The Myth of “the Market” : An Analysis of Stock Market Indices

Posted on August 1, 2009 by clockbackward

The theoretical U.S. “market” that is so often spoken of by stock investors is really just a convenient fiction. What does the term really mean? The difficulty with defining it can be seen as soon as we ask ourselves which stocks the market should include and which it should exclude. Should it consist of only U.S. stocks or are there reasons to include foreign companies that do a lot of business in the U.S.? If we decide to only include those from the United States, then are stocks to be counted only if they are headquartered in the U.S. or is trading on a U.S. exchange good enough? Should the market include only larger companies that we are probably more likely to buy, or should it include companies of varying sizes including penny stocks? Should stocks be limited to those that trade on major exchanges (like the NYSE and NASDAQ) or should it also include stocks from lesser exchanges (like the American Exchange) or even pink sheet and over the counter stocks?

Suppose, for the sake of argument, that we somehow decide which stocks to include and which to exclude in our definition of the market (we might call this our “universe” of stocks). Matters get further complicated when we try to figure out the performance of our market over a given time period (for example, if we want to answer the question of whether the market was “up” or “down” in the past week). Should the market’s percentage return be defined as the average percentage return of all of our chosen chosen stocks? Or could we use the median return of these stocks instead? Or perhaps we should take a weighted average of each of the stock returns, where the amount that each of these returns counts is proportional to the market capitalization (a.k.a. market cap, which is the number of shares outstanding times the share price) of each stock (as in the Russell 1000 index). On the other hand, rather than weighting by market cap, maybe we should weight each stocks return by its float, which adjusts the market cap to include only those shares that are publicly available for trading (as in the S&P 500 index). One might even suggest that we weight the returns of each stock by the stock’s price (as in the Dow Jones Industrial Average).

How is one to decide between all of these different selection and weighting alternatives? Some popular choices to use as our definition for the U.S. market are:

1. The Dow Jones Industrial Average (a.k.a. The Dow) : The Dow is an infrequently updated group of thirty stocks from U.S. exchanges (but never utility or transportation companies) that are selected by the editors of the Wall Street Journal. The returns of these stocks are weighted proportionally to each stock’s share price. The Dow is probably the most frequently quoted stock market index in the world today, as well as the oldest market indicator (started in 1896). Unfortunately, it is also one of the worst market indexes in existence, in part due to the technological limitations at the time of its creation. Although highly correlated with other indices like the S&P 500, the fact that the Dow consists of only 30 stocks means that at times it can deviate substantially from broader market indices due to the volatility of individual stocks. What’s more, the constituents of the Dow are not generally representative of the industry breakdown of the stock market as a whole or of the United States economy. Finally, its method of weighting stock returns by share price is nonsensical: the share price is essentially meaningless, heavily influenced as it is by irrelevant factors such as the number of stock splits a company has had and the price at which shares were initially offered. It is time for America to abandon this subpar market index. The only really legitimate use that the Dow has is for looking at stock market characteristics over very long time periods (owning to its very early creation date). Unfortunately, as things stand today, when U.S. investors say “the market” they are typically referring either to the Dow or the S&P 500.

2. The S&P 500 : A float (formerly market cap) weighted index of five hundred of the largest market cap stocks that trade on the NYSE and NASDAQ exchanges. These stocks are chosen by a committee at Standard and Poor’s with the goal that they are representative of the industry breakdown of the broader stock market, and also that each of the stocks has sufficient liquidity, “financial viability”, and other characteristics. This index is probably the second most often quoted after the Dow Jones, and dates back to 1957. The S&P makes a lot more sense than the Dow, given its float weighting (which, roughly speaking, counts the returns of each stock based on how much the stock’s tradable shares are worth as a fraction of the value of all tradable shares of stocks in the index). This makes much more sense than the Dow’s price weighting, and can be interpreted as trying to approximate the average performance of a randomly placed dollar placed in the market. What’s more, the S&P 500 consists of five hundred rather than thirty stocks, which makes it better able to capture broad market changes and less susceptible to individual stock volatility. Unfortunately, its choice of which five hundred stocks to include is somewhat arbitrary from the point of view of most investors. In terms of total market capitalization, the S&P 500 represents “approximately 75% of the U.S. equities market.”

