Restrictions on Short Selling and Exploitable Opportunities for Investors 69
Notice for the uninformed investors to set the price, in this case there
must be a very large number of uninformed investors. If the purchasing
power of the informed investors is greater than the market value of the
stock, the informed investors will set the price. In the above example of a
company with 100 million shares, if each informed investor purchases a
round lot (100 shares), the uninformed investors can only set the price if
there are less than a million informed investors. With the average being
1,000 shares (allowing for institutions), 100,000 investors are needed.
10
Notice that the more shares the average informed investors are will-
ing to purchase on average, the smaller the number of informed investors
that are needed to eliminate the underpricing. If the informed investors
will purchase an average of 1,000 shares, it takes only 100,000 to elimi-
nate the underpricing. Of course, the more extreme the underpricing, the
greater the potential returns. The greater the potential returns, the
greater the proportion of his wealth an investor will commit to an invest-
ment opportunity. Increasing the proportion of wealth committed to an
opportunity reduces the number of investors who can recognize an
undervaluation before it is eliminated. In the extreme, one investor with
sufficient resources could act on an idea (by taking over the company),
and eliminate the underinvestment. Thus, it is very unlikely there will be
grossly undervalued stocks that can be easily recognized.
As discussed below, this suggests a strategy of trying to win, not by
searching for grossly undervalued stocks, but by trying to identify and
avoid the overpriced ones. The case for this strategy is made stronger
when it is realized that while good information is readily disseminated,
there are obstacles to the dissemination of negative information.
Informational Considerations
In considering the likelihood of a hundred thousand people being
unaware of a factor that should raise the price of a stock (which

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.
The brokerage firms that employ analysts are also investment bank-
ing firms that bring out new issues. Publicizing bad news about a firm
does not help attract investment banking business from that firm.
Other investors (once they have accumulated a position) have an
incentive to publicize the case for making an investment. If others fol-
low them, the price may be bid up, making their own positions more
profitable. The quicker any underpricing is eliminated by others learn-
ing of the investment’s merits, the quicker profits can be taken (i.e., the
higher the annualized rate of return from the investment) and the funds
invested elsewhere. Also, it is pleasant at social gatherings to demon-
strate your brilliance by talking about why the stock you just bought is
11
Mark Davis, “Local Stocks: Analyst’s Optimistic Rating Pushes Up DST Stock,” The
Kansas City Star Web site (September 30, 2003), posted at />mld/kansascity/business/6891701.htm.
5-Miller-Restrictions Page 70 Thursday, August 5, 2004 11:10 AM

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
Terrance Odean, “Are Investors Reluctant to realize Their Losses?” Journal of Fi-
nance (October 1998), p. 1786.
5-Miller-Restrictions Page 71 Thursday, August 5, 2004 11:10 AM
72 THEORY AND EVIDENCE ON SHORT SELLING
tions which cause naive investors to overestimate the value of the company
do more harm than those which cause naive investors to underestimate a
stock’s value. This analysis of investing as a loser’s game provides an argu-
ment for conservative accounting.
14
Probably the most important number for investors that comes out of
the accounting process is earnings per share. This argument suggests that
conventions that often overstate earnings should be avoided even if alter-
native conventions understate earnings. Overstated earnings often lead
to overpriced stocks. Even if many analysts understand the true situa-
tion, there are likely to be enough who are misled for the stock to be

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
uses. Since the proceeds from the bond sales will be invested at a profit,
the earnings per share should go up. If the bond holders get a valuable
conversion option from the convertible feature, should not that be
reflected in the accounts?
A little background may be useful. At one time the earnings per share
for stocks were based just on the number of shares outstanding. This was
misleading because there would be more shares outstanding if the con-
vertible securities were converted. Firms could get their earning per share
up by selling convertible securities and using the proceeds to purchase
profit-earning assets (or using convertible securities to buy other compa-
nies). The interest charges were low because of the conversion feature.
However, until converted there was no dilution on the books. Investors
tended not to convert till required because of the lower risk of bonds than
equity, and the fact that the interest rate usually exceeded the dividend
rate (which was often near zero). The ability of outstanding convertible

