Are There Aliens in the Universe?

September 7th, 2009

IT is manifestly ridiculous to think that strange beings (perhaps with tentacles, three eyes, or infrared vision) are now blazing through the expanses of space in massive, nuclear powered spaceships. But of course, many ideas that sounded absurd at first have actually turned out to be true (e.g. black holes, dark matter and quantum mechanics). Let’s put aside our immediate gut reactions and dispassionately examine the evidence for the existence of alien life.

The Formation of Life

The theory of evolution tells us that given the right conditions (a sufficiently powerful source of energy, the right kinds of atoms, etc.) life can form through a natural and essentially automatic process. Scientists do not understand the precise details of how this occurred on our planet (which shouldn’t come as a surprise, given that the event happened billions of years ago on a microscopic scale during a time when earth had a very different chemical composition then it does today) but they do have reasonable conjectures. What seems very likely is that prior to life there existed what we might call pre-life: simple, self-replicating molecules, the first of which was formed by a lucky collision of atoms. These replicators would occasionally make errors while copying themselves, which most of the time would be disastrous to the reproductive capabilities of their offspring (destroying the possibility of further replication), but which every so often would lead to slightly more efficient replicators. Of course, copying requires the use of chemical materials, so the replicators would be in competition with each other for molecular resources. Over time, through the processes of natural selection, those replicators that were most efficient at surviving and copying themselves in the prevailing environment would spread wider and faster than the others. Over many generations, the lineages of replicators that survived would get progressively better suited for their environment, very slowly becoming what we would recognize as life.

If this process of life generation can spontaneously begin on earth, then it can occur on any other planet, assuming that the planet has sufficiently favorable conditions for a sufficiently long period of time. In particular, since the laws of physics on earth appear to be precisely the same as those that govern the rest of the universe, and since the universe looks to be approximately the same in every direction, we should anticipate seeing other earth-like bodies distributed throughout the universe (in terms of size, position within their solar systems, chemical composition, etc), and we should expect that these planets have a probability of developing life that is similar to the chance earth had. It may be possible that life could take forms that are difficult for us even to imagine, occurring on astronomical bodies that are not very much like earth at all, but since life occurred once on a earth-like planet, earth-like planets are our best guess for where we can expect to find alien life.

It is estimated that there are far more than a trillion planets†† in the universe, providing a staggering number of opportunities for life to begin. Furthermore, the universe is more than 13 billion years old†, so there has been an enormous amount of time for life creating processes to take place. Given enough planets, it is inevitable that at least one will be sufficiently like our early earth to house life. Given enough time, it is inevitable that life will eventually form on such a planet. Hence, the spontaneous formation of life on earth indicates that life very likely exists elsewhere in the universe, though estimating the actual probabilities involved is tricky. The question of exactly how much life has existed in our universe can be reduced to a question that can be studied empirically through scientific means. Essentially, one needs to calculate how many planets (or other astronomical bodies) in our universe today are likely to have undergone long periods during which conditions were suitable for life to begin. Unfortunately however, even with the best telescopes our ability to peer through the vast expanses of space is severely limited, and our understanding of planet formation and evolution is far from complete, so this question is unlikely to be adequately answered for a long time. Ultimately though, the question of the existence of aliens is a scientific one, and therefore we should expect scientists rather than philosophers to eventually have the greatest insight into its answer.

