared to be available for borrowing. For
most of these stocks, the borrowing would be done at a nominal fee.
The stocks that appeared to be possibly unavailable (i.e., not listed by
this lender), tended to be very low capitalization stocks and often too
small or too low priced to be of institutional interest. (Since most lend-
ing was coming from institutions, this is not surprising.)
On average 8.75% of stock loans were specified as “special.” The
value-weighted mean loan fee was much higher, at 4.69%. There was an
average of six stocks on any given day for which the rebate rate was
negative (i.e., the borrower of the stock did not receive interest on the
collateral and had to pay money to the lender as well). For these, the
19
Gene D’Avolio, “The Market for Borrowing Stock,” Journal of Financial Eco-
nomics (2002), pp. 271–306.
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80 THEORY AND EVIDENCE ON SHORT SELLING
implied fee averaged 19%. (The highest was 55% once for Krispy
Kreme and 50% for Stratos Lightwave).
Exhibit 5.4 shows the situation of a short seller who can receive
interest on the proceeds of a short sale (see below). The upper limit is
then a curved line growing at the interest rate earned. Unless the interest
earned on proceeds of short sales equals the competitive rate of return
earned on long positions, the two curves will differ by an amount that
increases with the period of time until the uncertainty is resolved.
Because the competitive rate of return on stocks (averaging about 10%)
is much higher than the Federal funds rate (at the historically low rate
of 1% at the time of writing), there would still be an appreciable gap
between the two curves, even if the full Federal funds rate was paid.
The large gap between the upper and the lower limits arises because a

the portfolio, a characteristic that can be measured by its beta. Because
of the negative beta of short positions, rational investors will often be
willing to accept a lower return than they otherwise would, possibly
even a negative return. Thus, the return a stock must earn if it is not to
be sold short is higher for high beta stocks. This effect moves the line
AC in Exhibit 5.4 downwards. However, high beta stocks also require a
higher return for inclusion in a portfolio on the long side. If both buyers
and short sellers use the capital asset pricing theory, the beta adjustment
in the rate of return for the upper limit and the lower limits are equal,
and the percentage difference in the rate of return is unchanged. The
implication still remains that the distance between the two curves
increases with time until resolution of the uncertainty.
Whether or not the effective upper limit to a stock price will be set
by those institutional short sellers (who are both not constrained from
selling short and able to receive a return on use of the proceeds), or by
individuals not able to receive use of the proceeds, depends on the rela-
tive numbers of the two groups of investors and the strength of the buy-
ing by the overly optimistic investors. Often, (especially for the smaller
capitalization stocks not widely traded by institutions) there will be too
few potential short sellers able to receive use of the proceeds. In this
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82 THEORY AND EVIDENCE ON SHORT SELLING
case, the price will be bid up by optimistic investors to levels where fur-
ther rise is limited by short selling by individuals (and possibly not even
by them). When this happens, those short sellers who can receive use of
the proceeds will be able to earn abnormal returns that cannot be
earned by individuals.
Since some institutional investors do get use of the proceeds, and
they are likely to have the analytical talent and expertise to identify
good short candidates, individual investors who do not get use of the

beta permit taking a riskier long position (i.e., instead of holding some
bonds to moderate risk, equities are held and short positions are used to
protect against a market decline). In other cases, the short sale may per-
mit taking a larger position in the same industry on the long side, or
being more aggressive in holding firm A. (This leads to paired trading.)
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Restrictions on Short Selling and Exploitable Opportunities for Investors 83
A money management firm that has mostly long-side clients may
find it profitable to introduce one or more short side (or long–short)
funds since the marginal cost of managing them will be low.
Other Obstacles to Short Selling
The example used above in Exhibits 5.3 and 5.4 to develop the theory was
highly unrealistic. It was designed to provide a very favorable case for short
sellers’ ability to provide a lid to stock prices even in the presence of less
informed investors. Remember, the example involved a company that was
scheduled to liquidate at a known date in the distant future. A liquidation
date means that just before that date the stock has to sell at the expected
liquidation value. This makes the stock act like a zero-coupon bond.
However, bonds typically have maturity dates, but not common
stocks. In practice, very few companies have a known, planned liquidation
date.
20
If one tries to project the price in 2010, one is really guessing what
will the market expectations be in 2010 about the future of the company
and about the dividends to be paid well after 2010. This infinite life makes
short selling riskier, and implies that short positions will seldom be entered
into for stock believed to be overvalued except when the overvaluation is
very extreme and the holding period is short.
To a professional fund manager, the idea expressed in Exhibit 5.3
that a stock would be a short sale candidate because it could be sold