3. The Wilshire 5000 : A market cap (or in one version, float) weighted index of all companies with U.S. based headquarters that trade actively on a U.S. exchange and have “readily available price data”. This index has some advantages over the S&P 500, in that it is much broader (containing well over five thousand stocks), including a great number of smaller companies that the S&P ignores, and therefore may work better as an indicator of the entire market. It should be noted, however, that since the Wilshire 5000 is market cap weighted, the largest stocks count far more than the smallest ones, and so as it turns out the movement of the S&P 500 and Wilshire 5000 are pretty similar in practice, both dominated by their largest constituents. That being said, sometimes the performance of small market cap companies can diverge substantially from large cap companies, which alone can lead to performance differences between the two indices. One draw back of the Wilshire 5000 is that highly illiquid stocks that have very large erratic (and sometimes practically meaningless) movements in their stock prices can add volatility to the index. Another problem that the Wilshire 5000 suffers is that it contains so many different stocks that it can be difficult to replicate its actually return. Buying the appropriate number of shares of each of its constituents is difficult, both because of the large number of stocks involved, and because of the potentially low trading volumes that these stocks may have. This can be be a substantial draw back, as there are many investors who are interested in being able to achieve the “market” return (or, at least, a very close approximation thereof).

4. The Russell 3000 and Russell 1000 : These market cap weighted market indices contain the three-thousand or one-thousand stocks (respectively) with largest market caps that have headquarters in the U.S.

5. The Russell 2000 and S&P 600: These market cap weighted indices are designed to track the results of the smaller companies in the market (and are generally known as small cap indices). The Russell 2000 consists of the two-thousand smallest stocks from the Russell 3000, and represents approximately 8% of the Russell 3000′s total market capitalization. The S&P 600 consists of six hundred stocks that are selected in a manner similar to that of the S&P 500, but which are limited to have market caps between $200 million and $1 billion, covering approximately 3% of the total market cap of U.S. equities markets. For some investors, the Russell 2000 or S&P 600 may be more reasonable benchmarks to compare their performance against than large cap indices like the S&P 500. Since the S&P 500 is market cap weighted, and the largest market cap stocks are so very much larger than the average stock, the S&P 500 has a tendency to have its movements be dominated by a small number of extremely large companies. For investors that tend to buy smaller companies, the performance of the S&P 500 simply may not be that relevant to them. In practice, small cap and large cap indices can diverge quite substantially in their performance, especially over periods on the order of a few months. It is worth noting that since most stocks in the market are not as large as those in the S&P 500, the small cap indices may do a better job of capturing the behavior of more “average” stocks. On the other hand though, since people tend to think of the large cap indices like the S&P 500 as being “the market”, the large cap indices may do a better job of capturing market sentiment than small cap indices.

6. S&P Equal Weight Index : This index is constructed just like the S&P 500, but instead of weighting stock returns by market cap, the returns of all the constituent stocks are simply averaged together. This leads to a different sector allocation than the S&P 500, and performance that can differ fairly substantially. This benchmark may be appropriate for, say, investors who are limited to invest in only stocks with a large amount of liquidity, but who (once this constraint is satisfied) are not more likely to prefer larger stocks over smaller ones. Equal weight indices effectively capture the average performance that would be achieved if stocks were picks at random from the chosen stock universe.

As you can see, there are a large number of different indices that are commonly used, each of which has at least some claim for being called “the market” (at least, from the point of different individual investors). Ultimately, the best choice of which index to use depends on one’s goals. In many cases market indices are used to benchmark an investor’s performance, essentially determining whether she has performed better than her competition or asset class. In that case, the choice of which stocks to include in your definition of the market should effectively represent the universe of assets from which the investor has decided (in advance) to select their investments. For example, if upon founding their business, an investor has determined to only buy large market cap companies from South East Asia, then the market for that investor should consist only of stocks that meet those specific criteria.