Traveling Through the Universe

Some people believe that intelligent life is unlikely to exist outside of our planet, because if it did, we likely would have encountered it by now. This belief reflects an ignorance of the incredible size and spaciousness of the universe. To give an illuminating example, suppose that humans were interested in traveling to the star (other than the sun) that is the closest to our earth. This star is Proxima Centauri (a red dwarf, it turns out), at a distance of about 4.2 light years from earth. That means that if a space shuttle traveled to Proxima and back at the speed of light, 8.4 years would have elapsed on earth by the time they returned. In practice though, the equations of Einstein’s theory of relativity tell us that it would take an infinite amount of energy to get a massive object to move at light speed. We therefore might employ the more realistic assumption that the space shuttle traveled at about 25% of the speed of light (or, as a physicist would say, 0.25 C). This would still be an incredible scientific achievement, considering that it is about 37,000 times the speed of the fastest plane. To get a space shuttle (weighing, say, 24,000 kg like some space shuttles do today) going at this speed would require a minimum (assuming perfect efficiency in converting potential energy to kinetic energy) of about 67 million terra joules (actually, slightly more, taking into account relativistic effects), which is approximately 280 times the energy released by the most powerful nuclear weapon ever created. Of course, naively setting off 280 nuclear weapons of this kind would be far more likely to kill all life on earth than to get an object close to the size of a space shuttle traveling at the desired speed. As a matter of fact, the process would have to progress rather slowly. Since the human body is limited in the amount of acceleration it can withstand (before blood pools heavily in the legs, and worse), it would take a minimum of 15 days of accelerating to get up to this enormous velocity (unless drastic means were taken, such as keeping the astronauts submerged in fluid during acceleration). In the end, even with the stupendous speed of 25% of the speed of light, a journey to Proxima and back would take over 33 years from the point of view of someone on earth, more than a third of a human life span, and long enough to ruin all of one’s personal relationships. And let us not forget, all this would get us is a roundtrip voyage to our second closest star! The universe is an extremely spacious place, and even for an alien civilization far more advanced than ours, it would take an enormous amount of time to explore even a single galaxy, let alone the more than a hundred billion galaxies that are thought to exist. Our own milky way galaxy is thought to contain approximately one hundred billion stars, and from the point of view of someone on earth, a traveler moving at the speed of light would take approximately 26,000 years to reach earth from our galaxy’s center. In particular, this means that aliens located at our galaxy’s center could not possibly be aware of the first human radio broadcasts for many thousands of more years. Finding alien civilizations, and exploring a galaxy is long, hard work!

There is an important point to be made about the way in which Einstein’s theory of relativity relates to travel at speeds approaching that of light. Because of an effect known as time dilation, time literally moves slower for a traveler that accelerates than it does for the people (or should I say creatures?) on the traveler’s home planet. At speeds like 25% the speed of light, the effect is a rather minor one, but at 99% the speed of light or faster it is very pronounced. In a sense, this provides a space travel loophole, because an alien could theoretically travel extremely long distances at close to the speed of light without aging very much (though, the rest of the universe would continue to age normally of course, so their loved ones would probably die off before they returned from their journey). For example, while a trip from our galactic center to earth would take about 26,000 years for a traveler moving at the speed of light from the point of view of someone still on earth, from the point of view of the traveler himself the journey would feel almost instantaneous. The trouble with using this method for space travel, however, is that the closer to the speed of light one wants to travel, the more energy is required to do so (with, as we have said, an infinite amount of energy being needed to travel at light speed exactly). Hence, time dilation comes at the price of dramatically increased energy requirements. It is also probably worth mentioning that a ship traveling at these sort of speeds would be insanely difficult to navigate. There would be very little time to change course to avoid any interstellar objects, and at the speed of even only 25% the speed of light, a rather small piece of rock or ice carries an enormously destructive amount of momentum. All this being sent, with phenomenal technology, an enormously plentiful energy source, lots of time for acceleration, incredibly good navigation systems, no desire ever to return home again, and a lot of luck, aliens might be able to get from planet to planet quickly without aging very much in the process. The amount of aging they would undergo on such journeys depends on how close to the speed of light they can get without destroying themselves or using up their energy source. A hypothetical method that has been proposed for achieving speeds close to that of light is the Bussard ramjet, which involves using powerful electromagnetic fields to harvest free floating space particles during flight, and converting them to energy with a fusion powered rocket.

What about traveling at speeds beyond that of light? Unfortunately, as far as physicists can tell, no object can ever go faster than light. Of course, we can never rule out the possibility that science not yet discovered will one day allow that possibility, but the extremely well validated theory of relativity currently denies it. That being said, there are at least a couple of ways that the light speed constraint can theoretically be circumvented without actually breaking the ultimate speed limit, but they may not be of any practical use.

Quantum theory predicts the existence of “wormholes”, which are essentially open passages that connect two points in spacetime. While wormholes have as of yet never been observed directly, they may exist at an extremely small scale, popping into existence for miniscule amounts of time and bridging together very short spacetime distances. Expanding or creating large wormholes, getting them to stabilize for reasonably long periods, and controlling which parts of spacetime they connect are currently very far beyond the scope of modern science. It could easily turn out that worm holes are essentially useless from a space traveler’s perspective, no matter how advanced technology has become. Some initial calculations done by physicists of what it would take to create a useful wormhole make demands that are probably beyond the scope of ANY civilization. Some physicists have argued that large, stable wormholes could already exist strewn throughout the universe, a consequence of the inflation of the universe after the big bang. While wormholes like these could potentially be useful for interstellar travel, locating them and actually getting to them could itself be extremely difficult, and since their pathways would already be determined they would not provide much flexibility to a traveler. It is worth mentioned that these strange tunnels can cut through time as well as through space, transporting a traveler into the past while at the same time altering his position (though a wormhole could not take you back to a time prior to when it was created).

