ABSTRACT
This paper will identify two sources of inefficiency in the equity markets. After tackling the problems with the Efficient Market Hypothesis, a new theory, the Ration Belief Equilibrium, will be presented. The new broadly encompassing theory allows markets to be reconceptualized so that reasons for mispricing may be perceived. We find that market prices are generally wrong because of beliefs and the correlation of investor’s behavior. A simple regression will implicate investor sentiment and Game Theory will show why investors want to correlate their behavior. There are a number of implications that can be derived from these findings such as the opportunity for active managers to exploit the markets. A study of investment managers shows that there is a common trend to beating the market and their long term results are not attributable to luck.
PREFACE
This paper was inspired by a phone call from a friend with a request for me to calculate the t-statistic for the investment performance of W.P. Stewart, Asset Management. The idea was that we could use statistics to show that the probability of their out performance of the S&P 500, by so much and for so long, was low enough to conclude that it was not attributable to luck. I did the calculations and found that there was less than a 5% chance their exceptional performance could be luck. W.P. Stewart beat the market and I wanted to understand how it was done. Academic finance teaches that in the long run everyone should earn market returns minus fees and expenses. There are people in the field like Stewart, Buffett, Lynch and Miller that consistently outperform. I proposed that the only way anyone can consistently do this is to make a good valuation of a company and take advantage of market inefficiencies. Immediately I had a paper.
In writing this paper I do not claim to be an expert on investing money. In fact I have only had a combined year of internships in the investment field, a year of stock trading on my Ameritrade account and a number of undergraduate classes in economics and finance. The purpose of this paper is to satisfy my need to understand. I played my first investment challenge eleven years ago, in the fifth grade. I did not do very well and I wanted to know why. I followed business news, unsuccessfully trying to make sense of it all. I will be working in finance next year and in writing this paper I have been able to learn of my own interests and understand the field of my potential career.
INTRODUCTION
There has been a heated debate over active versus passive wealth management since the development and subsequent general acceptance of the Efficient Market Hypothesis (EMH). The debate is heated because of the hypothesis’s implications. It was taken as proof that no investor can do better than the long run market averages. Therefore people should not pay high fees for professionals investment managers, everyone should just buy index funds. This idea obviously did not settle well with Wall Street professionals because people can and do beat the market.
This paper will begin by presenting the assumptions and implications of the EMH. Following will be the arguments against the hypothesis. It becomes obvious that the theory needs to be generalized upon. By dropping many of the weak assumptions for the EMH, a Stanford professor, Mordecai Kurz, was able to build the Rational Belief Equilibrium (RBE) model of the markets. The Rational Belief Equilibrium says that the market is always in equilibrium of the beliefs of market participants. There will be highly a simplified presentation of this model and then the paper will move to the main point; why markets generally misprice assets.
The psychological factor of investors has been investigated by behavioral finance and now formally modeled by Kurz. Allowing for beliefs will help explain the reason behind market bubbles and subsequent collapses. The correlation of behavior is a well documented phenomenon and will be presented as the second reason for market inefficiency. The herd mentality happens with humans and animals and later in the paper it will be explained in terms of investing. The Theory of Rational Beliefs helps create a better understanding of the equity markets that only previously existed as wisdom of experienced investors. The RBE is of particular interest to investors because the two presented sources of inefficiency will open opportunities for the market to be exploited.
This paper specifically avoids talking about Modern Portfolio Theory developed by Harry Markowitz in 1950, because the focus has become a better understanding of the way markets work instead of optimal investment management. From the Theory of RBE there are many new ways to understand optimal portfolio management that differ from Modern Portfolio Theory, but that is the topic of another paper all together.
The fact is that most professional managers do not beat the market. This paper is not only arguing that it can be done but also in a very broad sense this paper calls for the investment prescription for success. Make a good evaluation of a company and wait to take advantage of market inefficiencies.
SECTION I. EXISTING THEORY
- EFFICIENT MARKET HYPOTHESIS
The Efficient Market Hypothesis was cultivated from Eugene Fama’s doctorate dissertation in 1962. Fama proposed that any market of informed, intelligent participants actively trading assets will accurately reflect all known information. The term Efficient Market Hypothesis was coined by Harry Roberts in 1967 where he proposed that the markets always reflect the assets intrinsic value. Financial markets are so efficient at processing new information that at any given instant the stock price accurately reflects the true value of a company. There are so many investors watching the stock market ready to act on new information that the price will immediately move. An undervalued stock will be instantly bought until the price equals its true value. Conversely, an overpriced stock is instantaneously sold off until supply equals demand at its proper value. Prices move almost instantly, therefore investors cannot benefit from research and analysis. This is the basic idea of the EMH and it comes in three forms.
The weak form of the EMH says that all past information is included in the value of the stock and so technical analysis of a stock is useless. The semi-strong form says that the market has already incorporated all public information into the stock price. Here fundamental analysis will not help anyone to beat the market. The strong form of the EMH says that the market has already reflected the all known information, that includes all insider information and so no one can truly profit from information.
In reality most people have come to believe in the semi-strong form of the Efficient Market Hypothesis. Burton Malkiel, in his popular book A Random Walk Down Wall Street, argues that it is a real leap of faith to believe that insider trading is not profitable. The strong form cannot be true because insider trading does happen. For people to risk insider trading the payoff has to be greater than the expected punishment. There is a risk of getting caught and penalty for being caught, multiplied together equals the expected punishment for insider trading. Even if the probability of being caught is low there must be some payoff to insider trading.
The EMH makes a number of key assumptions for it to work. The first is that perfect pricing exists. This does not require that every investor know the correct price only that the market does. Expectations are going to be different and if investor’s behavior is completely uncorrelated then the mean of all expectations will be correct. The second assumption is that all news travels instantaneously. Third, no one possesses monopolistic power. Fourth, no one analyst recommendation can influence large blocks of trading. Last, market participants are highly rational. Surprisingly only this last assumption is true.
The EMH appears to explain the daily fluctuations in the price of a stock. Malkiel refers to the unpredictable price movements as a random walk. These unexplainable price fluctuations are caused by investor speculation and the fruitless effort of active trading to squeeze extra returns from the market. Malkiel argues that this effort to benefit from new information is fruitless and only adds to the volatility of the market.
The implication of the EMH is that well paid investment professionals are useless and active investment management will not be able to give anyone better returns in the long run. This gave rise to the idea of passive investment management. Broad market indexes such as the S&P 500 or the Russell 2000 Index will track the market to ensure that everyone will receive market returns. Low fees and low taxes will encourage passive management. It is inexpensive to invest in a market index because it does not require research and the low turnover rate defers capital gains taxes.
There has been a lot of effort on the part of academia to show that fundamental and technical analysis does not work to produce higher returns. Past performance of financial experts in the market is one such proof. Fama looked at all of the returns professional money managers were earning for their clients and found that only 8% beat the market after taxes and fees. The other is the time series graphs of information releases and market response. It shows just how rapidly markets move prices in response to new information so that it is impossible for anyone to react quickly enough to be ahead of the market.
The Efficient Market Hypothesis has gained enormous support and as a result index funds, once unheard of, now make up a large part of the average portfolio. Some $30 trillion is now passively invested world wide now because of the general acceptance of the EMH.
“Believing ensures falsity” argues John Allen Paulos in his book A Mathematician Plays the Stock Market. The EMH is a paradox. When investors believe that there are still opportunities to exploit, there will be more watchful eyes ready to jump all over market inefficiencies resulting in awesomely efficient markets. But if everyone were to give up on the idea that the market could be beaten and invested in passive funds then there would be no one to take advantage of market inefficiencies, leaving the markets inefficient.
The goal of professional investors is to buy undervalued assets and sell over valued ones. If the markets always perfectly valued assets then no one could ever beat the market, but people can and do. We will see that the EMH is based on a number of weak assumptions and becomes too exclusive to always be correct.
- BREAK DOWN OF EFFICIENT MAKRET HYPOTHESIS
“Mathematicians have observed that the markets are frequently efficient and wrongfully concluded that they are always efficient.” -John Allen Paulos
Democratization of the equity markets with computers and free real-time market information increases market efficiency. This in turn decreases the effectiveness of fundamental analysis and increases the complexity of the markets argues Paulos. Complexity is falsely interpreted as randomness by mathematicians who find it difficult to model investor sentiment. Before introducing a new model that includes a psychological effect it is helpful to go through the assumptions of the EMH and point out the problems.
Perfect pricing is essential to the definition of efficiency, but this assumption can only hold if investor actions are completely uncorrelated. One argument against the EMH is that investor behavior is interdependent, every decision one investor makes is influenced by every other market participant. Large swings in the market are due to the correlation of investor behavior and so it is difficult to argue that investors are independent of each other. Investor correlation is one of the key assumptions that a large part of this paper will be focusing on as a source of market inefficiency.
Everything comes back to supply and demand. Supply and demand for a specific stock are determined by many factors such as earning news, beliefs about the future, the economic situation and sometimes just emotions. The price of a stock will reflect all of this information but emotions do not accurately reflect fundamentals. This psychological factor of investors demand for a stock makes it hard to believe stocks are always accurately priced.
The second assumption of the EMH is that all news travels instantaneously. The speed at which news travels has approached infinity as technology and insider trading laws improve. Now anyone with a computer can get real-time news, earnings reports and up-to-the-minute stock quotes. Most investors do not buy that this is always the case because as shown above insider trading is profitable. The leak of news is staggered, first to insiders and then the public. If that news were acted upon my insiders before the public then there would not be efficiency in the markets because news did not move instantaneously.
The third assumption says that no market participant can possess monopoly power. The situation would be that one person can control the market price. It might be safe to assume that no one has pure monopoly power over the market but we can see that some investors have a large control over the market price of a stock, especially one that is thinly traded. There is a distinct difference between a stock like Wal-Mart where the average daily volume is roughly 10,000,000 shares traded per day and a stock like Bluefly.com where the average volume is 100,000 shares traded per day. One person has a lot more influence on the market for Bluefly.com than they do for a stock like Wal-Mart. A real world example of market participants controlling the situation is when George Soros caused a currency collapse in the United Kingdom from his own speculation and exploitation of Parliament’s stable currency policy. While no one investor possesses monopoly power over the market, thinly traded stocks are an exception in that anyone with the resources can manipulate a market price.
The fourth assumption made is that no one recommendation can influence trading. Experience can tell anyone that this is not the case. Any large brokerage house that changes their recommendation on a stock will have an impact on the stock price that day. Just the other day UPS declined over 1.0% because UBS dropped their rating on the stock. One could argue that this announcement just reflects what everyone else is thinking but the financial gurus of today have enormous influence on the price of a stock. Investors generally listen to what Warren Buffet and George Soros have to say. Krispy Kreme has doubled since Warren Buffet said he liked the stock. One final example, on Thursday the 24th of March an analyst at Lehman Brothers by the name of Adler upgraded GAP, Great Atlantic Pacific Co and the stock jumped 20%. Examples such as these make hard to believe the EMH[1].
Looking back over past prices it becomes quite easy to show that the market inaccurately prices stocks. Any financial bubble or crash can be a good example of this. The EMH can only explain this all too common occurrence with the irrationality of investors. Here is an example of the market undervaluing a stock after the correction of October 1987 and then overvaluing the stock 10 years later during the Internet Bubble.
Between 1988 and 1998 the 30-year Treasury Bonds averaged 7.5% to 8% return and the equity risk premium for these years was on average 4% to 4.5%. Adding these together the annual return on a stock should be roughly 12%. Then subtract out the average dividend yield of 1.5% and you are left with the capital gains yield of 10.5%. Looking at the company Automatic Data Processing it is possible to determine what the price should have been in 1988 to get a 10.5% capital gains return between 1988 and 1998. In 1998 the market price was $66 and so it should have been $24.32 while actually it was trading at about $10.38.[2] This example assumes that the price in 1998 is correct. If we assume the 1988 price were correct then the 1998 price should only be $28.17. The only explanation is that the market price was not correct in either 1988 or 1998 since the actual appreciation was 20.32%.
The Efficient Market Hypothesis has lead investors down the wrong path. The EMH can be true but only in narrow instances. It is safe to assume that during the 10 year period above that the stock was accurately priced at some time. It is clear that a more general theory needs to be developed to account for and make sense of investor sentiment.
- THE THEORY BEHIND LONG RUN RETURNS
Market history shows that on average stock ownership will return 12% in the long run. This study was wrongfully taken as proof of the inability of investment managers to outperform and the justification for passive portfolio management. Truthfully these results had no meaning until Warren Buffett published his theory of business growth, which he discussed in his paper “How Inflation Swindles the Equity Investor.” Over the long run market returns should mimic the underlying growth of the businesses they represent, business growth should equal market returns. The fundamentals of business growth are the theory and the market returns are the proof.
Buffett’s theory of business growth says that the long run average of a company’s growth will be 12% above book value. Companies usually follow the ‘S’ Curve of growth: Slow growth in the beginning as the business learns, then growth gradually accelerates until there is a period of high growth when the business finds what makes it successful. Finally as the Law of Large Numbers takes effect growth slows again. Plotted out over the life of a business the growth look like an ‘S.’