As far as how stock returns should be weighted when constructing an index for benchmarking an investor, the two most natural choices are market cap weighting and equal weighting. Market cap weighting produces an approximate measurement of the average performance of each dollar that is allocated to a universe of stocks, whereas equal weighting produces a measurement of the average performance of each of the stocks themselves. If we want to answer the question of whether an investor’s capital outperformed the average return of a random dollar allocated to her universe of stocks then market cap weighting is the natural choice, whereas if we want to see whether an investor’s performance beat how one would do if they selected stocks randomly then equal weighting makes sense. Unfortunately, since smaller market cap companies tend to have larger, more random and more erratic swings in price, equal weighting stocks (especially fairly illiquid ones) can lead to very volatile (and sometimes essentially meaningless) market indices. The S&P Equal Weight Index avoids these problems to a large degree by limiting its universe to only very large companies, which tend to be very liquid and hence less prone to large, sudden fluctuations in stock price.

It is worth noting that while market cap weighting does have a certain intuitive appeal, it does not, by any means, do a perfect job of measuring the average performance of each dollar in a market place. One major problem is that market cap is not a fully satisfying measure of how much money is currently invested in a given stock. The problem arises because the price that we can sell one share of a stock for today (which is the price used in the computation of market cap) is not necessarily the price per share at which we could sell as many shares as we own (in fact, if we own a large block of shares we will often have to move the price slightly below the current market price in order to get those shares sold). This being said, if there is a better way than market cap weighting to measure the average dollar performance in a universe of stocks, I am not familiar with it.

Beyond benchmarking purposes, people frequently use measures of market performance as economic indicators, essentially treating the stock market as a proxy for business as a whole, or as a measure of the average performance of a dollar invested in the stock market. In these cases, it is generally desirable to use indices like the Wilshire 5000 because it consists of a very large number of companies and is market cap weighted. Since smaller companies do account for a significant portion of both business activity and stock market investment in the U.S., narrower indices like the S&P 500 may not be adequate for these economic indicator purposes.

In conclusion, while there are many possible ways that we may define the market, some of which are quite similar to each other in construction or performance, we should attempt to find the best possible definition to suit the particular task at hand. Ultimately, with so many options available, there is no reason to settle for a market index that is only “good enough”, since better decisions can be made using an index that is “just right”.

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Distinguishing Evil and Insanity : The Role of Intentions in Ethics

Posted on July 29, 2009 by clockbackward

AFTER a little reflection, it is clear that the morality of a person who carries out an action doesn’t just depend on the action itself, but rather depends on the state of mind of the person who performs it. This holds for pretty much every commonly used definition of morality. Suppose, for example, that I was tricked into believing that giving money to a certain charity would help the poor, when in fact the donation was being funneled to gangsters. Generally, Christians, Buddhists, Utilitarians, Kantians, and most everyone else is in agreement that, although the consequences of my action were bad, I am not not bad for carrying out the action because I misunderstood the action’s nature. On the other hand, if I willingly chose to fund gangsters, almost everyone would be in agreement that the action would reflect poorly on my character, even if the net result of such funding was essentially the same as in the case where I thought I was donating to charity. To give another example, there are very few who would say that a person is good for giving money to the poor merely to impress a good looking date, whereas many would call the person good if they donated out of genuine concern for the welfare of others. Hence, pretty much however one defines ethics, there is widespread agreement that it is not our actions themselves that define how good we are, but rather the intentions underlying our actions. An action (e.g. giving money to charity) is compatible with us being a good person if our thoughts that motivate us to carry it out are considered good (e.g. a desire to help others), but may have no effect on our goodness or even make us a worse person if the motivating thoughts are considered bad (e.g. a desire to help only myself).

