If, merely by holding a diversified portfolio, the aggregate risk can be reduced, then one would expect the return demanded for such a portfolio to be less than the sum of the returns of the individual stocks. Yet this is not the case. So we must assume either the portfolio is overperforming, the individual stocks are underperforming, or both. On the other hand, it would seem that the risk premium of any individual stock would be arbitraged away by people holding the most diversified portfolios containing it, thus it is strange that an individual stock could retain an undiversified risk premium. Thus it must not, at least not fully. Its return (and the price it sells for) is also determined by the availability for sale of other not-fully-correlated stocks and their characteristics, even ones that have no material effect on the company’s performance. This is a sure sign of value arising from the demand for the instrument unrelated to its underlying. It would seem to be mispriced as an individual stock. Perhaps an equilibrium will be struck, but it is still paradoxical to talk about the risk premium of individual stocks as a property of that stock alone.

It seems like a nice idea, but something is off. Firstly, these are leveraged portfolios with forced daily rebalancing, so depending on the amount of daily price variability, there is a non-trivial loss of several percent a year on top of costs. If a long-term leveraged position is wanted, one may as well buy the appropriate derivatives that underlie these ETFs, if that can be done.

Secondly, leverage is not free. This WSJ article nails the fixation on returns …

Until recently, public companies, mutual funds and pension funds generally steered clear of such risks. But the lines between risk takers and mainstream investors are blurring. In part, that’s because stock-market returns aren’t what they were a few years back. Between 2000 and 2006, the average annual return on the S&P 500 stock index was 2.5%, down from 28.7% between 1995 and 1999. Using derivatives and borrowed money is one way to try to boost returns.

… but although the return is better, the risk-adjusted return is more useful to look at. With true 2x leverage, only the risk premium is doubled at best, not the total return. On the other hand, if true 2x total return is supplied as they say, the implied leverage, and hence risk, has to be much higher than 2x. That’s something to look out for. Granted, the amount of leverage can be adjusted by weighting with the 1x portfolio.

Here’s some random guy’s page. He’s a big proponent of using a total market portfolio: http://homepage.mac.com/j.norstad/finance/total.html

His hand-waving is almost convincing, almost. Okay, “J. Norstad”, let’s take you point by point.

Many people feel that the strongest arguments for investing in total markets are based on market history. Innumerable studies have shown that individual investors and even professionals like institutional fund managers and mutual fund managers have terrible track records trying to beat the market. For example, many studies have shown that total-market index mutual funds consistently outperform most actively managed mutual funds.

It is easy to see why most actively managed mutual funds must fail to beat their passive total-market index fund counterparts. The performance of “the market” is nothing more or less than the capitalization-weighted average of the performance of all the investors in the market. If some active managers outperform, other active managers must underperform. For every winner (a performer above the average), there must be a loser (a performer below the average). This is a matter of simple arithmetic. Index funds match the market’s performance minus their low expenses. Actively managed funds have considerably higher expenses than index funds because they must pay for expensive research into individual securities and sectors, and they must pay extra costs for frequent trading of individual securities. As a consequence, the average performance of all actively managed mutual funds must trail the performance of total-market index mutual funds by the significant difference in their expenses. John Bogle has done many studies that confirm that this is exactly what happens in practice.

The underlined part is a good observation. But to believe this weighting is efficient is suspect. Moreover, this guy likes to believe in “arithmetic”, well, precisely because this is a capitalization weighted average, it is quite possible on “arithmetic” alone for an overwhelming majority of participants (by number) to be outperforming the market by large margins, if they be of small capitalization (not saying it is so).

Bogle’s numbers are just averages. Over any given time period some active managers do in fact manage to outperform the market even if most of them do not. Is this luck or skill? If it is skill, we would expect those active managers who have outperformed in the past to continue to outperform in the future…

A few active managers like Warren Buffett and Peter Lynch have astounding track records over long periods of time. How is it possible to claim they were just lucky? Perhaps their success was indeed due to skill. Then again, perhaps even they were just lucky. After all, if you have 1,000 chimpanzees flip coins ten times in a row, it is likely that one of them will get heads all ten times. We call the chimpanzee lucky. If the chimpanzee were a mutual fund manager we would call it talented. In any case, whether it is luck or skill, these few long-term success stories are in the past. How is an investor supposed to identify the next Buffett or Lynch in advance?

This is a strong argument here. I give props.

The Efficient Market Hypothesis states that modern financial markets are “efficient.” This means that they quickly react so that prices reflect all available information. For example, new information can often cause prices to rise or fall on the world’s major stock and bond exchanges to adjust appropriately within only minutes. Prices of individual securities, market sectors and style segments, and entire stock and bond markets are therefore always “correct” in the sense that they always reflect the collective beliefs of all investors taken together as a whole about their future prospects.