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
desirability of including them as an expense. However, there is consider-
able dispute about how to value them and agreement that any formula will
be frequently misleading. For instance, Hewlett-Packard claimed that its
profits would have been cut 64% had it treated stock options paid to
employees and executives as a compensation expense, while Cisco Systems
said the proposed rule would have reduced 2002 earnings 80%.
17
There will be some investors who fail to recognize that the profitability
of firms making heavy use of options for compensation is overstated. These
investors will be willing to pay more for the stocks in question. They are
likely to be overrepresented among the optimistic investors who set the
price. Now suppose a conservative formula was used that often overstated
the value of the compensation. Many informed investors would recognize
the understatement of income. These more optimistic investors would be
the price-setting investors. Thus, this argument suggests that, if the goal is

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-
tors that the price will never fall below the line BC. This is because if it
did, the informed investors would place buy orders for the stock and bid
it back up to the line BC. If all investors were well informed, it would be
obvious that the prices at all times would be on the line. But as pointed
out earlier, there are likely to be quite a few badly informed investors. A
harder problem is whether the price could be held above the line by
uninformed investors.
The textbook answer to the problem of uninformed investors possi-
bly bidding the price up is similar to why the price could not be below
the line BC. Just as informed investors would buy if it was below the
line, informed investors would sell if it was above. This selling would
force the price back to the line.
However, the argument has a flaw. The informed investors may not
even own the stock they predicted to sell. If there are no informed inves-
tors who own the stock, how could selling by informed investors force

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
same expectations (homogeneous expectations). If all investors agreed
that a fair price for the stock lay along the curve BC, they would regard
any price above the line as a signal to sell the stock, and their selling
would force the price back to the line. Thus, with homogeneous expec-
tations (which textbooks tend to assume), efficient market pricing is
insured regardless of the institutional arrangements for short selling.
Pricing with Uninformed Investors
The argument presented above needs not hold if there are some unin-
formed investors. Suppose many investors believe the liquidating divi-
dend will be E. Their current willingness to pay will be D (i.e., the
present value of E). If there are enough such investors to absorb the
entire supply, the market price will be D. As the price rises above B, the
informed sell to the less informed. The informed investors drop out of
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78 THEORY AND EVIDENCE ON SHORT SELLING

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.
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Restrictions on Short Selling and Exploitable Opportunities for Investors 79
effect causing the proceeds to earn less than the market rate. Much of the
lending apparently comes from index funds that maintain a large inven-
tory of most securities and are more than happy to get some incremental
revenue from lending securities. Securities that are not held by index
funds, or for which there is a heavy demand for shorting, will be harder
to borrow, and the interest an institution receives will be less. In some
cases, it may be necessary to pay a per day fee to borrow a scarce stock.
D’Avolio got data from one of the largest lenders of securities in the
world for the period from April 2000 to September 2001.
19
The bor-
rowers of the stock were usually brokerage firms borrowing either for
themselves or for institutional short sellers (hedge funds, short selling
funds, long-short funds). The collateral for borrowing is cash 98% of

5-Miller-Restrictions Page 79 Thursday, August 5, 2004 11:10 AM
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
short seller does not receive full use of the proceeds of his short sale.
Instead a short seller deposits the proceeds as a security deposit with the
lender of the shares, where he either receives no interest (individuals) or
less than market interest (institutions). When the short seller does receive
EXHIBIT 5.4 Price Limits when Short Sellers Receive Interest on the Proceeds
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Restrictions on Short Selling and Exploitable Opportunities for Investors 81
interest on the proceeds, it is possible to lose money on the short sale
proper and still be financially ahead. The earnings from investing the pro-
ceeds can offset a loss on the stock as long as the rate of return on the
stock is below the rate earned on the proceeds. In these circumstances, it
is possible to violate the “buy low, sell high,” rule and still make money.
For instance, suppose a nondividend paying stock is sold short at $100
and bought back at $99 two years later. The short position has lost
money. However, if the $100 received for the stock could be invested at