It is not a coincident that in aggregate business grows at 12% and long run market returns fall near this number. The Fortune 500 companies grew, on average, 11.2% between 1955 and 1965, and then 11.8% from 1965 to 1975[3]. Benjamin Graham said “in the long run the market is a weighing machine.” Market returns should reflect the true change in value of the business. In the next section there is an explanation for why the short run market cannot properly reflect true business growth.
Over the past few decades this is exactly what we have seen. Business growth of the S&P 500 as measure of growth above book value has been just shy of 12%. Some companies grow faster and some slower but with the longer time is stretched the closer we see the numbers revert to the mean. The boom and bust cycle will bring deviations from the mean but and there is no reason to expect 12% to change.
SECTON II. NEW THEORY & SOURCES OF INEFFICIENCY
- RATIONAL BELIEF EQUILBRIUM
Irrational investors in the late nineties bought stocks at 100+ times earnings. It is true but actually there was nothing irrational about it; investors were just working under a wrong set of beliefs. The common belief was that high prices were justified because the economy had entered a new period of ultra growth. The more general theory of Rational Belief Equilibrium can logically explain why so many intelligent people acted so apparently irrational. The RBE is a new theory developed by Mordecai Kurz at Stanford University and most the interpretations found in this paper can be attributed to a brilliant mathematical economist, Horace W. Brock.
The Rational Belief Equilibrium model of the equity markets relaxes one of Robert Lucas’s fundamental assumptions under the REE. Lucas claims that everyone knows the exact probability of future events. This implies that the economy is predictable. The probability to future events are calculated using past data so that everyone knows the probability of next year’s economic situation: interest rates, exchange rates, inflation rates etc. Using these probabilities it then easy to calculate expected values and create a forecast. Looking at the past it is hard to believe that anyone can know the probability of future events. There could be a natural disaster or a war that will affect the economy. Long Term Capital Management learned this lesson in 1997 when their complex mathematical models did not take into account any probability of the real estate crash in Southeast Asia and the Russian debt default and currency crisis. LTCM could not have predicted these events based on previous data and the severity of their mistake almost brought down the world financial markets and would have if the United States government hadn’t bailed them out.
Investors need to have something to generate forecasts. The RBE differs in that it drops the assumption of probabilities and substitutes it for beliefs. Beliefs are based on past data but do not imply the mathematical correctness of probability. People can only create beliefs about the future because the future is unpredictable. Lucas believed that the economy is predictable in that using past data anyone can calculate an expected value for the future economic circumstances. The problem is that future events are unpredictable even though over time there are patterns. Kurz explains this cognitive duality by describing the economy as a stable, non-stationary system. Stable meaning that there are laws to the economy that are unchanging over a long period of time. Stable does not imply static, only that the mean appears to be fixed. A non-stationary economy implies that it is continuously changing and is not regular. In the RBE model there cannot be trends and therefore the structure of the economy is unpredictable.
The economy is a stable system because as far back as data has been recorded there seems to be rules such as the average price to earning ratio is roughly 13.5 and the capital to output ratio is 3:1. Stable in the sense that these number always revert to the mean and new data does not move the average. Non-stationary is that the economy will follow the mean but not remain stagnant. For example, no one could have predicted the massive inflation of the 1970’s due to OPEC raising oil prices based on previous data. But we know form Game Theory that cartels always break up and so inflation has to eventually return to some long run average. These long-run averages will not predict circumstances of the near future because the economy is continuously changing.[4] Even thought these fundamental numbers appear chaotic at times, over long periods they follow the average asymptotically.
The important difference between the two models is the way in which data is interpreted and used to create a forecast. Instead of expectations investors use their own beliefs about future economic environment. The RBE assumes that the same set of data is available to everyone but that there can be as many different beliefs as participants, none of which is necessarily correct. The interpretation of data is based on beliefs about the structural knowledge of the economy and therefore the market is always in equilibrium of the beliefs. The RBE allows for every player to act rationally under his own set of beliefs. Therefore the rationality of investors is one key assumption that always holds because, given the set of beliefs, any forecast no matter how ridiculous cannot be refuted.
There are four principal results that can be derived from this new theory. The markets usually misprice assets. Incorrect prices are due to the evaluation of information. Prices become increasingly volatile. And the theory of active asset management can be re-conceptualized. For the purpose of this paper it is only necessary to focus on the first three results. The fourth can be the topic of an altogether different paper.
The market price of an asset is incorrect. This first result is common knowledge for professional investors and difficult for academics to accept. The explanation using RBE combines three assumptions. First, markets are made up of rational investors all using the same data with different sets of beliefs. It is safe to assume that all market participants with meaningful amounts of capital are rational. This excludes the average person investing their own money because their small amount of money is insignificant in affecting market prices. Everyone has access to the same news but will not interpret it in the same way because they believe circumstances to be different. Second, beliefs are used to interpret data and create a forecast. As mentioned above, it is not probabilities that are used to interpret data, it is beliefs. There can only be one correct subset of beliefs and therefore only one correct interpretation and forecast. That infers the existence of many wrong sets of beliefs. Incorrect beliefs will always exist because forecasts are irrefutable when data is interpreted with its respective subset of beliefs. The steps are logical just not correct. Third, the market price of an asset reflects the average of all the participant’s forecasts after making a utility-maximizing number of trades.[5] The correct set of beliefs comes from a superior structural knowledge of our economy. The investor with an inferential advantage can generate a better probability forecast of the future irregular economic circumstances. The average of all sets of beliefs cannot lead to the correct price because there is something fundamentally different (the superior knowledge) about the correct set. Finding the average does not require superior knowledge. Infrequently, by chance, the average forecast can fall onto the correct price, but there is no reason for it to do so. This limited case is where EMH works and that is why we can conclude “in general” market prices are incorrect.
Incorrectly priced assets are caused by the evaluation of the information and not the efficiency with which new data is processed. New data is rapidly processed, as we assumed before, but most beliefs will be incorrect as a consequence of the complexity of creating a forecast for a stable, non-stationary economy. People tend to confuse short term trends with a fundamentally different economy. In the late 1990’s people believed we had entered the age of a fundamentally different economy where explosive growth was sustainable and therefore high P/E ratios were justified. This misunderstanding of expectations and beliefs is what causes apparent irrationality. This is how beliefs tend to bunch. It is conceivable that the market could reflect the correct price if investor’s behavior were uncorrelated. A large number of wrong beliefs scattered evenly around the correct one would cancel each other out. Arbitrage pricing theory suggests that smart investors do move to keep this balance of wrong beliefs. But we know that prices are wrong because investors do correlate their behavior. Actions are correlated due to the interdependence of participants within the system. No investor is statistically independent of the market because (as we will show later) investors want to correlate their behavior.
Stock prices are increasingly volatile due to ongoing process of readjusting forecasts.[6] News companies like Bloomberg and CNBC are continuously sending new information to every participant of this interdependent system. We call the markets interdependent because the behavior of each investor will affect every other participant. People watch the market to see how others will react to new information before making their own decisions. Sometimes investors do not know how to react to an announcement of something like a merger and so they wait to see how the “leaders” will react before going ahead with any action. Individuals will want to alter their beliefs as new data comes in, but each change will influence some revision of every other set of beliefs. Changing data and beliefs means the forecast constantly needs to be readjusted and possibly a new optimal portfolio will present itself. As investors trade to adjust their positions price volatility becomes amplified. We know that trading and volatility increase together. For example a house is an asset which is traded infrequently and we also notice the price is very stable. Also, over the counter stocks are traded much less frequently and with less volume than a stock listed on an exchange. We also notice the price of an OTC stock will move less than those traded on the NYSE.
The Efficient Market Hypothesis is good in a limited number of circumstances. The Rational Belief Equilibrium is a powerful theory because it is more inclusive. The important implication of the RBE is that markets are inefficient. This implication is the priority of this paper because its existence legitimizes active investment management. With the RBE we can identify two sources of inefficiency; investor sentiment and correlation of behavior.
- INVESTOR SENTIMENT
Investor sentiment is one reason why markets are seldom efficient. Beliefs can change as easily as mood and does not require any new information. Belief alterations cause price change as investor move into different positions. These non-information movements of price are evidence of investor sentiment because nothing about the company has fundamentally changed. There are stocks that are reported on sporadically but the stock price generally moves every day. There is no way to know if today’s price is accurate. What can be known is that if today’s is accurate then tomorrow’s new price cannot be accurate, since news changes so infrequently. Benjamin Graham said “in the short run the market is a voting machine.” This implies popularity over fundamental value is the determinant of a stock price. Before Behavioral Finance and the RBE theories of markets, investor sentiment was not included in the factors contributing to stock price. The effects of investor sentiment are not something that can be quantified only learned through experience.
Some examples of large non-information price movements include Black Monday. On October 19th, 1987 the market lost 22.6% in a day without any real information catalyst. In fact fifty of the largest one-day market movements since WWII were not causes by any major announcement.[7] They were caused by a sudden change in temperament. As an experiment to see if the price of a stock is grounded in the fundamentals I set up a regression to test the earnings multiple.
The price of a stock is determined by two components; earnings per share and the earnings multiple. A company’s EPS is a fundamental value that is reported every quarter. We know one thing to be true about this number, the higher the EPS the higher the stock price. The multiple is the component of the stock that accounts for everything else about the stock, from the future of the economy to risk. As theory suggests the earnings multiple, a.k.a. the price to earnings ratio, reflects the expected growth in earning of the company, the key word being expected. The higher the expected growth rate the higher the multiple is supposed to be, the higher the multiple the higher the stock price. At any given moment these two components can be multiplied together to receive the market stock price.
Wall Street analysts are very good at giving short-term earnings expectations for any given company. Each quarter the Street will post the average expected EPS and wait 3 months for the company to release their numbers. To test and see just how accurate analysts are the average percentage error of the forecast will be calculated. All of the following regressions will use the same 247 companies which reported their quarterly earnings and expected earnings per share during February 2005. The results show that the average forecasting error is 0.173%. To put this in perspective this means for a company with EPS of $1.00, on average, analysts will be $0.00173 off in their estimate. This number is not significantly different from zero. So it is safe to assume a quarter in advance, analyst’s estimates are good. And since analysts forecasts are published, everyone knows the short term growth rate of company’s earnings.
As a warning, the further into the future an estimate is made the less accurate it is going to be. Long term growth rates are difficult to determine and even worse analysts assign the appropriate P/E based on long term estimates. For example the consensus on Wall Street right now is that Google will be able to keep up their triple digit revenue growth for the next few years, thus Google is given an earnings multiple of close to 100. These long term forecasts are often wrong so we will just have to wait and see. One year ago this month, the brokerage houses released their one year price target for Cisco Systems. Oppenheimer gave Cisco a $26 price target, Citigroup gave it a $40 price target and First Fidelity Global was the only one to accurately price the stock at $18. Juniper, Royal Bank of Canada and Charles Schwab also way over shot their targets.[8]
Using a highly probable short term expected growth rate we should see a relatively stable earnings multiple and a predictable market price. Ideally a linear regression of earnings growth should let everyone know what the proper P/E ratio should be. At the very least there should be some correlation between the earnings growth and the earning multiple.
An investor should only willing to pay a certain price for a stock if that stocks earning multiple is justified by the reality of future earnings growth potential. Typically high growth stocks are given a high earnings multiple because investors know that earnings will catch up and they will be rewarded later. Lower growth stocks will be given a low multiple because investors are expecting growth to slow down. Using this common logic we should be able to find a correlation between the actual expected earnings growth rate and the earnings multiple that investors assign. If we cannot find any correlation then it is safe to assume investor sentiment plays a large factor in determining the price of a stock.
Now we have the expected growth rate and the actual growth rate of 247 companies. We need some kind of average P/E ratio for each of the companies to be the dependent variable. The 50-Day and 200-Day moving averages divided by the EPS will give us an average P/E ratio for the past 50 and 200 days, respectively. Logically we would not want the average for the entire year because the expected earnings growth numbers would not be available yet. Here are the results from four linear regressions using combinations of the 50 and 200 Day moving averages as the independent variable with the expected growth rate and the actual growth rate of EPS as the dependent variable. Here are the results. The numbers in the parenthesis are the t-statistics, observations is always 247.
| 1) |
| Y = 50-Day Average P/E Ratio |
| E(g) = Expected Growth Rate |
| Y = 72.122 + 4.825*E(g) + e |
| (8.21) (0.82) |
| Adjusted R Square = -0.001 |
| Standard Error = 127.426 |
| 3) |
| Y = 200 Day Average P/E Ratio |
| E(g) = Expected Growth Rate |
| Y = 69.653 + 2.814*E(g) + e |
| (8.13) (0.49) |
| Adjusted R Square = -0.003 |
| Standard Error = 124.40 |
| 2) |
| Y = 50 Day Average P/E Ratio |
| g = Actual Earning Growth Rate |
| Y = 70.354 + 6.665*g + e |
| (7.91) (1.22) |
| Adjusted R Square = 0.002 |
| Standard Error = 127.212 |
| 4) |
| Y = 200 Day Average P/E Ratio |
| g = Actual Earnings Growth Rate |
| Y = 68.355 + 4.280*g + e |
| (7.86) (0.80) |
| Adjusted R Square = -0.001 |
| Standard Error = 124.295 |
These results show that the earnings growth rate has no correlation to the earnings multiple. The low Adjusted R Square indicates that the earnings growth rates explains none of the difference in the earnings multiple. The low t-statistics show the actual rate of growth is not a significant factor in determining the multiple. This can only lead us back to the hypothesis, not conclusion, that the earnings multiple is not grounded to actual earnings growth rates.