grossly overpriced stocks, but describes no attempts to hold positions
for years.
21
Academics have recently discovered this problem, producing
the limits to the arbitrage literature.
22
This is a fundamental difference with long positions. If one is certain
a stock will have a much higher price in the future (sufficiently higher to
provide a suitable risk-adjusted rate of return), a long-term investor can
buy it in confidence and expect to end up with a profit even if the stock’s
price falls before it starts rising. (This assumes he is not trading on mar-
gin.) This is not true for short positions. Even in the absence of mainte-
nance margin requirements, those considering lending stocks would still
require security deposits. There would be limits on how large positions
investors could take. A mark-to-market provision is needed to protect
the stock lenders. Such a provision means short sellers can be forced to
cover even if they are right about the stock’s long-run value.
Also because the standard stock lending agreement provides for the
stock to be returned on demand, a short seller is always concerned not
only with whether he can borrow the stock, but with whether he can
keep it borrowed (normally if the lender wants the stock certificate
returned the short seller can borrow it from another lender, but this is
not guaranteed). Short squeezes have occurred. Many other potential
short sellers are deterred from making short sales in thinly traded stock
because of a justified fear that the stock will be called away from them
before the position has proved profitable. Because index funds are not
active traders, borrowers can borrow stock from them with less worry
about having the certificates recalled because the original owner wishes
to sell the stock. This makes them preferred lenders.
The research of D’Avolio shows that this risk of recall is real, but per-

profits from the short position. When the short was part of a hedge, the
short seller loses his hedge for this time period.
In the United States there is an uptick rule in which short sales on
exchanges can only be made on an uptick. The regulatory goal seems to
prevent short selling from driving prices down. If this goal was achieved, it
could be argued that it made it harder for market prices to reflect all opin-
ions, including the negative ones. However, this is probably not a major
problem over the long run. Even what looks like a steady decline is usually
interrupted by upticks on which short sales could be made. To the extent
this is done, short sales may interrupt attempts at price recoveries and
result in lower prices. Still, the need to sell on an uptick probably means
that short sellers get worse executions in setting up their positions and this
lower their returns. This is one more obstacle to short sales.
Regardless of how long the positions are open, United States income
tax law treats profits from short sales as short-term capital gains and taxes
them at higher rates than long-term gains. This lowers the profits for tax-
able investors and is one more obstacle to taking long-term short positions.
Legal obstacles should not be forgotten. In many countries short
sales are prohibited. In Chapter 13, Bris, Goetzmann, and Zhu provide
a table showing which countries permit short selling and some details.
As of December 2001 the countries prohibiting short selling included
Colombia, Greece, Indonesia, Jordan, Pakistan, Peru, Singapore, the
Slovak Republic, South Korea, Taiwan, Venezuela, and Zimbabwe. In
another group of countries short selling was prohibited for some period
during the 1990s. These included Hong Kong, Norway, Sweden, Malay-
sia, and Thailand. Then there was a group of countries where short sell-
ing was allowed but apparently rarely practiced, including Argentina,
5-Miller-Restrictions Page 85 Thursday, August 5, 2004 11:10 AM
86 THEORY AND EVIDENCE ON SHORT SELLING
Brazil, Chile, Finland, India, Israel, New Zealand, the Philippines,

Unfortunately, the otherwise excellent Elton and Gruber text
24
Lianfa Li and Belton M. Fleisher, “Heterogeneous Expectations and Stock Prices
in Segmented Markets: Applications to Chinese Firms,” working paper, Ohio State
University, 2002.
25
A. Almazan, K. C. Brown, M. Carlson, and D. A. Chapman, “Why Constrain
Your Mutual Fund Manager?” working paper, University of Texas at Austin, 2000.
26
J. L. Koski and J. Pontiff, “How are Derivatives Used: Evidence from the Mutual
Funds Industry,” Journal of Finance (1999), pp. 791–816.
27
Actually, there is one case in which this portfolio may be a useful conceptual de-
vice. Imagine a large institutional investor that in the absence of beliefs would hold
an index portfolio with all the stocks of interest in it. He could overlay on this port-
folio a zero investment arbitrage portfolio where there were negative weights on
many securities. The proceeds from selling the securities that were labeled short in
the “arbitrage” portfolio could then be used to increase the long positions in other
securities. If not carried too far, there would be no actual short positions and the
earnings of the new portfolio would be the sum of the index earnings plus the arbi-
trage portfolio earnings.
Given that many large institutions seem to be closet indexers, the outcomes of
studies using the arbitrage portfolio approach could actually be useful to them.
5-Miller-Restrictions Page 86 Thursday, August 5, 2004 11:10 AM
Restrictions on Short Selling and Exploitable Opportunities for Investors 87
illustrates Markowitz optimization with a exercise in which the portfolio
takes long and short positions totaling many millions with only a small
initial investment.
28
This violates the Federal Reserve margin rules.