Another, totally different way that the speed constraint of relativity is sometimes circumvented is through the phenomenon known as quantum tunneling, where tiny particles jump locations approximately instantaneously. Unfortunately though, this is inherently an unpredictable process, and therefore not useful for controlled traveling. What’s more, like worm holes, this phenomenon is only known to happen at miniature scales, far smaller than even a single celled organism. In the macroscopic world of massive objects like people and spaceships, quantum tunneling is never observed.

As we have said, if aliens managed to achieve speeds nearing that of light, they would be able to explore the planets of their galaxy without aging a great deal. However, from the point of view of planet earth the process would still be extremely slow (the aliens would experience time dilation due to their enormous acceleration, causing time to run more slowly for them than usual, but we would age at our normal pace). If, for example, there were aliens at the center of our galaxy traveling at almost the speed of light directly towards earth, they might find earth in what to them is a few years, but what for us is more than 500 generations. Hence, even if aliens knew where we were located, had a desire to get to us, and didn’t care about ever returning home (after all, their own civilization might be extinct by the time they returned) we would be waiting an enormous amount of time before they got here. By the time they arrived so much time would elapsed that our planet might be destroyed, or our technology might have become as good as their own (making us a potential threat). Unless an alien civilization was lucky (or unlucky) enough to have evolved on a planet very nearby us (by which I mean, within a few dozen light years), even discovering where we are located would be highly problematic. While it is true that the radio waves that we transmit travel at the speed of light, and might potentially be detected by another civilization, these signals grow dramatically weaker as they propagate away from earth, and by the time they are a hundred light years out may be extremely hard to detect (especially when mingled with many natural interstellar sources of noise).

It is probably worth mentioning that there are some reasons to think that aliens might not travel all that much around their galaxies even after they are able achieve speeds near that of light. For one thing, humans already have the technology to destroy all life on earth, and we aren’t yet anywhere close to having ships that can quickly carry humans through interstellar space. It may well be the case that most alien civilizations that exist destroy themselves long before gaining these capabilities. If, as seems to be the case, creating massively devastating weapons is much easier than near light speed travel, civilizations might generally not last long enough to travel. On the other hand, if near light speed travel is sufficiently difficult to achieve (requiring, say hundreds of thousands of years of research by modern humans), then species might tend to be destroyed by natural disasters (such as supernova) before acquiring the technology. What is more, it is interesting to consider the role that virtual reality would likely play in an extremely technologically advanced civilization. If essentially any experience can be had virtually, the need felt to travel outside of one’s own planet (let alone, to ever leave the virtually constructed world) may become limited. Once a civilization comes to construct and accept a virtual world that accurately simulates experiences, but in which one can create or do whatever one one wishes (perhaps even invoke pleasurable feelings upon command), how much time would creatures really choose to spend in the real world?

Aliens Here On Earth?

What is a person to make of the innumerable tales of alien abductions, alien autopsies, crop circles, and spaceship sightings that have been floating around since the 1940’s? While it is impossible to examine every single one of these cases (there are far too many), upon close examination every case that I know of that was thoroughly investigated did not provide solid evidence for alien life on earth. Most of the alien abduction stories come with no corroborating evidence whatsoever (only witness testimony), and most of them occur just after (or during) sleep. Hence, it is impossible to rule out the very mundane explanations of lucid dreaming, sleep paralysis, deliberate fraud, misperception, drug use, illness, and psychosis as explanations for these alleged experiences. Once the idea of aliens became popularized back in the 1950’s alien creatures began to appear in great numbers in people’s dreams and hallucinations. As far as crop circles go, those have essentially been debunked as the work of mischievous (and creative) humans. A number of UFO sightings have turned out to be either unusual aircraft (such as air balloons), normal aircraft flying in formation, normal aircraft with unusual lighting, meteorological events, or tricks of the nighttime sky coupled with human perception errors. While many UFO sightings have gone unexplained, a lack of explanation is a far cry from proving that aliens are here on earth as there are dozens of possible explanations for a person claiming to see moving lights in the sky. In order to prove a point, professional skeptic James Randi once claimed on a radio show to have just seen a UFO. People began calling into the show, claiming also to have seen the same UFO that evenining, unaware that he had made the sighting up. Unfortunately, even photos of UFO’s do not provide good evidence as they can easily be forged (in fact, many of them are known to have been), or are ambiguous as to their interpretation. As far as alien autopsy videos go, those I have seen are obvious or known fakes (like the alleged Roswell autopsy video). Essentially, there doesn’t seem to be any strong evidence behind the alien sighting phenomenon, and it is clear that there is an enormous amount of human psychology involved. Even if aliens are on earth, the vast majority of alleged alien sightings are undoubtedly not genuine. Until actual alien technology is found (that has a function or material composition unachievable with human technology), an alien is actually detained, or video of aliens is taken that could not have been forged using computer generated imaging, it is wise to remain skeptical of stories about aliens.