The set of regressions does not prove that investor sentiment determines the price of a stock. What it does though is continues to show support for the RBE. One other reason that this regression cannot be conclusive is that the P/E ratio could be a fair valuation not just of the next period but of all future growth. There is not way to calculate this, anyone’s guess is good. But if all future earning potential is anyone’s guess then most likely it is not a quantifiable and determined by beliefs. Emotion is unquantifiable because it is a function of investor sentiment.
Investor sentiment is still part of our theory so back to the main point, that markets are inefficient. Beliefs are part of the function of valuation of a stock. Beliefs are not grounded in fundamentals and therefore cannot be efficient in terms of reflecting the true value of any company. Market price is not true price in terms of fundamentals, markets are inefficient. In market down times the stock will under perform the underlying business.[9] In fact many stock market crashes have had no relation to a recession in the economy. The economy and the stock market are independent by a factor of beliefs, and when the market and underlying business are not aligned we call this inefficient.
- CORRELATION OF BEHAVIOR
The Rational Expectations Equilibrium theory says perfect pricing can only exist if investor’s behavior is uncorrelated. The hypothesis allowed for investors to be irrational. As long as their beliefs were randomly irrational they would cancel each other out and the equilibrium price will end up at the correct price. Studies in Behavioral Finance have concluded that investor’s behavior is correlated. It can be shown that no investor is statistically independent of other investor’s actions. The reaction, whatever it will be, of each market participant will influence the behavior of everyone else. Kurz, through his RBE, has modeled this interdependent behavior and proven the correlation of investor’s behavior. The use of Game Theory can explain why investors want to correlate their actions.
Warren Buffet said that “investors are paying a high price for a cheery consensus.” Said in terms of economics and game theory what is going on is that traders (notice not investors) are buying the stock that they think every other investor is going to want to buy. Traders know that if they pick the stock that most investors are going to want to buy then they will make money off the large and rapid price movements.
Professional investing is a game of Tacit Coordination. Tacit means all players have a common interest, coordination means to win the game all players need to act together. In modeling this game it is possible to vastly simplify it down to a static normal form game. To set this up like any Game Theory game we need to first list the players; everyone trading stocks. The options are to buy and sell. The payoffs are 1 if everyone buys, 1 if everyone sells and zero if some choose buy and some sell. There is a catch this is a signaling game and there is no direct communication between investors. In normal form this is what the game looks like.
| P1/P2 | Buy | Sell | |
| Buy | 1,1 | 0,0 | |
| Sell | 0,0 | 1,1 |
The only correct answer is to do what everyone else is doing. This game can be thought of as going on for every investor for every stock traded on the market. Each investor tries to buy the same stocks that they expect everyone else to buy and sell the stocks that they expect everyone else to sell. This seems easy except that there is no direct communication.
One solution is using signals. For example when a better informed player takes action this is a signal to the less informed players. This general rule applies to all types of games with asymmetric information. Thomas Schelling suggests, in his book The Strategy of Conflict, that focal points are the clue to coordination. A focal point represents the convergence of expectations. A focal point forms as the answer that everyone expects everyone else will pick to be the answer, when any arbitrary answer will suffice.
Schelling gave many reasons for the development of focal points such as uniqueness, convention and unambiguousness. Schelling gives many examples of coordination games such as the coin game. In this game two players have to pick the side of a coin, heads or tails, to win. Schelling plays this game and finds that heads is the most common answer. There is no reason for heads over tails but it develops as a focal point because of convention. Another example is coordinating a time for two people to meet up without communication. Both players win if they can meet at the same time and both lose if they cannot. The most common time given is noon, probably because it is unique. These reasons do not apply directly to stocks. Traders need to know what stocks to buy and the development of focal points seems to be a clue.
These focal points develop in the stock market as media coverage increases. The stocks that are covered most frequently become focal points and send a signal for traders to coordinate their actions on. Of the world of 10,000 securities actively traded we know that there are some stocks that receive much more attention than other. The S&P 500 is one group of stocks that is watched more closely than the rest. But these are not the focal points. Focal points must be talked about reported on more than any other stock. Typically these stocks are sexy high growth stocks. Everyone gets excited about a few stocks and so they know that everyone else knows that everyone else is excited about the stocks.
Focal points can develop for the up and down side. Consistent good news and good analyst reports creates the expectation that everyone else is expecting everyone else to buy. Just the same as consistent bad news will create the expectation that everyone will expect everyone else to sell. It is true that bad news causes people to re-evaluate their expectations for a company but Behavioral Finance has proven that some of the selling off is due purely to other investor’s behavior i.e. the interdependence of investor’s actions. The result is self fulfilling. Since news is not always unambiguously good or bad the hypothesis is just that news coverage and chatter will cause increased volume of trading.
The experiment uses the same 247 stocks as before, this time setting up a regression with news coverage as the independent variable and volume as the dependent variable. New coverage measured in number of headlines in the past three weeks. Volume is just number of shares traded on Monday March 21st, 2005. Here are the results from the regression.
Y = Volume on 3/21/05
N = headlines in the previous 3 weeks
Y = 335180.3 + 88112.57*N + e
(1.13) (13.38)
Adjusted R Square = 0.420
Standard Error = 3970086.03
These results show that the number of headlines is a significant determinant of the trading volume. As the only independent variable it does not explain all of the variance in the volume for the day. Theory would suggest that stocks with larger market capitalization and more shares outstanding would have higher trading volume. But when the regression is done for both head lines and market capitalization as independent variables, market cap is an insignificant factor and the adjusted R square only increases by .01. Another factor could be average volume. If a stock finds favor of a few traders in the know then this could send a signal to other investors. This is an example of how asymmetric information could lead less informed player to follow the actions of the better informed players. Adding the average volume for the past 3 months as an independent variable, here are the results.
Y = Volume on 3/21/05
N = number of headlines in the previous 3 weeks
MC = market capitalization (billions of dollars)
AV = average volume for the past the months
Y = -127332.64 + 49083.87*N + 2702.11*MC + 0.53*AV + e
(-0.52) (6.24) (0.32) (10.94)
Adjusted R Square = 0.61
Standard Error = 3243358.75
This set of results show that average volume is a significant factor in the daily volume. The adjusted R square increased to show that the new factors help explain more of the variance in daily volume. The two possible signals in the coordination game are news excitement and average volume. These possible signals provide the existence of a solution to the tacit coordination game and explain why many investors have noticed that traders follow noise over news, so to speak. Noise in this case is news coverage not announcements about the fundamentals of a company.
Traders know that signaling will stimulate buying even if nothing fundamentally has changed with the company. Focal points are how every investor knows what everyone else is going to pick so they know what to pick. In the words of Keynes “what the average opinion expects the average opinion to be.” Intuitively investors know that if everyone else is going to buy there is an opportunity for capital gains. And conversely if everyone is going to sell a security that stock will have a capital loss. The stock will see some sharp movement up as volume increases.
News coverage seems to be a general signal to the market to trade one stock more than another. There are specific announcements that will signal investors to take specific action, buying or selling. When a company announces a stock repurchase this will send a signal to investors to buy. Finance theory suggests that a repurchase is a low return investment and should not increase the value of a firm. Markets see an increase in price after the announcement to repurchase shares because investors know it is an opportunity to make money; everyone expects everyone else will buy. Conversely, a seasoned equity offering sends the signal to investors to sell stock. Investors worry about equity dilution but finance theory tells us that the value of the firm should increase when the money from the issued equity is invested into the company. But again finance theory has no bearing on market reactions. The stock price will drop because every investor knows this announcement will create expectations of a sell off, and the outcome is inevitable. A stock split sends a signal to investors to buy. If the market price accurately reflected the value of a firm then a split should not do anything to the price of a stock. Two shares that are each worth half are equal to one.[10] But investors know that everyone is going to buy after this announcement and there is an opportunity to make money without a fundamental change.
The result, investor’s behavior becomes correlated. Here is an analogy given to me by Mr. Brock to illustrate the correlation of investor behavior. The business cycle is a boat and investors are cannon balls. As the boat rocks back and forth the cannon balls on the deck of the ship will move from one side to the other amplifying the movement of the ship up and down. The up and down movement of the ship is an analogy to the rocking of the stock market and this behavior can explain the existence of bubble and crashes.
Back to what Warren Buffet says about investors paying a high price for a cheery consensus. These focal points are receiving a cheery consensus from investors because each investor is reassured by other investors also buying the stock, raising prices and therefore overvaluing the stock. The movement is greater than the fundamental business cycle that we would expect to cause swings in the stock market.
As we know from our Rational Belief Equilibrium volatility equals inefficiency. Inefficiency creates opportunity, as long as investors have a good evaluation. This will be the key to explaining short run gains in the market. Typical investor reactions to focal points in the market can be exploited.
- EXPLOITING INEFFICIENCIES
The goal of ever investor is to maximize returns from investing. No matter who or what an investor compares his or her returns to, the goal is to get the highest possible. The way investors go about doing this is much more difficult than it sounds but buying a good stock at a good price is the simplest way of putting it. This means that investors should do their research to make a proper valuation and take advantage of market inefficiencies. This paper will not discuss making a valuation of a company; first because I have never done a formal evaluation and second because there are many ways to do it.
Finding a good company is the easy part. Investors will tend to agree on the good companies because they will find good management, sound financial and a superior position in a growth industry. The non-professionals will find it harder to identify a good company. Speculative companies have a lot of glamour in the media and offer promising returns. Usually these companies have inexperienced management, lots of debt and are in a volatile industry. So a good company can safely be recognized as one that has proven itself over time.
In the long run the underlying company is all that matters. The Efficient Market Hypothesis tied to make this point with it’s conclusion that no one can do better than the long run market returns. This is only true if the market prices everything accurately all the time. The returns from ownership in a company are equal to the true growth of that company plus the capital gains or losses from changes in the market price less the real company growth (or just the market returns). Assets periodically become under and over valued. The goal of any investment manager is to buy undervalued assets and sell over valued ones. So if an asset can be purchased at a discount to the true value, determined by the actual growth rate, excess returns can be made.
Here is the other easy part, wait until the market under prices a stock, buy it and wait until it becomes over priced to sell. Easy is a joking exaggeration but having confidence in the evaluation will help. Under pricing occurs because of bad news or general disapproval of the overall market. Inexperienced investors have a myopic view of investing so one bad report or analyst opinion is misinterpreted as a change in the long term forecast. A good evaluation will help distinguish insignificant reports from the news that marks a fundamental change in a company.
The idea of excess returns from inefficiently priced assets is common in the bond market. Investors in the bond market can be thought of as analogous to the stock market. The bond holder is guaranteed the coupon on the bond; this is the same as the fundamental growth of the company. The difference is that the coupon is known and the true growth is not. But bond investors look for an excess capital gain by the appreciation of the price of a bond caused by a decrease in the interest rate. Investors always look for under priced assets. Only in the bond market there must be some prediction about the future decrease in interest rates while the growth of a company depends on many more complex variables.
The idea of staying behind the news is fundamentally different from common opinion about beating the market. The consensus is that it is better to be ahead of the market. Since the market is efficient at reacting to new information and insider trading is illegal, trying to react to news faster than others is generally ineffective. So instead of being ahead of the news it is better to wait and see how the market reacts. The typical investor reactions can be exploited.
The previous example of Automatic Data Processing shows exactly how added returns can be made from taking advantage of market inefficiencies. In 1988 anyone was able to purchase ADP at a price of $10.66 because of the crash of 1987 it was at a huge discount. When the price appreciated to $66 in the next ten years we can assume the market realized something closer to the true value, after the huge under pricing. Excluding dividends this was a 20.32% annual capital gain yield. Assuming the market does not undervalue the company forever there is opportunity in market inefficiencies.