What is curious is that while there is little dispute that it is legitimate to evaluate the goodness of people based on the goodness of their intentions rather than on the goodness of the consequences of their actions, many people are not willing to carry this logic out to its ultimate, somewhat startling conclusion, namely that a number of people that are generally thought of as “evil” may not really be, and in some cases, may even be “good”.

To illustrate this point, consider the hypothetical case of a person who is schizophrenic, and whose delusional thinking has led him to believe that the only way to save the world from unprecedented disaster is to blow up a certain office building while it’s full of workers. If this man were to carry out this terrible act, our instincts would inevitably be to label him as evil, whereas his intentions could demonstrate that he is quite the opposite. If he not only did not want to blow up the building, but was in fact repulsed by the idea of hurting other people, and only carried out the bombing due to his mistaken belief about the action saving the world, then it seems as though he was in fact being genuinely good rather than evil since his intentions were very good, and he likely underwent enormous stress and effort (including overcoming his psychological revulsion to murder) only for the purpose of doing what he felt was right.

At this point, some people may object that such a person with schizophrenia should still be blamed for his bad action, since he has a responsibility to act in “accord with truth”, and to verify the reality of his beliefs prior to acting. But this argument fails to take into account the experience of people suffering from schizophrenia: in some cases they have no inkling whatsoever that they are delusional. If a person’s delusion does not seem delusional to them in the least, how can they be blamed for failing to see or question their delusional?

Another objection that may arise relates to the belief some people have that “good cannot come from evil” (or, similarly, that “evil cannot come from good”), which in this context may imply that even though the mentally ill person believes that they are doing a good thing by blowing up a building, the potential goodness of their intention is tainted by the evilness of the consequences. An example can help illustrate the problem with this way of thinking.

Consider a hypothetical situation where we are forced to make the choice of pulling either one of two levers. Suppose that the first lever will lead, with 90% probability, to the horrifying torture and death of one thousand people, and with 10% probability to us receiving one million dollars in cash. The second lever will lead, with 90% probability, to us receiving moderate injuries, and with 10% probability to one person being subjected to horrifying torture and death. Pretty much everyone who believes in morality, I think, would agree that pulling the second lever is the moral thing to do (since it makes the torture and death of others much less likely), whereas (psychological consequences aside) it is selfishly better for the individual to pull the first lever (since, that way injuries to our own body are avoided and there is a chance at nabbing the million dollars of cash). On the other hand, if a person were to really pull the second lever, despite that being the obvious ethical choice, there is still a 10% chance that a stranger would be subjected to horrifying torture and death because of that decision. To argue that “good cannot come from evil” (in the way discussed above) is to imply that the morality of my choice depends on whether (due to random chance alone) pulling the second lever led to bad consequences. When attempting to act ethically, however, all I can do is act in the way that (probabilistically) maximizes the amount of good that I believe my action tends to do. To hold me accountable for the actual realized consequences of my action, even though those consequences could never be known to me in advance, is to effectively determine how good I am based on the random roll of a die. The implication would be that ten people could carry out the same action for precisely the same reason, and yet nine of them would be labeled good, and the tenth labeled bad, simply because the tenth was unlucky. This is a conclusion that, I think, few people are willing to live with.

But what are the practical, real world consequences of goodness being based on intentions rather than actions? We have seen already that it may alter our assessment of the insane. More bizarrely though, it may influence our opinion of the deeply religious as well. People who commit acts that (they genuinely believe) are inspired by God’s will but (according to those who do not believe in the same religion) are of a heinous and destructive nature, are very often labeled as “evil”. But in many cases religious fanatics are absolutely convinced that their actions are “right” and even good for human kind. In such circumstances, it seems that “delusional” would be a fairer label to apply than “bad”. Going a step further, it seems likely that many extraordinarily good people, who devoted their lives to doing what they knew was right, were in fact doing great harm because of false religious or spiritual beliefs. Take, for example, the case of Christian witch burners, some of whom must have genuinely believed that by murdering (what we know to be) innocent people, were removing a great evil from the earth.