tematic risk (as in the textbook arbitrage example), the investor may
find he has more cash than desired.
However, the rate of return on cash is different from the rate on
long-term bonds. It is usually presumed that the bond rate will be higher
(in a rational expectations model with no risk it will not be). Presum-
ably, most long-term investors would prefer bonds to cash for the risk-
free part of their portfolio, if any. This may not make a big difference
28
See Edwin J. Elton and Martin Gruber, Modern Portfolio Theory and Investment
Analysis (New York: John Wiley & Sons, 1995).
5-Miller-Restrictions Page 87 Thursday, August 5, 2004 11:10 AM
88 THEORY AND EVIDENCE ON SHORT SELLING
since Treasury securities can be used as collateral (with an explicit fee
paid for borrowing the stock to sell short). However, there remains a
high possibility that the investor is still forced to hold more low risk
assets than he would prefer.
Especially, for the investor who would like to hold matched long
and short positions that essentially eliminate market risk, this need to
hold collateral does reduce the attractiveness of long–short portfolios.
Suppose the investor has discovered a strategy that earns 3% over the
risk-free or the bond rate, and has diversified away all nonmarket risk.
With the collateral requirements, his earnings are now 3% above the
risk-free rate (with the zero-coupon bond rate taken to be the risk-free
rate for investors whose horizon equals the maturity of the bonds).
Is this attractive? If the investor would otherwise hold bonds or
cash, it is. In asserting it is, I have disregarded the residual risk which is
always in long-short portfolios. However, for investors who believe the
equity risk premium is positive (and the evidence is that over the long-
term stocks have outperformed bonds by a big margin), 3% above the
bond rate would still be unattractive because they would do better with

today would be sold short. If the stock is dividend paying, the short sell-
ers must pay the dividends. A profit is not earned on a stock that went
down by less than the dividends paid. Thus, a short-selling candidate is
one whose expected total return (capital gains plus dividends) is nega-
tive for the investor who does not receive interest on the collateral.
While it might be thought that prices normally drop by the amount
of the dividend when a stock goes ex-dividend, this is not quite true.
The reason is that taxable investors prefer capital gains (less so than it
used to be before the reduction in the tax rates on dividends) and prefer
to delay buying till after the dividend, and to do selling just before. The
result is that the need to pay dividends is an additional drag on the prof-
its from short selling a dividend paying stock.
Another obstacle to short selling in the United States is that it must
be made in a margin account, and short sales are counted against the Fed-
eral Reserve Rule margin limits (except for broker dealers, or those large
investors who avoid this restriction by booking transactions overseas).
Investors with a given amount of capital can be expected to rank their
opportunities in the order of return. After ranking, investors will find
that they can only accept investments whose estimated excess return
annualized is much higher than x%, where x is perhaps 5% (just for illus-
trations). This would mean accepting for long positions stocks that will
yield more than 5% over an index (or over the prediction of the capital
asset pricing model or other model specifying minimum risk-adjusted
returns). For short positions this would mean stocks whose total return is
less than minus 5% (i.e., a nondividend paying stock whose price declines
by over 5% per year). Shown in Exhibit 5.5 the upper limit is then much
higher, and thus is higher the further the position is from planned liquida-
tion. In practice, many of the good analysts and hedge funds managers
will generate more profitable ideas than they can exploit with the funds
available to them. Thus, this constraint will be binding.

positions), and to mutual funds that take both long and short positions.
EXHIBIT 5.5
Price Limits for Stocks on Special
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Restrictions on Short Selling and Exploitable Opportunities for Investors 91
While a single short sale is risky, the addition of a short position to the
typical institutional portfolio reduces total risks rather than raising it.
One suspects adding short selling (or managing funds that permit short
selling) to the services offered by an investment management firm can
provide a nice incremental return on its staff and analytical resources.
Thus, on close analysis the standard efficient market fails because of
the restrictions on short selling make it likely that divergence of opinion
will result in some stocks being overvalued, and overvalued in such a
way that they can be identified from publicly available information.
If short selling does not eliminate identifiable overpricings, the situ-
ation is one of “bounded efficient markets.” Let us return to the impli-
cations for practitioners of there being overvalued securities that can be
identified by using publicly available information.
THE BOUNDED EFFICIENT MARKETS HYPOTHESIS
The above example critiques the efficient market hypothesis by showing
that trading by informed investors cannot prevent certain stocks from
being overpriced, causing the upper limit to stock prices to be above the
lower limit.
Exhibits 5.3 and 5.4 shows the upper and lower limits grow steadily
further apart as time increases. This is the usual effect of compound
interest. The two curves differ by the present value of the proceeds of a
short sale compounded at the difference between the competitive market
rate and the rate earned on the proceeds of short sales (often zero). The
longer the period in which these have to compound, the greater the price
difference that can arise without providing profitable opportunities for