Bad news can be good as it presents opportunity for investors. The stock market crash after the internet bubble created opportunity for investors to get into tech stocks at a cheap price. The inherent distrust of tech stocks left them suddenly out of favor and on sitting in the market at a huge discount. It was apparent that not all internet companies were going to go out of business. With a little research it is clear that some will continue earning money and eventually be valuated fairly (not correctly) by the market. As a prediction Merck and Pfizer are great buys right now. They are both large medical companies that were recently devastated by some bad news about one of their arthritis drugs. Investors made a huge sell off and pushed P/E ratios almost down to the single digits creating an opportunity to get these companies at a good price.[11]
Good news also creates opportunity. For current positions that an investor may be holding, the price could rise above fair value making it over priced. All of a sudden there could be positive news and lots of investor excitement. The price will be bid up and a smart investor will notice the chance to exploit the market overpricing and take in their gains. Short sell any stock that is over priced is also a way to take advantage of these fluctuations.
Beliefs and the correlation of behavior present endless opportunity to exploit the market. These two sources need to be thought of as distinct from one another to really understand the effects of both. It is quite possible to think about inefficiency as the correlation of beliefs, which is not untrue. But beliefs are justifiable until proven otherwise while jumping on the bandwagon is one source easily identifiable and does not require any incorrect subset of beliefs. A correct valuation and experience will help to identify the infinite prospects.
SECTION III. IMPLICATIONS
- ACTIVE MANAGEMENT
Proving inefficiency exists is the justification for active investment management. The Efficient Market Hypothesis argued that active management is useless because everything will return the same over time. Paulos claims investing is like betting on horse race. Betting on the favorite has a higher probability of winning but a lower payoff, while the long shot has a low probability and a high payoff. When multiplied together there should be the same expected payoff. This example only compares equities to equities. The inefficiencies will show that over time assets can become under and over valued. Moving into undervalued assets and out of overvalued assets is the only way to earn extra returns.
The paradox of the efficient markets (described in Section I.) explains the need for professional investment management. Markets are more complex than ever before as more market participants believe that markets can be exploited then there will be more people ready to jump all over any arbitrage opportunity. Traders watch all day for something to be out of line. And with the democratization of the markets there are more participants then ever, so efficiency increases. As the efficiency of the markets increase then the effectiveness of good analysis decreases and the markets become more complex. The complexity of the markets appears to be randomness created by a dependence on beliefs.
Random is an improper description of the markets. Mathematicians like to call this complexity randomness. Complexity is not randomness. This is a misnomer because it is extremely difficult to model. The appearance of randomness is due to the psychological factor of human behavior when participating in the markets. The random walk that is referred to in mathematical books about the stock market are another way of saying, we don’t have an equation. That is what makes the Rational Belief Equilibrium so powerful; it has been able to model the emotional element of investing.
The real justification to investors is that even after expensive research it is possible for investors to gain a few extra percentage points a year. It does not seem like a good risk to take but so many people do it because of the power of compounding interest. Compounding interest is almost like magic. One extra percentage point over the S&P 500 compounded over the last 20 years really adds up. The past 20 years the S&P 500 has returned an average of 13% annually. That means 1 dollar invested 20 years ago would be 11.52 dollars today. If just one percentage point higher were made through active management, 14% annually compounded, one dollar would be 13.74 dollars today. This difference of $2.22 becomes significant when talking about a persons retirement account. Starting with 100,000 dollars, an active investor would have $222,000 more after 20 years than someone that had just invested in the S&P 500.
Can and do are two different things. Proving the need for professional investment managers does not mean that this will ensure above average results. There is no scarcity of professional investment managers, each with a different strategy to maximize returns, but all produce different results. The EMH explains that above average returns are due to luck, even though there are a few managers that will consistently perform.
- DOES ACTIVE MANAGEMENT WORK?
Active investment managers have come under a lot of scrutiny since the development of CAMP and Modern Portfolio Theory. Managers are measured up against the S&P 500 because it has become the least risky way to get into stocks, thanks to the birth of index funds. There have been studies of mutual fund managers and their performance. It has become widely published that most mutual fund managers do not measure up, and that even the ones that do perform well are not consistent. The conclusion is that active investment management is not better than the passive management, i.e. index funds. Proponents of passive management argue that mutual funds can never beat the market in the long run because no one can consistently out perform and capital gain taxes and high management fees are much higher.
The bench mark is typically the S&P 500 annual or quarterly returns and there are two reasons for this. This index is broad enough to give some indication of the performance of the stock market as a whole, and these 500 stocks are supposed to be the top performing and so their returns should be higher than the rest. The S&P 500 index fund is considered the best way to guarantee market returns.
In comparison to the benchmark there is no need to adjust returns for risk because there is no way to measure risk. In a traditional, academic sense volatility is the measurement of risk. In numerical terms it is measured by standard deviation and beta. Uncertainty is the only real definition of risk. Volatility cannot be risk because no investor would call a large upwards movement risk. Investors call downward movement in the price of a stock risk.[12] Investors don’t know which way the stock will move because of the complexity of the markets, uncertainty about the fundamentals, this is risk. Market fundamentals always come out in the long run so it is the uncertainty about the underlying company that we should consider risk. Volatility is a proxy for uncertainty and is caused by high levels of trading. Fama disproved the validity of Beta when he found the returns on high Beta stocks were not inline with expectations.[13] So since there is no way to measure risk it is useless to try and adjust assets for risk. Plus, do investors really care how high returns are made. Given two stocks with the same expected return but one is more volatile an investor should prefer the more volatile stock. Volatility is opportunity; with a few trades the actual return that can be made will be higher.
An interesting idea can be derived from this more accurate depiction of risk. It is possible to earn high returns with low risk. A low risk stock is one that has very little uncertainty; these are the GE’s of the country. Low risk companies are ones that have proven their self to have the ability to sustain long run growth, companies with good management in a healthy industry and consistently and completely reveal their data to the public. In a volatile market where assets can be traded, bought when undervalued and sold when overvalued, it is possible to have high returns on a low risk stock.[14] This requires a high level of accuracy in the evaluation of the stock and the experience to exploit the typical investor’s reactions. Conversely it is possible for high risk stocks to have low returns. This idea is not all that profound since stocks with a lot of uncertainty can quiet possibly not do well. This idea completely conflicts with Modern Portfolio Theory, which says that the only way to get higher returns is to take on more risk.
Some professional managers do surpass the bench mark quarter after quarter, year after year. To prove that managers can have a strategy that will consistently beat the market we will have to show that it is not luck. Taking the returns of the best money mangers and calculating a standard deviation form the bench mark. Then we can calculate a t-statistic for the manager to see if their relative performance is statistically better than the market. The t-statistic will show if there is a low probability of a manager getting these returns every year. If the manager’s performance is significantly above the S&P 500 performance we may be able to infer that it is not just luck.
The study uses five professional managers, W.P. Stewart asset managers, Excelsior Value Restructuring Fund, Legg Mason’s Value Trust Fund managed by Bill Miller, the Longleaf Partners Fund and the Tweety Brown Global Value Fund. Using the performance since inception compared to the matching S&P 500 performance we can calculate a t-statistic for each manager. The average returns are the annual performance since inception. The t-statistic will show the probability of out performing the S&P 500. Any t-statistic above a 1.96 is significant to the 5% level.
Average Returns T-Statistic
- W.P. Stewart 19.1% 1.98
- Legg Mason Value Trust Fund (Bill Miller) 16.5% 1.55
- Tweedy Brown Global Value Fund 12.5% *need quarterly data
- Longleaf Partners Fund 17.1% *need quarterly data
- Excelsior Value Restructuring Fund 17.9% *need quarterly data
Quarterly data is needed on all of these managers to accurately compare performance and even when there is quarterly data sometimes there is just not enough to be conclusive. We do not have to worry about the problem of backward looking selection bias because the goal is to select only the best and test the probability of out performance on a long run basis. So when we identify the managers that we find to be statistically performing better than the market and investigate to see if there is any common trend between them, something that makes them do well or something about their methods. There is no guarantee that these five investment managers will continue to outperform the market and there is not certainty that next year will be a year of out performance again. But we do know that these five managers appear to have a method that has consistently worked over a long period of time.
Investors would like to know if there is a common thread among the top performing asset managers. This will also help to prove that there is superior skill and strategy instead of consistent luck. A real quick comparison of the names reveals the word value. This is the Warren Buffett mantra. Excelsior Value Restructuring Fund buys when the market depresses a stock due to uncertainty about the restructuring of a company. This is equivalent to a value buy, as long as research will let the investor know the company has a high probability of success. W.P. Stewart’s investment strategy is to “buy good companies at a good price and hold.” The good price theory seems to be the winning solution to investing. So why can’t most investment mangers do it?
- EXCESSIVE DIVERSIFICATION
The reason that managers cannot beat the market is because the pressure of bench marking makes manager hyper-diversify. With no lack of promising mutual funds, managers know that one year’s bad performance will send investors on to the next hot fund. Fund managers will not get paid and so they must at least market perform.
On average a mutual fund will hold around 100 stocks at any one time. The typical turnover rate is about 90% in any year. Some mutual fund will change more than 100% of their stocks in a year. The typical mutual fund will have exposure to 200 different positions per year. Using the rules of statistics a mutual fund is basically a sample of the market. In statistics a random sample will represent the whole. This could be a sample of 500 people to see who they are going to vote for in the next election and this might give everyone some indication of who is going to win. But it has to be a random sample of 500 people to ensure that it is a representative sample.
With a universe of 10,000 publicly held companies a sample of 100 stocks is a sample of 1% of the whole. One percent is a pretty good sized sample considering that if someone polled 1% of America before the election that would be 3,000,000 people. Any statistician would find this appropriate for a representative sample. And with a large turnover rate the typical mutual fund is seeing performance of twice as many companies. The only problem is that the sample is probably not going to stand up to the test that it is random. These mutual fund managers pick the stock specifically for performance and so they are not a randomly generated sample of stocks. We would expect some bias in that these stocks should only be the top performing.
Fund managers are benchmarked against the S&P 500. Mutual fund managers are probably selecting largely from these top performing stocks that are relatively safe. Any chosen sample of 100 stocks from the universe of 500 top performing, low risk stocks are going to be a representative sample. This means that the returns on any mutual fund should look exactly like the returns of the S&P 500, derived by the rules of statistics. This is exactly what Eugene Fama found when he was looking for proof of market efficiency. It would be impossible for mutual funds to beat the bench mark because they are the bench mark. And funds will constantly under perform the market after fees and taxes.
A fund that looks like the market cannot beat the market.[15] This is true by definition. The implications of this are that a portfolio can only beat the market if it is not a sample, in other words it is better to hold fewer positions.
- FOCUS
Everyone can learn something from Warren Buffett. Buffett has written about his winning strategy of focus investing. He says the when investing one ought to be very selective, think about each company and load up on it. The average investor should only make twenty investments in a life time. Every decision should be carefully contemplated. No one should haplessly diversify.
The marginal resource costs that are required to follow an additional stock are high. Each new stock takes away from the thorough examination of all others. We justify this because of a new definition of risk, which is uncertainty. The more a person can study a company and understand the fundamentals, the less risk is involved in owning the stock. Each new stock that is owned takes away from the certainty that investors have about that stock. There are increasing marginal detractions from certainty. The first stock is say 100% certainty, while the next one will take away very little certainty from the first and still be able to have high degrees of certainty about each. The next stock will detract a little more, and so on. Unfortunately this requires an ability to evaluate a company, something many investors do not have. But we can assume that all professionals have some ability, albeit not equal.
The best investors will only choose a small number of stocks to invest in. I like to say that as people hold more positions they are diversifying away their gains. Assuming that people will pick the best stocks first, then their next stock will be because they do not believe it to be as good. So when it gets to picking say the 20th stock it will not be as good as the previous picks, so why buy.
Diversifying has been proven with data points to create a less risky portfolio. People do not know the exact future conditions of the economy and so they can hedge their risk by buying negatively correlated assets. The correlation of the assets is supposed to keep the portfolio more stable and reduce risk. Investors believe in this approach because either they have a poor probability forecast of the future economic conditions or they do not believe in active portfolio management. Brock explains in his paper “The Logical Justification for ‘Active’ Investment Management” that the optimal way to manage money is to constantly move it from over to under valued assets.
The reason investors actively manage a portfolio of assets is to take advantage of opportunity. Cash, bonds and stocks are they three typical assets an investor can easily move between. Sometimes it is better to hold cash, sometimes bonds are generating the best returns and then other times stocks are having a hot growth period. There is also movement within and in the mix. For example, investors can move money between sectors. The key here is the ability to generate a good probability forecast.
CONCLUSION
Investing is all about getting a proper evaluation and taking advantage of market inefficiencies. This paper begins by showing that markets are not efficient; breaking down this academically accepted premise is essential. Starting from scratch we then try to build an understanding of the equity markets by using the Rational Belief Equilibrium and using ideas from Behavioral Finance and Game Theory. We proved that investor sentiment plays are much larger role than thought previously. From this better understanding of the markets we were able to show how inefficiencies occur.
Possibly the topic of another paper could be the rational explanation of the earning multiple by showing it has some fundamental meaning. With this the fundamental value, the stock’s correct price, could easily be calculated with this years earning per share number. We failed miserably when we tried to prove that there was some correlation between the expected earning growth rate and the P/E ratio. Maybe if the stocks that were earning zero or less were eliminated from the data we could obtain a better estimate. These stocks that are loosing money rely only on investors beliefs while stocks that are earning money have some valid reason for one growth multiple over another.