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The Missing Definition of Morality

Posted on July 22, 2009 by clockbackward

It is common to hear discussions of whether an action is moral, as if “moral” was a word with a specific agreed upon meaning. Unfortunately, the word has so many meanings that its interpretation is extremely difficult without extra information. For example, if I say “murder is immoral”, I could actually mean any of the following:

1. Murder violates an abstract principle that I would like all people to live by.

2. The Bible (or some other religious text) forbids murder.

3. As a result of evolution and natural selection most people have an innate emotional aversion towards murder.

4. Murder is against the law.

5. Murder is labeled as being “immoral” by most people in my society.

6. Murder usually reduces the total net happiness of society.

7. The idea of murder provokes in me an emotional state that I associate with “wrongness”.

8. Nearly all religions urge us not to murder.

9. Nearly all societies have laws that punish murderers or have customs that ostracize them.

10. Most people would feel a sense of guilt if they committed murder.

Unfortunately, even dictionaries cannot clarify for us what the word “moral” means. Merriam-Webster’s dictionary defines “moral” as “conforming to a standard of right behavior”. Looking up the relevant definition of “right”, we find “being in accordance with what is just, good, or proper”. But the definition given for “good” is just as vague and circular as were the definitions for “moral” and “right”. The Compact Oxford English Dictionary is no better. It defines “moral” as “conforming to accepted standards of behavior.” Accepted by whom, and for what reason? The dictionary does not answer these questions, and hence does not provide us with an unambiguous explanation of what “moral” means.

A great many well respected philosophers begin by assuming that morality is a single, well defined thing (without actually defining it) and then spend their time arguing about what properties it must have. But if we haven’t defined morality, how can we derive it’s properties? If we cannot define what exactly we are discussing, how can we even be sure that we are really discussing a single entity at all? As the list above shows, there are many very different things that we might reasonably call “morality”, including our genetic moral intuitions created by natural selection, the societal rules that are deeply ingrained in us, religious laws, and certain abstract concepts about how to treat each other.

Some people claim that whenever someone says that an action is “moral”, all that person is doing is expressing a feeling or emotion about that action. This idea is easily proven to be false by the counter examples of, for example, Christians, Kantians and Utilitarians, who frequently use the world “moral” to refer to actions that are compatible with biblical teachings, the categorical imperative, and the happiness principle, respectively. These individuals likely have an emotional feeling that their systems of ethics are worthwhile, but nonetheless, they often speak of morality in direct reference to their philosophical systems, independent of their personal feelings. What is more, many if not most people believe that ethics actually refer to something true and objective (and perhaps even absolute and unchangeable). Even if they cannot exactly define what it is they are talking about, that does not at all imply that they are merely expressing their subjective emotion. It simply means that their conversation may be confused and may not convey much information, as generally happens when there is a lot of uncertainty over the meaning of the words that we are using. Nonetheless, many people who speak about what is ethical genuinely believe themselves to be expressing a true fact.

Ultimately, before we can decide whether a statement like “murder is immoral” is true, we must first decide what we mean by “moral”. When we don’t know the definition of a word, it is difficult to have a meaningful discussion that relies on it. If we decide that morality is simply whatever the law says, or is determined by what the Bible says, or is a genetic characteristic of human beings, then the question of whether “murder is immoral” becomes primarily an empirical and factual one. We need only check the laws for our country, or search through the Bible, or study human genetics and behavior in order to answer questions about what is moral. In practice though, typically when statements about morality are made there is rarely any explicit or even implicit definition of morality being used. Your average person relies on an intuitive sense of what is right and wrong. This intuitive sense is influenced by many factors including our genetics, the standards of the society that we live in, the religion that we practice, our personal experiences, and the philosophies that appeal to us. Unfortunately, it appears as though questions such as whether “is killing moral?” are unanswerable without further information about the sense in which “moral” is being used.