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
5-Miller-Restrictions Page 81 Thursday, August 5, 2004 11:10 AM
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
proceeds (or get even worse terms) should be very careful about short
selling. It is plausible that competition between the hedge funds and
other institutional investors has reduced the rate of return on short sell-
ing candidates to a negative number, making short sales profitable only
for those who can earn interest on the proceeds of the sale.
On the long side, institutions have no such advantage. Individuals
and institutions earn the same return from a long position. In fact, indi-
viduals trading in smaller amounts may even be able to avoid the price
impact that many institutions experience when they trade in large quan-
tities. However, because some institutions are willing to engage in short
selling, those who can borrow stocks on favorable terms may find the
opportunities desirable. Since much of the cost of the required expertise
will be required to take long positions, the marginal cost of the research
required for short selling may be low. Someone who is already following
an industry may come across short candidates as a byproduct. For

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
short now for $101, and bought back in 2010 for $100 would be laugh-
able. Why wouldn’t he take that deal since it would be extra profit? One
reason was given above. It would tie up part of his margin limit, pre-
venting him from exploiting what could be much better opportunities to
sell short other stocks or to buy stocks on margin.
Another reason is that one must comply with maintenance margin
rules. A stock that is slightly overpriced today could be much more over-
priced next year. On the way to $100, the stock now priced at $101 could
go to $200 or $300. This would cause margin calls that could force the
short position to be closed out at a very large loss. During the Internet
boom, many investors correctly concluded certain stocks were grossly
overvalued. They also correctly concluded they would eventually return to
much more reasonable levels. Surely, making a short sale now with the
intention of buying back the stock later should have been profitable. What
actually happened was that the overpriced stocks became more overpriced

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-
haps not as serious as some feared during the time period he studied.
23
During the 18 months of his study, about 105 of stocks would have been
subject to a recall. In the few cases where buyers were forced to cover, the
21
Manuel P. Asensio, Sold Short: Uncovering Deception in the Markets (New York:
John Wiley & Sons, 2001).
22
Andrei Shleifer and Robert W. Vishny, “The Limits of Arbitrage,” Journal of Fi-
nance (March 1997), pp. 35–55.
23
D’Avolio, “The Market for Borrowing Stock.”
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Restrictions on Short Selling and Exploitable Opportunities for Investors 85
average returns were apparently negative on the day of the forced cover-

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,
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86 THEORY AND EVIDENCE ON SHORT SELLING
Brazil, Chile, Finland, India, Israel, New Zealand, the Philippines,
Poland, Spain, and Turkey. In China the short sales restrictions are
binding for the A shares (domestic), but not for the B shares (for for-
eigners).
24
While the countries without short selling tend to be the
smaller emerging market ones, it is a rather long list and, in the aggre-
gate, economically important.
In the United States there are obstacles for most institutions. Since
short selling is traditionally considered speculative and prudent men do
not speculate with other people’s money, endowments, trust funds, and
certain others appear very reluctant to make short sales. Almazan et al.
report that 70% of investment managers are precluded by charter and
strategy restrictions from short selling.
25
Fewer than 10% of those eligible

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.
Of course, if I could persuade you to lend me some stocks on my
promise to return them in a few years, I could sell the stocks and invest
in others. If my security selection was good, I would earn enough to buy
the stocks I needed to repay you and leave a profit for me.
Alas, in practice it is very hard to get friends to lend you a few dollars
for a short term need. It is unlikely a friend would lend you stocks worth
thousands or millions merely upon your promise to repay them. In prac-
tice, lenders of securities require collateral so that they are not taking an
appreciable risk. This collateral is at least the market value of the securi-
ties (and usually 102% of this value in the United States and 105% for
international securities). Since the lender is holding the collateral, it is not
available for taking long positions. In practice this collateral is virtually
always cash, although Treasury bonds are sometimes used. The theoreti-
cal case of using the long securities as collateral (probably with an excess
deposit for safety to the lender) is apparently not observed, although it is