I should not create a hypothesis of stable P/E ratios unless I first have a theory behind it. The theory should sound something like ‘the market average P/E ratio is 15; it always has been forever, because at this rate investors will always gain a fair equity risk premium.’ But when the ratio is higher the EPS is going to grow faster and so as a balance the P/E must increase to bring the equity risk premium back to market average. With this analogy investing is like a horse race where the expected payoff of the long shots is that same as for the favorites. Although there is a psychological effect on the results of stocks that does will not affect the outcome of a horse race.
The investment experts do not feel they are ever taking a gamble when they make transactions in the market and this better understanding could help people to rationally invest. Proof of this is easy to find. Any day on CNBC there will be two intelligent finance professionals arguing about a specific stock. Usually they will disagree on the stock, one will say I am buy and the other selling or short selling because of x y and z. These two market participants cannot have the correct determination of the stock price, however one could be right and one wrong.
REFERENCES
Allison, John & Harry Segalas. “The Rewards of Low Risk.” W.P. Stewart, 1997, pp. 37-42.
Brock, Horace W. “A Quantum Leap in Our Understanding of Financial Markets.” Strategic Economic Decisions, Inc., 2004.
Brock Horace W. “Chapter III: Rational Versus Irrational Forecasts.” Unpublished.
Brock, Horace. “The Logical Justification for ‘Active’ Investment Management.” Soon to be published.
Buffett, Warren & Charlie Munger. Outstanding Investors Digest. Berkshire Hathaway, 2002. End of the Year 2001 Edition, pp. 37-40.
Buffett, Warren E. “You Pay a Very High Price in the Stock Market for a Cheery Consensus.” Investing Classics. 1989, pp. 501-505.
Buffett, Warren & Charlie Munger. Outstanding Investor Digest. Outstanding Investors Digest, May 5, 1995 Edition.
Buffett, Warren E. “How Inflation Swindles the Equity Investor.” Investing Classics. 1989, pp. 483-500.
Buffet, Warren. “Mr. Market, Investment Success and You.” The Investment Classics. 1989, pp. 273-275.
Dixit, Avinash & Susan Skeath. Games of Strategy. Second Edition. W.W. Norton & Co. New York. 2004. pp. 263-284.
Kahn, Robert. “The Road Less Traveled.” Unpublished.
Malkiel, Burton. A Random Walk Down Wall Street. W.W. Norton & Company Inc., 2003.
Pareto, Cathy. “Revisiting the Efficient Market Hypothesis.” Investor Solutions, Inc. 2004.
Paulos, John A. A Mathematician Plays the Stock Market. Basic Books, 2003.
Schelling, Thomas C. The Strategy of Conflict. Harvard University Press, Cambridge Massachusetts, 1963.
Shleifer, Andrei. Inefficient Markets an Introduction to Behavioral Finance. Oxford University Press, 2000.
Smith, Rich. “Simplify, Simplify Your Stocks.” The Motley Fool, www.fool.com. Released May 13, 2005.
Swibel, Matthew. “Russian Roulette Investing.” Forbes. December, 2004. pp. 194-196.
APPENDIX A
This Appendix shows all of the earnings data for the 247 companies that are used in the regressions of the P/E ratio.
| Date Released | COMPANY | Ticker Symbol | EPS Reported | Expected | Last Year |
| 1/31/2005 | Allegheyn Technologies | ATI | 0.35 | 0.35 | -0.43 |
| Entergy | ETR | 0.5 | 0.49 | 0.38 | |
| Exxon Mobil | XOM | 1.3 | 1.07 | 0.68 | |
| Hilton Hotels | HLT | 0.18 | 0.16 | 0.11 | |
| Kellogg | K | 0.45 | 0.46 | 0.46 | |
| Mattel | MAT | 0.52 | 0.48 | 0.5 | |
| Mead Westvaco | MWV | 0.26 | 0.22 | 0.14 | |
| SYSCO | SYY | 0.36 | 0.36 | 0.34 | |
| Tyson Foods | TSN | 0.11 | 0.26 | 0.32 | |
| Wyeth | WYE | 0.64 | 0.67 | 0.6 | |
| 2/1/2005 | Alliance Gaming | AGI | -0.01 | -0.02 | 0.28 |
| American Standard Companies | ASD | 0.46 | 0.42 | 0.38 | |
| Archstone-Smith | ASN | 0.4 | 0.43 | 0.63 | |
| BJ Services | BJS | 0.58 | 0.55 | 0.38 | |
| Emerson Electric | EMR | 0.7 | 0.7 | 0.58 | |
| Georgia Pacific | GP | 0.51 | 0.47 | 0.52 | |
| HCA | HCA | 0.7 | 0.66 | 0.58 | |
| Ingersoll-Rand | IR | 1.31 | 1.24 | 1.11 | |
| L3 Communication | LLL | 1.04 | 1.01 | 0.94 | |
| MGM Mirage | MGG | 0.51 | 0.44 | 0.38 | |
| PACCAR | PCAR | 1.51 | 1.49 | 0.9 | |
| Royal Caribbean Cruises | RCL | -0.13 | -0.04 | -0.1 | |
| Tyco | TYC | 0.42 | 0.42 | 0.34 | |
| Valero Energy | VLO | 1.89 | 1.41 | 0.52 | |
| Xcel Energy | XEL | 0.31 | 0.3 | 0.35 | |
| 2/3/2005 | Alliance Data Systems Corporate | ADS | 0.38 | 0.34 | 0.3 |
| Amazon.com | AMZN | 0.35 | 0.4 | 0.29 | |
| Anheuser Busch | BUD | 0.39 | 0.39 | 0.36 | |
| Barr Laboratories | BRL | 0.56 | 0.56 | 0.54 | |
| Countrywide Financial | CFC | 0.65 | 0.82 | 0.91 | |
| CVS | CVS | 0.56 | 0.55 | 0.64 | |
| Devon Energy | DVN | 1.31 | 1.22 | 0.81 | |
| drugstore.com | DSCM | -0.06 | -0.02 | -0.03 | |
| Duke Energy | DUK | 0.24 | 0.23 | 0.22 | |
| Equity Residential | EQR | 0.56 | 0.56 | 0.33 | |
| Fluor | FLR | 0.57 | 0.57 | 0.63 | |
| Fox Entertainment | FOX | 0.44 | 0.39 | 0.36 | |
| Harrahs Entertainment | HET | 0.72 | 0.67 | 0.5 | |
| J.B. Hunt Transport | JBHT | 0.64 | 0.59 | 0.32 | |
| NICE-Systems | NICE | 0.47 | 0.45 | 0.42 | |
| Northrop Grumman | NOC | 0.81 | 0.8 | 0.56 | |
| Pitney Bowes | PBI | 0.71 | 0.68 | 0.66 | |
| Ralph Lauren Polo CP | RL | 0.72 | 0.71 | 0.47 | |
| PP&L Resources | PPL | 0.93 | 0.92 | 0.98 | |
| Quest Software | QSFT | 0.23 | 0.15 | 0.16 | |
| Rohm and Haas | ROH | 0.61 | 0.54 | 0.45 | |
| St. Joe Co. | JOE | 0.37 | 0.31 | 0.37 | |
| TXU Corporation | TXU | 0.67 | 0.43 | 0.2 | |
| American Power Conversion | APCC | 0.27 | 0.25 | 0.29 | |
| Ask Jeeves | ASKJ | 0.35 | 0.32 | 0.14 | |
| BMC Software | BMC | 0.22 | 0.2 | 0.19 | |
| Century Telephone | CTL | 0.62 | 0.6 | 0.61 | |
| Comcast | CMCSA | 0.19 | 0.13 | 0.17 | |
| Cray | CRAY | -0.34 | -0.15 | 0.09 | |
| Double Click | DCLK | 0.08 | 0.06 | 0.03 | |
| Ecolab | ECL | 0.27 | 0.28 | 0.26 | |
| Equity Office Properties | EOP | 0.62 | 0.63 | 0.45 | |
| Gillette | GP | 0.41 | 0.41 | 0.35 | |
| ICOS | ICOS | -0.53 | -0.5 | -0.54 | |
| International Paper | IP | 0.42 | 0.42 | 0.23 | |
| j2 Global Communications | JCOM | 0.37 | 0.34 | 0.32 | |
| K-Swiss | KSWS | 0.23 | 0.21 | 0.2 | |
| Lyondell Chemical | LYO | 0.33 | 0.28 | -0.41 | |
| Maxtor | MXO | -0.28 | -0.18 | 0.24 | |
| Med Immune | MEDI | 0.21 | 0.17 | 0.32 | |
| Mylan Laboratories | MYL | 0.13 | 0.18 | 0.31 | |
| Penn National Gaming | PENN | 0.44 | 0.42 | 0.32 | |
| Pepsi Co. | PEP | 0.59 | 0.58 | 0.52 | |
| Public Service Enterprise Group | PEG | 0.48 | 0.52 | 0.69 | |
| Raytheon | RTN | 0.54 | 0.46 | 0.55 | |
| SEI Investments | SEIC | 0.41 | 0.4 | 0.36 | |
| Sherwin Williams | SHW | 0.57 | 0.57 | 0.48 | |
| Snap On | SNA | 0.44 | 0.37 | 0.37 | |
| Sprint FON Group | FON | 0.31 | 0.32 | 0.39 | |
| Starwood Hotel & Resort | HOT | 0.57 | 0.45 | 0.42 | |
| Tesoro Petroleum | TSO | 0.15 | 0.17 | -0.02 | |
| Tractor Supply | TSCO | 0.55 | 0.5 | 0.41 | |
| 2/4/2005 | Cardinal Health | CAH | 0.73 | 0.77 | 0.86 |
| Ryder System | R | 0.82 | 0.79 | 0.64 | |
| Time Warner | TWX | 0.2 | 0.16 | 0.24 | |
| 2/7/2005 | Activision | ATVI | 0.63 | 0.56 | 0.53 |
| Aeroflex | ARXX | 0.1 | 0.1 | 0.09 | |
| Allergan | AGN | 0.86 | 0.83 | 0.67 | |
| Business Objects | BOBJ | 0.3 | 0.26 | 0.29 | |
| Clorox | CLX | 0.59 | 0.52 | 0.52 | |
| Electronic Data Systems | EDS | 0.25 | 0.22 | 0.12 | |
| Hasbro | HAS | 0.44 | 0.5 | 0.61 | |
| Humana | HUM | 0.26 | 0.27 | 0.41 | |
| Kyphon | KYPH | 0.14 | 0.13 | 0.08 | |
| Sohu.com | SOHU | 0.17 | 0.18 | 0.28 | |
| Wellpoint | WLP | 1.69 | 1.68 | 1.43 | |
| 2/8/2005 | Alcan Inc. | AL | 0.52 | 0.54 | 0.42 |
| Ameren | AEE | 0.42 | 0.35 | 0.24 | |
| C.H. Robinson Worldwide | CHRW | 0.44 | 0.42 | 0.34 | |