the upper and the lower limits are the same, the two models are identical.
The Evidence Regarding Bounded Efficiency
There have been numerous tests for abnormal profits available from
information relevant to long periods of time. Evidence is accumulating
that markets may not be fully efficient against some such long-term
information.
30
The now well-known small-firm anomaly is an example since it may
be years before the error (if it is one) of avoiding small firms shows up in
investment returns.
31
The evidence that returns on small capitalization
stocks have been abnormally high and those on large stocks abnormally
low is consistent with there being no stocks identifiable from publicly
available information that can be profitably sold short.
Suppose someone realized that large firms promised subnormal returns,
and hence concluded that they were overpriced (as they may be). If he
responded by selling short a diversified portfolio of large capitalization
stocks following a buy-and-hold strategy, he would have lost a fortune. For
instance the Lustig-Leinbach study suggests a small firm effect from 1931–
1979.
32
Since the smallest quintile of stocks are outside of the S&P 500
29
Edward M. Miller, “Bounded Efficient Markets: A New Wrinkle to the EMH,”
Journal of Portfolio Management (Summer 1987), pp. 4–13.
30
For early evidence see Donald B. Keim, “The CAPM and Equity Return Regular-
ities,” Financial Analysts Journal (May/June 1986), pp. 43–48; or Bruce J. Jacobs
and Kenneth N. Levy, “Disentangling Equity Return Regularities: New Insights and

be predicted using market indices, a measure of capitalization, and a
measure that identifies value stocks (they prefer book to value, but price
earning ratios and cash flow to price also work).
35
While they have cho-
sen to interpret their results as being explained by risk considerations,
most observers interpret this as evidence that certain types of stocks
have tended to outperform the market. Because of the strong uptrend in
the market, it appears that one who thought growth stocks or large
stocks were overvalued and shorted them would have lost money. Simi-
lar comments could be made for the use of momentum variables, and
for many other variables which have been shown to have some long-
term predictive power.
36
33
Avner Arbel, Steven Carvell, and Paul Strebel, “Giraffes, Institutions and Neglect-
ed Firms,” Financial Analysts Journal (May/June 1983), pp. 57–63.
34
See S. Basu, “Investment Performance of Common Stocks in Relation to Their
Price-Earnings Ratios: A Test of the Efficient Markets Hypothesis,” Journal of Fi-
nance (June 1977), pp. 663–682; or Jeffrey Jaffre, Donald B. Keim, and Randolph
Westerfield, “Earnings Yields, Market Values, and Stock Returns,” Journal of Fi-
nance (March 1989), pp. 135–148.
35
Eugene F. Fama and Kenneth R. French, “The Cross-Section of Expected Stock
Returns,” Journal of Finance (1992), pp. 427–465; Eugene F. Fama and Kenneth R.
French, “Common Risk Factors in Returns on Stocks and Bonds,” Journal of Finan-
cial Economics (1993) pp. 3–56; and Eugene F. Fama and Kenneth R. French, “Val-
ue Versus Growth: The International Evidence,” Journal of Finance (December
1998), pp. 1975–1999.

the resulting buying and selling by the informed investors, keeps the
market bounded efficient.
Suppose the return on unmanaged portfolios is about 10% per year.
Suppose analysis that reduces the number of avoidable mistakes is an
extra 2% per year, making an achievable goal 12% per year. If these fig-
ures are of the right order of magnitude, they explain why we find ana-
lysts available for hire. The common question of one purporting to be
an expert analyst is “If you’re so smart, how come you are not rich?” In
a bounded efficient market where there are no grossly undervalued secu-
rities, even the best analysts do only a little better than random selec-
tion. Thus, they cannot become rich just by investing and managing
their own money (although they may insure a comfortable retirement).
Thus, if they are to enjoy a high standard of living they must sell their
services.
The bounded efficient markets model also explains why analysts’
services are bought. For even a 100 million dollar pension fund, an
extra 2% is an extra 2 million dollars, and this will justify hiring quite a
37
Edward M. Miller, “A Problem in Textbook Arbitrage Pricing Theory Examples,”
Financial Management (Summer 1989), pp. 9–10.
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