If the argument made thus far is true, then how can we understand the fact that nearly everyone seems to agree when it comes to certain ethical statements? For example, how can we account for the fact that almost all people in most of the societies that have ever existed have believed that many kinds of murder are immoral? Well, to begin with, it seems very likely that a strong predisposition to disliking murder (especially the murder of family members) is inherent in the human genetic code. More generally, our sense of what is morally wrong appears to be strongly correlated with what we feel an emotional revulsion towards, and those things that we find repulsive are influenced by our genetics. If most humans share a “moral feeling” that is caused by the genes that we share in common, then that provides a plausible explanation of why, for example, murder is generally thought to be immoral. It is not difficult to imagine that when pre-humans lived in groups, an aversion towards certain types of murder could increase an individual’s chance of survival (perhaps because would-be murderers had a high chance of being killed by their intended victim or the victim’s family). If this were the case then the process of natural selection could help make a revulsion towards murder a common trait among our ancestors. It may be illuminating to note that many types of carnivores, though feeding daily on other (typically smaller) species, very rarely kill members of their own species (even during fights that break out). This is likely due, at least in part, to the fact that members of a single species are usually fairly evenly matched in strength and fighting skills. A lion is very unlikely to be killed attempting to kill an antelope, but is fairly likely to be killed when attempting to kill another lion, so lions that focus on eating antelope rather than killing other lions may tend to pass down their genes more effectively (even though there are obvious reasons why one lion might be benefited if it does manage to kill another). What’s more, social species may ostracize the members of their group who they feel threatened by, which could dramatically reduce the chance of survival for a “murderer” (by which, in this context, I mean a creature that kills members of its own species). A “moral feeling” would be one possible way, among many, that our genes could urge us not to kill members of our own species.

It is worth noting that even if genetics is not the best explanation for why there are some generally agreed upon moral principles (e.g. “the murder of innocent people for personal gain is immoral”) , that still does not imply that morality is a single, well defined concept. The trouble is that people may come to the same conclusion for very different reasons. If a Utilitarian believes that murder is immoral because it increases suffering, whereas a Kantian believes it is immoral because it violates a universal principle, that does not by any means imply that the Utilitarian and the Kantian mean the same thing by the word “immoral”, or that their principles are generally compatible. Likewise, a Christian may ultimately feel that murder is wrong because of the Biblical commandment “though shalt not kill”, but will likely disagree with the Utilitarian about many other ethical questions (such as the wrongness of homosexuality or premarital sex) since the underlying principles guiding their beliefs are very different. The point is that although there is a reasonable amount of agreement that some kinds of murder are immoral, there is much disagreement as to why they are immoral.

The most difficult part about addressing moral questions such as “is murder immoral?” is providing strong reasons for choosing one definition of morality over another. For some reason though, the definition of morality rarely comes up in discussions about ethical questions. Unfortunately, if we fail to make a choice of definition then our conversation must remain vague or rhetorical. We may be able to convince other people to take our point of view (e.g. by appealing to their emotions, or demonstrating inconsistencies in what they say), but we cannot be sure that they (or even we) genuinely understand what we are discussing. It is a bit like having a discussion about interior design with someone who uses our definition of “table” as their definition of “chair”. We might sometimes have what may sound like a more or less intelligible conversation, and we may even convince each other of certain things, but we cannot truly understand each other.

You may find this discussion of morals very unsatisfying because deep down you are absolutely convinced that morality is a real thing, and that certain actions are universally and undeniably wrong. But your strong feelings about morality do not contradict the idea that “morality” is a highly ambiguous word. I am not arguing here that morality is meaningless, nor am I arguing that morality has no well defined definition to individual people or even to specific groups of people. Utilitarians, for example, can talk about morality with each other with little confusion, since they are working with a common definition. My argument, simply stated, is that the word “morality” means many different things to different people, and that discussions about what is moral often rely on the false assumption that all parties involved can understand each other’s words.

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