| Cisco | CSCO | 0.22 | 0.22 | 0.18 | |
| Computer Sciences Corporation | CSC | 0.8 | 0.8 | 0.71 | |
| Elan Corporation | ELN | -0.23 | -0.28 | -0.63 | |
| Level 3 Communications | LVLT | -0.18 | -0.2 | -0.3 | |
| Marriott International Inc. | MAR | 0.79 | 0.74 | 0.69 | |
| Open Text | OTEX | 0.3 | 0.27 | 0.2 | |
| TASER International | TASR | 0.08 | 0.11 | 0.05 | |
| 2/9/2005 | American International Group | AIG | 1.17 | 1.17 | 1.05 |
| Applebee’s | APPB | 0.29 | 0.29 | 0.27 | |
| Aramark Corporation | RMK | 0.38 | 0.35 | 0.35 | |
| Atari | ATAR | 0.16 | 0.15 | 0.19 | |
| Boyd Gaming | BYD | 0.5 | 0.37 | 0.19 | |
| Cigna | CI | 2.41 | 1.59 | 1.65 | |
| Diamond Offshore Drilling | DO | 0.16 | 0.14 | 0.01 | |
| eResearch Technology | ERES | 0.13 | 0.12 | 0.1 | |
| Garmin Ltd. | GRMN | 0.63 | 0.55 | 0.47 | |
| LifePoint Hospitals | LPNT | 0.58 | 0.53 | 0.5 | |
| Lincoln National | LNC | 1.07 | 0.98 | 0.99 | |
| Metlife | MET | 0.87 | 0.83 | 0.74 | |
| SkyWest | SKYW | 0.37 | 0.38 | 0.3 | |
| Timberland | TBL | 1.29 | 1.24 | 1.1 | |
| Whole Foods | WFMI | 0.73 | 0.68 | 0.6 | |
| Zebra Technologies | ZBRA | 0.44 | 0.44 | 0.34 | |
| 2/10/2005 | Actuate | ACTU | 0.04 | 0.01 | 0.02 |
| Aetna | AET | 1.82 | 1.79 | 1.32 | |
| Analog Devices | ADI | 0.28 | 0.29 | 0.3 | |
| Cognizant Technology | CTSH | 0.21 | 0.19 | 0.13 | |
| Dean Foods | DF | 0.64 | 0.65 | 0.56 | |
| Dell | DELL | 0.37 | 0.36 | 0.29 | |
| LM Ericsson | ERICY | 0.5 | 0.53 | 0.07 | |
| May Department Stores | MAY | 1.24 | 1.29 | 1.39 | |
| Office Depot | ODP | 0.3 | 0.2 | 0.22 | |
| OraSure | OSUR | -0.01 | -0.02 | 0.01 | |
| Pixar | PIXR | 0.91 | 0.76 | 1.44 | |
| Service Master | SVM | 0.08 | 0.08 | 0.08 | |
| Sinclair Broadcast Group | SBGI | 0.19 | 0.11 | 0.17 | |
| Waste Management | WMI | 0.39 | 0.37 | 0.39 | |
| Watson Pharmaceuticals | WPI | 0.46 | 0.45 | 0.48 | |
| XM Satellite Radio | XMSR | -0.72 | -0.84 | -1.12 | |
| 2/14/2005 | Agilent | A | 0.2 | 0.19 | 0.21 |
| Bob Evans Farms | BOBE | 0.19 | 0.19 | 0.44 | |
| Omi Corporation | OMM | 1.18 | 1.12 | 0.34 | |
| 2/15/2005 | Abercrombie & Fitch | ANF | 1.15 | 1.12 | 0.96 |
| Applied Materials | AMAT | 0.17 | 0.16 | 0.12 | |
| Deere | DE | 0.89 | 0.91 | 0.68 | |
| Fidelity National Financial | FNF | 1.08 | 0.96 | 1.16 | |
| FirstEnergy | FE | 0.72 | 0.57 | 0.42 | |
| Fresh Del Monte Produce | FDP | 0.33 | 0.24 | 0.4 | |
| Inco Ltd. | N | 1.19 | 0.99 | 0.57 | |
| Laboratory Corporation of America | LH | 0.61 | 0.61 | 0.54 | |
| Nordstrom | JWN | 1.03 | 1.02 | 0.74 | |
| Qwest | Q | -0.06 | -0.13 | -0.13 | |
| Teva Pharmaceutical | TEVA | 0.42 | 0.39 | 0.31 | |
| American Capital Strategies | ACAS | 0.74 | 0.72 | 0.69 | |
| Caremark | CMX | 0.45 | 0.43 | 0.32 | |
| Coca-Cola | KO | 0.4 | 0.4 | 0.46 | |
| Cooper Tire & Rubber | CTB | 0.04 | 0.41 | 0.43 | |
| Guess | GES | 0.33 | 0.31 | 0.29 | |
| InterActiveCorp | IACI | 0.33 | 0.27 | 0.29 | |
| Jones Apparel | JNY | 0.28 | 0.29 | 0.33 | |
| Moody’s Corporation | MCO | 0.81 | 0.74 | 0.65 | |
| Outback Steakhouse | OSI | 0.53 | 0.57 | 0.58 | |
| 2/17/2005 | Advanced Energy Industries | AEIS | -0.14 | -0.16 | -0.05 |
| Akamai | AKAM | 0.1 | 0.09 | -0.01 | |
| Baker Hughes | BHI | 0.53 | 0.46 | 0.32 | |
| Barrick Goldn | ABX | 0.06 | 0.06 | 0.14 | |
| CBRL Group | CBRL | 0.63 | 0.62 | 0.57 | |
| Coca-Cola Enterprises | CCE | 0.13 | 0.13 | 0.17 | |
| E-Loan | EELN | 0.02 | 0 | 0 | |
| Entravision Communication Corp | EVC | 0.02 | 0 | -0.05 | |
| Genzyme | GENZ | 0.52 | 0.47 | 0.38 | |
| Intervideo | IVII | 0.25 | 0.09 | 0.15 | |
| Intuit | INTU | 0.82 | 0.76 | 0.77 | |
| Nextel | NXTL | 0.41 | 0.4 | 0.48 | |
| Nvidia | NVDA | 0.27 | 0.21 | 0.14 | |
| Panera Bread | PNRA | 0.45 | 0.45 | 0.34 | |
| priceline.com | PCLN | 0.22 | 0.16 | 0.06 | |
| RadioShack | RSH | 0.81 | 0.83 | 0.77 | |
| Target | TGT | 0.9 | 0.9 | 0.91 | |
| ValueClick | VCLK | 0.16 | 0.1 | 0.07 | |
| Wal Mart | WMT | 0.75 | 0.74 | 0.63 | |
| 2/18/2005 | Campbell Soup | CPB | 0.57 | 0.59 | 0.57 |
| J.M. Smucker | SJM | 0.7 | 0.71 | 0.65 | |
| PG&E | PCG | 0.44 | 0.42 | 0.34 | |
| 2/22/2005 | Chesapeake Energy | CHK | 0.44 | 0.36 | 0.37 |
| Cumulus Media | CMLS | 0.14 | 0.13 | 0.09 | |
| Federated Department Stores | FD | 2.55 | 2.54 | 2.29 | |
| Genuine Parts | GPC | 0.55 | 0.54 | 0.5 | |
| Home Depot | HD | 0.47 | 0.47 | 0.42 | |
| I-Flow | IFLO | -0.16 | -0.09 | -0.05 | |
| Omnicom | OMC | 1.28 | 1.25 | 1.17 | |
| Tuesday Morning | TUES | 0.88 | 0.88 | 0.89 | |
| United Surgical Partners International | USPI | 0.32 | 0.31 | 0.31 | |
| Wild Oats Markets | OATS | -0.1 | -0.07 | 0.05 | |
| 2/23/2005 | Cablevision | CVC | -0.3 | -0.35 | -0.69 |
| Ciena | CIEN | -0.05 | -0.05 | -0.08 | |
| Cox Radio | CXR | 0.18 | 0.18 | 0.18 | |
| Dana Corporation | DCN | 0.41 | 0.3 | 0.41 | |
| Dollar Tree Stores | DLTR | 0.77 | 0.78 | 0.69 | |
| EnCana | ECA | 1.23 | 1.46 | 0.67 | |
| Entercom Communications | ETM | 0.4 | 0.4 | 0.42 | |
| General Maritime | GMR | 3.7 | 3.29 | 0.7 | |
| Lowes | LOW | 0.65 | 0.59 | 0.5 | |
| Martha Stewart Living Omnimedia | MSO | -0.14 | -0.16 | 0.1 | |
| Nanometrics | NANO | 0.18 | 0.25 | -0.07 | |
| Plug Power | PLUG | -0.16 | -0.15 | -0.21 | |
| QLT | QLTI | 0.21 | 0.2 | 0.13 | |
| TJX Companies | TJX | 0.4 | 0.4 | 0.47 | |
| Toll Brothers | TOL | 1.33 | 1.14 | 0.62 | |
| Williams Companies | WMB | 0.12 | 0.08 | 0.11 | |
| 2/24/2005 | Allied Capital | ALD | 0.4 | 0.41 | 0.62 |
| Calpine | CPN | -0.39 | -0.23 | -0.15 | |
| Grey Wolf | GW | 0.04 | 0.04 | 0 | |
| J. C. Penney | JCP | 1.16 | 1.11 | 0.83 | |
| Limited Brands | LTD | 0.95 | 0.89 | 0.74 | |
| NEWMONT MINING CORP | NEM | 0.37 | 0.33 | 0.36 | |
| Omnicare | OCR | 0.56 | 0.58 | 0.59 | |
| Pharmceutical Resources | PRX | 0.12 | 0.41 | 1.08 | |
| Placer Dome Inc. | PDG | 0.1 | 0.11 | 0.15 | |
| Safeway | SWY | 0.56 | 0.49 | 0.66 | |
| Staples | SPLS | 0.5 | 0.5 | 0.42 | |
| 2/25/2005 | Clear Channel | CCU | 0.37 | 0.37 | 0.3 |
| Pan American Silver | PAAS | 0.05 | 0.05 | -0.06 | |
| Westwood One Inc. | WON | 0.31 | 0.33 | 0.31 | |
| 2/28/2005 | ADC Telecommunications | ADCT | 0.01 | 0.01 | 0 |
| Cell Therapeutics | CTIC | -0.72 | -0.57 | -1.09 | |
| Heinz | HNZ | 0.6 | 0.59 | 0.58 | |
| OmniVision Technologies | OVTI | 0.33 | 0.28 | 0.28 | |
| Tiffany | TIF | 0.81 | 0.79 | 0.74 | |
| Univision | UVN | 0.19 | 0.2 | 0.17 | |
| 3/2/2005 | American Eagle Outfitters | AEOS | 1.4 | 1.39 | 0.57 |
| AutoZone | AZO | 1.29 | 1.19 | 1.04 | |
| Chico’s FAS | CHS | 0.2 | 0.2 | 0.14 | |
| Costco | COST | 0.54 | 0.55 | 0.48 | |
| Express Scripts | ESRX | 1.07 | 1.06 | 0.86 | |
| Haverty Furniture | HVT | 0.37 | 0.38 | 0.43 | |
| Iron Mountain | IRM | 0.23 | 0.16 | 0.22 | |
| Liz Claiborne | LIZ | 0.74 | 0.74 | 0.66 | |
| PetSmart | PETM | 0.44 | 0.45 | 0.39 | |
| Titan Corporation | TTN | 0.25 | 0.23 | 0.23 | |
| 3/3/2005 | KOS Pharmaceuticals | KOSP | 1.15 | 0.95 | 0.49 |
| Laserscope | LSCP | 0.23 | 0.22 | 0.07 | |
| SPX Corporation | SPW | -1.88 | 0.84 | 1.44 | |
| 3/4/2005 | Ceradyn | CRDN | 0.41 | 0.35 | 0.17 |
| Saks | SKS | 0.67 | 0.67 | 0.7 | |
| 3/10/2005 | A.C. Moore Arts & Crafts | ACMR | 0.77 | 0.74 | 0.73 |
| Andrx | ADRX | 0.28 | 0.14 | 0.22 | |
| Boston Beer | SAM | 0.19 | 0.19 | 0.25 | |
| Chicago Bridge & Iron Company | CBI | 0.5 | 0.48 | 0.39 | |
| Chinadotcom | CHINA | 0.03 | 0.03 | 0.04 | |
| Kmart | KMRT | 2.59 | 2.8 | 2.78 | |
| Net2Phone | NTOP | -0.07 | -0.09 | -0.12 | |
| Quantum Fuel Systems Technolog | QTWW | -0.09 | -0.08 | -0.1 |
APPENDIX B
This is the data used to calculate the average P/E ratio for the stock over the two time periods. The calculation was simply taking the Price divided by the EPS from the expected and actual EPS from above. And the data used to calculate the trading volume.