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
a pure long portfolio. Those investment managers who have expertise in
equities are normally hired by investors who want to earn equity level
returns. For these investors, short positions with a need to post collat-
eral may reduce returns (even risk-adjusted returns), even though the
managers can identify stocks that will underperform on a risk-adjusted
basis. In these circumstances, there is no reason to believe short selling
will always be able to eliminate overpricing that is identifiable on the
basis of publicly available information.
There is one possible class of investors for whom the need to post
collateral will not be a major problem. These are broker dealers who
hold a large inventory of customer’s securities in margin accounts. The
standard margin agreements permit these to be lent out (and contain no
provision for crediting the owners with any profits earned). If these are
used for making short sales, the broker brings in cash which is available
for other purposes. Because such brokers normally are heavily indebted

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.
There are probably many individual investors who have a very good
knowledge of a narrow set of companies (probably because they are in
the relevant industry or in one that deals with them). As individuals,
they are likely to be capital limited (with risk consideration limiting the
fraction of their wealth they are willing to invest in their ideas) and
rather frequently a good long idea may displace a good short idea.
One other restriction on short selling should be noted. Insiders are
forbidden to sell short (at least not without refunding any profits to the
company). This probably has little effect on most stockholders who are
classified as insiders because of the size of their holdings. They can just
5-Miller-Restrictions Page 89 Thursday, August 5, 2004 11:10 AM
90 THEORY AND EVIDENCE ON SHORT SELLING
reduce their long positions. However, there probably are many officers
and directors who are prevented from taking short positions by this pro-
hibition. Because these individuals must keep up to date on public infor-

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
trading by informed investors (unless they already have positions).
Many have tried to extend, without examination, a belief that the
“market imperfection” of commissions and other transactions costs did
not prevent markets from being “reasonably” efficient to a belief that
problems with short selling (dismissed as a friction) cannot prevent mar-
kets from being “reasonably” efficient. Unfortunately, no matter how
broadly “reasonably” is defined, the power of compound interest is such
that over a long enough period of time, overly optimistic investors can
cause prices to deviate by more than a specified amount from the effi-
cient market level.
Often, the assumption of prompt and full use of proceeds of short
sales is not made explicitly in efficient market arguments, but it is consid-
ered an implication of the perfect market assumption. This is unfortunate
because such a key and incorrect assumption should be explicitly made.
5-Miller-Restrictions Page 91 Thursday, August 5, 2004 11:10 AM

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
Investment Opportunities,” Financial Analysts Journal (May/June 1988), pp. 18–44
for a summary and references.
31
This was originally publicized in Donald B. Keim, “Size Related Anomalies and
Stock Return Seasonality: Further Empirical Evidence,” Journal of Financial Eco-
nomics (June 1983), pp. 13–32.
32
Ivan L. Lustig and Philip A. Leinbach, “The Small Firm Effect,” Financial Analysts
Journal (May/June 1983), pp. 46–49.
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Restrictions on Short Selling and Exploitable Opportunities for Investors 93
universe, selling the S&P 500 short in 1931 would be the strategy for some-
one thinking large capitalization stocks were overvalued.
Of course, this would have been a money losing strategy. The actual
return from the beginning of 1931 to the end of 1979 for the S&P 500

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.
36
Narasimhan Jegadeesh and Sheridan Titman, “Returns to Buying Winners and
Selling Losers: Implications for Stock Market Efficiency,” Journal of Finance (March
1993), pp. 65–91.
5-Miller-Restrictions Page 93 Thursday, August 5, 2004 11:10 AM