An important point to keep in mind is that the fastest way that aliens have to discover that intelligent life exists on earth is to detect the radio or microwave signals that we produce. However, if the alien’s home planet is hundreds of light years away then our earliest signals would not even have reached them by now! In particular, since the invention of radio is less than 150 years old, the only possible civilizations that could have discovered that there is intelligent life on earth must be within 150 light years of us. Even worse, if aliens travel at a maximum speed of 25% of the speed of light, the only way that they could have both detected our signals and traveled to earth is if they were within 30 light years of earth when we first started broadcasting, which is a very tiny sphere compared to the size of our galaxy.

Contacting Aliens

While it is very unlikely that aliens have arrived here already, if humans continue to exist for another one hundred thousand years (admittedly a somewhat dubious prospect), it would not be terribly surprising if contact with aliens occurred at some point, most likely through electromagnetic signals rather than through direct face to face contact. Astronomers have now broadcasted messages into space, designed specifically to be detected and interpreted by technologically advanced aliens. Because of their design, these signals are more likely to be detected and properly interpreted than ordinary radio or television broadcasts. Unfortunately, contact with aliens may well be a very bad idea from the point of view of human survival. While aliens could potentially be friendly, there is reason to expect the opposite. Evolution, wherever it occurs, is a highly competitive process, requiring creatures to kill each other for resources. As essentially all creatures on earth (including humans) have many selfish and exploitative tendencies, it seems likely that aliens will as well. Under natural circumstances, creature that are too altruistic tend to be taken advantage of by more selfish individuals, and hence weeded out of the gene pool.

If humans are detected by an alien civilization in the next hundred years, the aliens will almost certainly have far superior technology to our own (by the very fact that they are able to detect us at all), and therefore could likely annihilate us with ease if they felt we might one day be a threat. With sufficiently powerful technology, for example, they could launch a weapon at us at near light speed. By the time we could even detect such an object (if indeed we would be able to detect it at all), there would be little time for us to understand it or react to prevent our destruction. The sad truth is that much of the time when groups of humans have encountered those who are much less technologically advanced than themselves (but who, nonetheless, are in control of useful resources), the weaker group has been suppressed, enslaved, or annihilated. Just look, for example, at the colonization of North America and Africa by Europeans. Unfortunately, it is not terribly unlikely that aliens would be similar to us in this regard. Even if there were only a 30% that the aliens would decide to kill us all, would that really be worth the risk? One thing to keep in mind is that if aliens do ever receive our signals and choose to respond to them in kind, the wise thing for them to do would be to obscure the origin of their messages, perhaps by reflecting them off of astronomical objects (to avoid the danger that we one day develop technologically strong enough to harm them). Hence, it is unlikely that contact with advanced aliens will actually allow us to identify their location.

Conclusion

While technologically advanced alien life is quite likely to exist elsewhere in the universe, it seems that it would be very difficult for these creatures to travel to earth, and perhaps even detect our existence in the first place. Moreover, if they did try to travel to us, it would almost certainly take an extremely long time (from our point of view) for them to make the journey. Finally, if aliens do visit us, there are reasons to think that the visit may be hostile. Unfortunately (or, perhaps quite fortunately) our only interactions with aliens in the next hundred years will almost certainly be only in our imaginations.

Posted in Evolution, Science, Skepticism, Truth | 2 Comments »

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

August 1st, 2009

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”.

Posted in Finance, Skepticism | No Comments »

Distinguishing Evil and Insanity : The Role of Intentions in Ethics

July 29th, 2009

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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