| Headlines | Avg. Volume | |||||
| Ticker Symbol | Volume 3/21/05 | (3/1/05 – 3/21/05) | (3 mon.) | Mkt. Cap. | 50-Day Avg. | 200-Day Avg. |
| ATI | 1,469,100 | 6 | 1,172,181 | 2.367B | 22.416 | 19.384 |
| ETR | 651,100 | 19 | 940,363 | 15.093B | 68.022 | 62.747 |
| XOM | 17,830,900 | 187 | 17,108,227 | 400.2B | 56.29 | 49.767 |
| HLT | 1,184,300 | 31 | 2,421,000 | 8.598B | 22.2 | 19.927 |
| K | 1,770,400 | 21 | 1,116,681 | 17.876B | 44.224 | 42.954 |
| MAT | 1,603,000 | 22 | 1,761,636 | 8.580B | 20.047 | 18.394 |
| MWV | 540,500 | 3 | 947,681 | 6.732B | 31.2 | 30.901 |
| SYY | 1,813,000 | 3 | 1,912,500 | 21.687B | 34.996 | 34.365 |
| TSN | 1,144,600 | 14 | 1,356,363 | 6.003B | 17.256 | 17.625 |
| WYE | 3,608,400 | 26 | 4,743,954 | 54.417B | 40.956 | 38.646 |
| AGI | 522,400 | 7 | 1,074,636 | 508.3M | 11.078 | 13.058 |
| ASD | 1,253,100 | 6 | 978,136 | 10.167B | 43.713 | 39.92 |
| ASN | 732,100 | 10 | 1,277,772 | 6.853B | 34.567 | 32.917 |
| BJS | 2,233,400 | 3 | 2,952,318 | 8.341B | 47.592 | 47.877 |
| EMR | 1,238,500 | 7 | 1,212,363 | 28.241B | 67.068 | 64.521 |
| GP | 691,700 | 11 | 1,264,181 | 9.366B | 35.141 | 35.138 |
| HCA | 1,223,800 | 11 | 2,453,136 | 21.303B | 45.538 | 40.682 |
| IR | 774,200 | 5 | 1,212,090 | 14.680B | 79.8 | 72.059 |
| LLL | 3,829,100 | 20 | 806,318 | 8.219B | 72.089 | 67.384 |
| MGG | 612,300 | 31 | 960,227 | 10.830B | 74.887 | 57.02 |
| PCAR | 541,289 | 5 | 1,025,181 | 12.821B | 73.16 | 67.728 |
| RCL | 3,301,800 | 13 | 1,383,318 | 8.990B | 49.448 | 46.23 |
| TYC | 6,207,000 | 40 | 9,063,318 | 70.724B | 34.843 | 32.792 |
| VLO | 4,368,300 | 11 | 4,123,045 | 18.232B | 59.449 | 60.225 |
| XEL | 1,063,900 | 10 | 1,065,318 | 6.952B | 17.875 | 17.533 |
| ADS | 355,500 | 5 | 618,454 | 3.338B | 41.62 | 41.129 |
| AMZN | 6,085,309 | 62 | 8,964,363 | 13.869B | 38.02 | 40.815 |
| BUD | 1,617,500 | 30 | 2,746,500 | 36.999B | 48.407 | 50.86 |
| BRL | 516,700 | 5 | 671,227 | 4.985B | 47.328 | 40.97 |
| CFC | 3,892,900 | 20 | 3,869,409 | 19.006B | 35.592 | 46.12 |
| CVS | 1,621,500 | 31 | 1,964,727 | 21.388B | 48.825 | 44.326 |
| DVN | 2,653,900 | 13 | 2,862,181 | 23.137B | 42.697 | 57.559 |
| DSCM | 196,323 | 7 | 378,681 | 236.1M | 2.715 | 3.059 |
| DUK | 2,848,900 | 12 | 3,056,136 | 26.949B | 26.557 | 23.712 |
| EQR | 669,600 | 6 | 1,113,181 | 9.162B | 33.036 | 32.261 |
| FLR | 439,100 | 6 | 598,636 | 4.873B | 56.463 | 48.71 |
| FOX | 2,422,400 | 54 | 2,898,318 | N/A | 0 | 29.585 |
| HET | 781,800 | 28 | 1,224,863 | 7.431B | 66.156 | 57.196 |
| JBHT | 726,859 | 9 | 767,181 | 3.859B | 44.9 | 39.782 |
| NICE | 134,942 | 5 | 149,181 | 552.2M | 32.329 | 25.546 |
| NOC | 1,557,700 | 52 | 1,585,318 | 18.972B | 52.891 | 56.898 |
| PBI | 610,900 | 13 | 605,681 | 10.445B | 45.601 | 44.279 |
| RL | 191,500 | 3 | 432,545 | 4.188B | 39.984 | 37.349 |
| PPL | 658,100 | 5 | 771,545 | 10.086B | 53.773 | 49.636 |
| QSFT | 246,293 | 8 | 795,500 | 1.271B | 14.159 | 13.166 |
| ROH | 792,200 | 8 | 847,863 | 11.037B | 46.4 | 42.516 |
| JOE | 873,700 | 12 | 501,954 | 5.331B | 70.432 | 53.501 |
| TXU | 2,889,900 | 15 | 2,222,681 | 19.238B | 71.884 | 54.858 |
| APCC | 924,151 | 9 | 1,312,818 | 4.694B | 22.001 | 19.252 |
| ASKJ | 43,132,880 | 71 | 3,748,454 | 1.659B | 25.216 | 28.742 |
| BMC | 576,700 | 7 | 1,798,545 | 3.438B | 16.033 | 16.522 |
| CTL | 895,300 | 3 | 896,227 | 4.420B | 33.61 | 32.646 |
| CMCSA | 8,640,382 | 118 | 7,723,818 | 75.405B | 32.738 | 29.891 |
| CRAY | 1,408,130 | 16 | 1,323,727 | 207.0M | 3.601 | 4.155 |
| DCLK | 770,536 | 6 | 1,658,181 | 974.2M | 7.843 | 7.019 |
| ECL | 733,100 | 5 | 877,727 | 8.409B | 32.937 | 32.337 |
| EOP | 1,026,000 | 9 | 1,858,272 | 12.271B | 29.398 | 28.094 |
| GP | 2,211,700 | 34 | 4,707,500 | 9.366B | 35.141 | 43.842 |
| ICOS | 415,532 | 4 | 643,227 | 1.477B | 24 | 24.798 |
| IP | 1,858,500 | 13 | 2,627,318 | 18.662B | 39.048 | 40.731 |
| JCOM | 685,960 | 4 | 530,636 | 959.7M | 35.949 | 30.795 |
| KSWS | 107,018 | 3 | 291,045 | 1.093B | 30.9 | 24.16 |
| LYO | 2,504,600 | 7 | 2,233,954 | 7.577B | 30.951 | 23.763 |
| MXO | 1,924,200 | 18 | 2,148,545 | 1.374B | 5.446 | 5.088 |
| MEDI | 1,250,514 | 12 | 2,252,363 | 5.855B | 24.204 | 24.714 |
| MYL | 1,669,800 | 17 | 1,885,181 | 4.798B | 16.96 | 17.926 |
| PENN | 481,371 | 6 | 1,384,500 | 2.448B | 57.705 | 45.401 |
| PEP | 2,668,500 | 44 | 3,264,545 | 88.473B | 53.607 | 51.795 |
| PEG | 559,500 | 12 | 1,332,272 | 12.914B | 52.963 | 45.072 |
| RTN | 1,385,200 | 17 | 1,387,636 | 17.354B | 37.804 | 36.59 |
| SEIC | 393,557 | 4 | 413,227 | 3.798B | 37.327 | 34.891 |
| SHW | 663,400 | 2 | 595,590 | 6.283B | 44.398 | 42.531 |
| SNA | 139,800 | 5 | 293,590 | 1.829B | 33.371 | 32.214 |
| FON | 8,499,900 | 97 | 12,978,590 | 33.758B | 23.596 | 21.054 |
| HOT | 827,900 | 26 | 1,497,636 | 12.200B | 58.24 | 50.068 |
| TSO | 1,023,800 | 5 | 1,059,454 | 2.395B | 32.978 | 29.389 |
| TSCO | 217,999 | 2 | 382,000 | 1.660B | 40.04 | 37.01 |
| CAH | 874,900 | 8 | 1,826,409 | 24.325B | 56.639 | 52.447 |
| R | 715,300 | 3 | 644,681 | 2.746B | 44.43 | 45.341 |
| TWX | 26,247,200 | 227 | 15,598,500 | 83.737B | 18.103 | 17.385 |
| ATVI | 1,083,085 | 20 | 2,704,181 | 3.211B | 21.992 | 16.86 |
| ARXX | 453,683 | 7 | 568,818 | 713.8M | 10.114 | 11.047 |
| AGN | 1,053,300 | 4 | 772,681 | 9.562B | 75.833 | 77.223 |
| BOBJ | 467,068 | 22 | 828,545 | 2.391B | 25.488 | 22.836 |
| CLX | 1,405,100 | 8 | 862,090 | 9.475B | 58.545 | 55.229 |
| EDS | 1,798,200 | 25 | 2,199,272 | 10.596B | 21.028 | 20.001 |
| HAS | 778,100 | 27 | 885,545 | 3.661B | 19.989 | 18.88 |
| HUM | 1,441,100 | 8 | 1,345,636 | 5.110B | 33.136 | 23.614 |
| KYPH | 126,912 | 6 | 420,318 | 1.037B | 25.316 | 25.223 |
| SOHU | 607,835 | 4 | 1,398,227 | 653.3M | 16.711 | 17.477 |
| WLP | 1,204,500 | 11 | 1,866,482 | 37.407B | 121.123 | 97.991 |
| AL | 455,900 | 18 | 1,141,863 | 14.739B | 40.393 | 43.651 |
| AEE | 461,900 | 12 | 634,590 | 9.527B | 50.279 | 47.314 |
| CHRW | 518,167 | 2 | 546,772 | 4.500B | 53.09 | 48.969 |
| CSCO | 38,510,016 | 133 | 60,245,181 | 117.0B | 18.035 | 19.595 |
| CSC | 1,040,200 | 12 | 1,163,909 | 8.737B | 48.791 | 48.562 |
| ELN | 7,290,900 | 128 | 15,741,500 | 2.842B | 21.447 | 23.403 |
| LVLT | 4,006,331 | 26 | 11,260,000 | 1.494B | 2.543 | 2.994 |
| MAR | 687,400 | 36 | 1,106,318 | 14.686B | 64.205 | 55.421 |
| OTEX | 208,818 | 3 | 537,181 | 868.1M | 19.338 | 20.683 |
| TASR | 3,582,562 | 24 | 10,715,590 | 723.3M | 16.21 | 30.464 |
| AIG | 21,482,700 | 206 | 7,892,363 | 148.5B | 66.887 | 67.338 |
| APPB | 370,117 | 13 | 710,272 | 2.269B | 27.433 | 26.22 |
| RMK | 274,100 | 3 | 580,272 | 4.861B | 26.593 | 25.822 |
| ATAR | 374,391 | 7 | 515,045 | 395.4M | 2.688 | 2.176 |
| BYD | 1,295,900 | 17 | 685,772 | 4.844B | 45.853 | 33.926 |
| CI | 973,200 | 14 | 1,032,954 | 11.437B | 85.151 | 72.713 |
| DO | 1,589,400 | 4 | 1,415,363 | 6.546B | 45.56 | 33.629 |
| ERES | 1,076,892 | 14 | 1,410,818 | 619.4M | 13.784 | 17.372 |
| GRMN | 451,257 | 5 | 801,136 | 5.175B | 52.463 | 45.822 |
| LPNT | 255,788 | 12 | 598,500 | 1.567B | 38.75 | 34.892 |
| LNC | 942,500 | 8 | 759,454 | 8.076B | 46.797 | 45.784 |
| MET | 1,051,700 | 28 | 1,920,636 | 28.840B | 40.398 | 38.117 |
| SKYW | 438,466 | 14 | 388,500 | 1.076B | 17.284 | 16.494 |
| TBL | 114,500 | 13 | 332,909 | 2.437B | 67.633 | 62.715 |
| WFMI | 659,192 | 17 | 913,590 | 6.577B | 97.339 | 89.473 |
| ZBRA | 290,543 | 8 | 556,318 | 3.367B | 50.637 | 62.421 |
| ACTU | 66,779 | 4 | 282,318 | 168.2M | 2.576 | 2.936 |
| AET | 2,172,500 | 21 | 2,723,227 | 22.098B | 128.951 | 105.356 |
| ADI | 3,221,000 | 10 | 3,351,090 | 13.627B | 36.307 | 38.685 |
| CTSH | 1,042,778 | 7 | 1,948,954 | 6.207B | 42.054 | 34.769 |
| DF | 462,000 | 4 | 707,772 | 5.015B | 34.196 | 33.745 |
| DELL | 14,412,885 | 155 | 13,992,545 | 94.962B | 40.345 | 37.653 |
| ERICY | 2,239,703 | 46 | 4,113,863 | 45.598B | 29.648 | 29.48 |
| MAY | 2,188,500 | 37 | 4,337,818 | 10.707B | 33.195 | 28.473 |
| ODP | 3,172,800 | 45 | 2,525,863 | 7.166B | 18.412 | 16.95 |
| OSUR | 133,426 | 5 | 263,863 | 303.4M | 6.292 | 6.826 |
| PIXR | 822,381 | 57 | 525,409 | 5.458B | 88.702 | 79.96 |
| SVM | 495,800 | 6 | 442,045 | 4.027B | 13.269 | 12.68 |
| SBGI | 138,771 | 7 | 289,454 | 662.0M | 8.053 | 8.394 |
| WMI | 1,296,500 | 5 | 1,482,909 | 16.804B | 29.398 | 28.828 |
| WPI | 834,200 | 2 | 1,058,863 | 3.537B | 30.59 | 29.377 |
| XMSR | 3,774,768 | 59 | 4,944,727 | 6.023B | 32.49 | 30.619 |
| A | 2,207,600 | 39 | 2,309,727 | 11.154B | 23.04 | 23.647 |
| BOBE | 128,298 | 10 | 174,318 | 843.7M | 23.834 | 25.365 |
| OMM | 1,001,600 | 1 | 1,693,636 | 1.681B | 18.134 | 16.044 |
| ANF | 1,283,800 | 24 | 1,562,909 | 4.788B | 53.153 | 41.425 |
| AMAT | 21,258,464 | 31 | 33,291,363 | 26.919B | 16.617 | 16.915 |
| DE | 1,472,400 | 21 | 1,815,181 | 16.915B | 69.138 | 66.477 |
| FNF | 2,905,100 | 20 | 1,380,863 | 7.102B | 44.539 | 40.156 |
| FE | 651,200 | 19 | 1,058,727 | 13.665B | 40.303 | 40.067 |
| FDP | 158,700 | 5 | 195,363 | 1.774B | 30.47 | 27.395 |
| N | 1,054,800 | 3 | 1,676,363 | 7.779B | 37.018 | 35.707 |
| LH | 495,900 | 8 | 743,318 | 6.186B | 47.915 | 44.342 |
| JWN | 1,436,600 | 18 | 1,047,818 | 7.410B | 50.786 | 44.266 |
| Q | 4,994,000 | 188 | 12,145,500 | 6.940B | 4.136 | 3.685 |
| TEVA | 1,669,680 | 18 | 4,988,363 | 18.385B | 28.947 | 32.263 |
| ACAS | 984,200 | 6 | 630,318 | 2.896B | 33.772 | 31.276 |
| CMX | 1,542,700 | 13 | 2,388,681 | 17.397B | 39.575 | 34.148 |
| KO | 5,586,100 | 86 | 5,847,000 | 100.5B | 42.148 | 43.435 |
| CTB | 1,034,900 | 8 | 777,090 | 1.294B | 20.582 | 21.218 |
| GES | 186,400 | 9 | 231,000 | 651.9M | 14.386 | 15.243 |
| IACI | 30,119,188 | 93 | 4,661,227 | 15.305B | 23.569 | 24.738 |
| JNY | 510,900 | 9 | 849,681 | 3.915B | 33.775 | 35.734 |
| MCO | 574,100 | 15 | 582,181 | 12.362B | 84.151 | 75.68 |
| OSI | 501,100 | 13 | 495,227 | 3.375B | 45.55 | 42.352 |
| AEIS | 181,398 | 2 | 408,863 | 303.0M | 8.282 | 9.979 |
| AKAM | 1,595,597 | 16 | 2,200,409 | 1.582B | 11.807 | 13.62 |
| BHI | 2,112,600 | 21 | 2,498,272 | 15.141B | 44.437 | 41.586 |
| ABX | 1,326,300 | 12 | 1,627,636 | 13.050B | 23.474 | 21.703 |
| CBRL | 643,781 | 9 | 533,363 | 2.085B | 41.648 | 36.885 |
| CCE | 1,385,100 | 9 | 1,444,590 | 9.796B | 21.577 | 22.082 |
| EELN | 232,908 | 1 | 881,454 | 198.8M | 3.192 | 2.615 |
| EVC | 140,700 | 4 | 296,818 | 1.052B | 8.053 | 7.93 |
| GENZ | 1,517,898 | 16 | 2,441,772 | 14.370B | 58.033 | 53.454 |
| IVII | 30,077 | 11 | 53,318 | 150.0M | 12.654 | 12.124 |
| INTU | 1,647,972 | 15 | 1,816,545 | 8.194B | 40.733 | 41.57 |
| NXTL | 5,414,705 | 63 | 12,968,363 | 32.269B | 29.206 | 26.439 |
| NVDA | 5,241,129 | 16 | 5,886,590 | 4.152B | 24.709 | 18.853 |
| PNRA | 880,414 | 11 | 834,818 | 1.793B | 50.633 | 40.656 |
| PCLN | 862,494 | 12 | 749,318 | 920.6M | 22.656 | 22.828 |
| RSH | 2,756,900 | 37 | 1,564,136 | 3.922B | 31.125 | 29.869 |
| TGT | 2,455,600 | 62 | 3,571,636 | 45.568B | 50.613 | 47.753 |
| VCLK | 1,028,336 | 9 | 1,765,272 | 902.8M | 12.581 | 10.877 |
| WMT | 20,645,200 | 334 | 10,755,000 | 216.9B | 52.705 | 53.389 |
| CPB | 1,558,100 | 19 | 1,114,636 | 11.788B | 28.7 | 27.327 |
| SJM | 211,500 | 2 | 220,181 | 2.851B | 48.179 | 46.18 |
| PCG | 3,046,500 | 17 | 2,008,636 | 11.246B | 34.783 | 31.397 |
| CHK | 2,914,700 | 9 | 3,503,727 | 7.058B | 19.098 | 16.427 |
| CMLS | 232,656 | 1 | 578,772 | 996.5M | 14.18 | 15.05 |
| FD | 1,893,000 | 52 | 2,307,000 | 10.528B | 58.397 | 51.526 |
| GPC | 488,600 | 4 | 373,545 | 7.455B | 43.327 | 40.565 |
| HD | 11,299,500 | 37 | 6,296,045 | 84.061B | 40.969 | 38.89 |
| IFLO | 236,092 | 4 | 241,545 | 350.4M | 17.434 | 15.456 |
| OMC | 525,300 | 43 | 958,136 | 16.345B | 86.608 | 78.141 |
| TUES | 249,442 | 2 | 258,363 | 1.203B | 29.98 | 31.179 |
| USPI | 427,109 | 3 | 233,000 | 1.310B | 40.209 | 37.865 |
| OATS | 1,802,984 | 8 | 595,636 | 257.3M | 7.328 | 9.035 |
| CVC | 776,000 | 79 | 2,880,727 | 8.585B | 27.682 | 22.15 |
| CIEN | 13,829,294 | 17 | 12,993,909 | 1.087B | 2.486 | 2.542 |
| CXR | 97,000 | 4 | 340,181 | 1.679B | 16.145 | 16.271 |
| DCN | 687,700 | 12 | 789,772 | 2.062B | 15.383 | 17.122 |
| DLTR | 1,128,096 | 15 | 1,257,772 | 3.183B | 27.474 | 27.173 |
| ECA | 1,135,500 | 13 | 974,227 | 31.518B | 62.395 | 50.732 |
| ETM | 190,800 | 8 | 394,681 | 1.705B | 33.234 | 35.267 |
| GMR | 282,600 | 2 | 859,000 | 1.847B | 45.28 | 36.547 |
| LOW | 2,385,000 | 10 | 2,709,181 | 43.986B | 57.588 | 54.884 |
| MSO | 1,132,200 | 101 | 1,968,318 | 1.060B | 30.404 | 19.184 |
| NANO | 210,544 | 7 | 346,045 | 151.4M | 12.832 | 12.336 |
| PLUG | 913,028 | 5 | 715,409 | 505.4M | 6.244 | 6.244 |
| QLTI | 661,258 | 3 | 1,212,136 | 1.228B | 15.067 | 16.469 |
| TJX | 1,497,800 | 4 | 1,723,409 | 11.897B | 24.909 | 23.764 |
| TOL | 2,717,500 | 23 | 2,065,727 | 6.114B | 78.465 | 54.937 |
| WMB | 2,807,200 | 12 | 3,378,181 | 10.751B | 17.444 | 14.149 |
| ALD | 576,700 | 4 | 604,136 | 3.413B | 26.233 | 25.829 |
| CPN | 7,851,600 | 13 | 8,134,045 | 1.640B | 3.37 | 3.468 |
| GW | 1,632,700 | 5 | 1,865,909 | 1.293B | 5.715 | 4.908 |
| JCP | 1,640,100 | 34 | 2,239,181 | 12.691B | 43.877 | 39.672 |
| LTD | 1,263,900 | 25 | 1,804,636 | 9.718B | 23.75 | 22.311 |
| NEM | 3,889,500 | 28 | 4,448,863 | 19.490B | 42.969 | 43.294 |
| OCR | 557,000 | 7 | 965,454 | 3.705B | 32.727 | 32.769 |
| PRX | 494,700 | 1 | 718,954 | 1.265B | 38.743 | 38.353 |
| PDG | 2,110,400 | 6 | 2,070,909 | 7.336B | 17.568 | 18.14 |
| SWY | 2,722,900 | 22 | 2,235,272 | 8.101B | 18.613 | 20.172 |
| SPLS | 4,010,364 | 26 | 2,643,045 | 15.105B | 32.056 | 30.38 |
| CCU | 2,541,800 | 19 | 3,418,772 | 18.600B | 33.111 | 34.06 |
| PAAS | 779,476 | 0 | 684,772 | 1.079B | 15.856 | 15.437 |
| WON | 463,700 | 2 | 698,727 | 1.918B | 23.705 | 23.196 |
| ADCT | 5,342,743 | 9 | 7,483,772 | 1.613B | 2.381 | 2.338 |
| CTIC | 1,161,494 | 21 | 2,899,909 | 281.9M | 8.319 | 7.052 |
| HNZ | 1,424,900 | 6 | 1,089,000 | 12.749B | 37.45 | 37.384 |
| OVTI | 2,561,630 | 8 | 2,863,500 | 954.0M | 17.125 | 15.394 |
| TIF | 2,258,400 | 16 | 1,310,500 | 4.835B | 31.231 | 32.027 |
| UVN | 624,200 | 16 | 2,199,909 | 8.802B | 27.483 | 30.181 |
| AEOS | 1,958,423 | 54 | 3,018,318 | 4.150B | 47.538 | 39.16 |
| AZO | 1,349,000 | 53 | 858,272 | 6.824B | 92.804 | 84.251 |
| CHS | 1,708,500 | 26 | 2,170,636 | 4.854B | 43.653 | 41.83 |
| COST | 3,182,339 | 55 | 2,822,045 | 20.695B | 46.376 | 44.474 |
| ESRX | 919,649 | 24 | 756,863 | 6.252B | 77.851 | 71.849 |
| HVT | 37,700 | 8 | 83,636 | 370.1M | 16.889 | 17.414 |
| IRM | 552,800 | 11 | 746,954 | 3.892B | 28.975 | 32.814 |
| LIZ | 520,800 | 20 | 546,454 | 4.283B | 41.379 | 38.844 |
| PETM | 1,109,621 | 25 | 1,647,636 | 4.056B | 30.873 | 31.244 |
| TTN | 586,000 | 28 | 1,006,363 | 1.549B | 16.977 | 15.295 |
| KOSP | 433,504 | 18 | 413,727 | 1.287B | 33.304 | 35.248 |
| LSCP | 336,711 | 6 | 433,863 | 613.1M | 29.865 | 26.211 |
| SPW | 697,900 | 27 | 846,454 | 3.240B | 42.149 | 40.466 |
| CRDN | 1,316,176 | 14 | 1,026,363 | 590.5M | 33.57 | 40.197 |
| SKS | 835,000 | 42 | 1,167,454 | 2.183B | 14.869 | 13.641 |
| ACMR | 102,391 | 10 | 179,227 | 517.4M | 26.789 | 25.861 |
| ADRX | 1,033,391 | 11 | 1,027,590 | 1.650B | 22.082 | 22.344 |
| SAM | 33,500 | 10 | 42,454 | 319.1M | 23.496 | 22.716 |
| CBI | 188,100 | 13 | 219,909 | 2.235B | 41.389 | 33.788 |
| CHINA | 600,860 | 13 | 1,151,909 | 337.6M | 3.646 | 4.875 |
| KMRT | 3,167,195 | 104 | 2,093,409 | 12.287B | 101.758 | 88.74 |
| NTOP | 853,074 | 13 | 562,954 | 132.8M | 2.519 | 3.317 |
| QTWW | 315,803 | 12 | 397,272 | 251.9M | 5.338 | 5.68 |
ENDNOTES
[1] All of these examples were observed on CNBC in the past few months while writing the paper.
[2] This example was taken directly from Robert Kahn’s paper “The Road Less Traveled.” The numbers could be calculated for any company in this period.
[3] All of this information comes from Buffett’s paper “How Inflation Swindles the Equity Investor.
[4] All of this information comes from “Rational Versus Irrational Forecast” by Horace Brock.
[5] Mr. Brock’s explanation for the market price presented in his paper “Rational Versus Irrational Forecasts” is similar to Adam Smith’s explanation for the price being the market clearing price.
[6] This is one of the results found in Kurz’s Rational Belief Equilibrium model. The simplification can be found in Brock’s “Rational Versus Irrational Forecasts.” All of the results are from the RBE and are used without getting into their dense and complex proofs.
[7] This information can be found in Andrei Shleifer’s book Inefficient Markets; An Introduction to Behavioral Finance.
[8] This information was all released on www.fool.com, Friday, May 13, 2005, in an article called “Simplify, Simplify Your Stocks,” by Rich Smith.
[9] This is from Warren Buffett’s paper “Mr. Market, Investment Success and You.”
[10] All of these stock announcements and their proof of why the value of a company does not change following the actions can be found in any undergraduate finance course book.
[11] Since the announcement the price has partially corrected, more so for Merck than Pfizer.
[12] Bill Hall should receive credit for this explanation of why volatility cannot be risk.
[13] This was the principal result found in the paper by Eugene Fama and Kenneth French “The Cross Sections of Expected Stock Returns” published in 1992 by the Journal of Finance.
[14] This idea is not found in any of the references. It came from the genius investor William Stewart, Founder and CEO of W.P. Stewart Asset management. Their very successful method is to trade only a few safe stocks, proving it is possible to have high returns and low risk.
[15] Bill Hall also needs to receive credit for this idea. He is not in any of the references because all of his ideas were presented to me in conversation.