I take some issue with this “correctness” argument. This collective “belief” as reflected in the price is a capitalization weighted average. Participants naturally have different objectives and beliefs, but are only able to assert their beliefs in accordance with their share in the market, which are determined by their wealth and willingness to take risk, not by any notion of correctness or diligence.

One major consequence of the EMH is that unless an investor is just plain lucky, it is impossible to exploit the market to make an abnormal profit by using any information that the market already knows. Another consequence is that for someone without any such private information, it does not make any sense to talk about “undervalued” or “overvalued” individual securities, sectors, styles, or markets.

Another consequence of the EMH is that the total market is always perfectly diversified. Other portfolios that deviate from the total-market portfolio are never “more diversified” than the total-market portfolio. In other words, it is impossible for any other portfolio to have both a higher expected return and lower risk than the total-market portfolio. (The technical way to say this is that the total-market portfolio is always located on the “efficient frontier” in academic risk/return models. This is true in both the classical single-factor risk model of Markowitz and Sharpe and in the newer three-factor risk model of Fama and French.)

There are several serious problems with this efficiency claim. First of all, any claim of market efficiency is dependent on the existence of arbitrageurs making it so. Even if risk and return of every asset can be perfectly predicted, it is not true that the market operates efficiently. This is clearly seen in various portfolio scenarios wherein a point on the efficient frontier is not obtained by averaging the assets held in the two extemal efficient points associated with minimal and maximal risk. Again, if the market consisted of two such extremal investors (each perfectly rational), the average allocation still would not be operating at an efficient point, in the absence of arbitrageurs.

Second, it seems to me the kind of arbitraging needed to achieve another point on the efficient frontier would be to borrow an inefficient portfolio, liquidate it and use proceeds to purchase the efficient portfolio of the same risk, then liquidate that at a later date, and use the proceeds to repurchase and repay the inefficient portfolio, in turn keeping the excess return. However, it isn’t clear what this “later date” would be to ensure an excess return.

Third, the market allocation that happens to optimize the needs of all arbitrageurs (each with own risk/return appetite) according to their peculiar capital investment amounts in the market has nothing to do with being efficient as an overall portfolio. It may very well be that no arbitrageur is holding the overall market portfolio, and that because it isn’t efficient.

Fourth and a major complication, forward-going risk and return are not known quantities, and are merely assessed by the participants of the market on an individual basis. So returns and risks of particular assets can at best be modeled as random variables (each with a distribution). It might make some sense for a class of participants who impute the same future risk/return on the assets to drive some arbitraging process that allocates as in the previous paragraph; but then, the distribution of efficient allocations among arbitrageurs holding different estimates on risk/return would not average to the efficient allocation given by taking the market mean future risk/return assessment of each asset as the actual risk/return. Even worse, arbitrageurs have no real way of making a survey of risk/return assessment to find the mean and they do not actually operate this way.

The EMH does not require that investors behave rationally. This is a common misconception. When faced with new information, some investors may overreact and some may underreact. Indeed, this behavior is expected and common. Markets would not behave the way they do in the real world if everyone always reacted in the same perfectly rational way to new information. All that is required by the EMH is that these overreactions and underreactions be random enough and cancel each other out enough so that the net effect on market prices cannot be exploited to make an abnormal profit. Stated another way, irrationality is irrelevant as long as it is unpredictable and unexploitable. Even the entire market can behave irrationally for a long period of time and still be consistent with the EMH, again as long as this irrational behavior is not predictable or exploitable. Thus crashes, panics, bubbles, and depressions are all consistent with a belief that markets are efficient.

It isn’t clear what is being discussed here: behavioral irrationality or underlying uncertainty. Pricing uncertainty may be unexploitable on average if fluctuations are noisy (one can always use luck), reflecting the randomness of the arrival of information, but that isn’t a sign of investor irrationality. Crashes and depressions aren’t necessarily irrational, though bubbles and panics may be. This sounds like word games, but if a certain behavior is called “irrational”, it is certainly judged against some information that contradicts it, and if that be the case, then certainly the behavior is exploitable on average (perhaps over a long time).

Here are a few examples of efficient reasons to differ from the total market:

1. A young investor with a stable job, a good education, and a solid foundation in his trade or profession feels capable of being more aggressive than average and holds, for example, an 80/20 stock/bond portfolio.

2. A retired investor with no pension uses his or her investment portfolio to supply living expenses and feels less capable of taking on risk than average. This investor, for example, might hold a 40/60 stock/bond portfolio.

–snip 10 more bullets–

Notice how these examples are in pairs. In an efficient market, for every set of investors with good reasons to deviate from the average in one direction, there is some other set of investors with equally good reasons to deviate in the opposite direction. These investors are in effect using the markets to make trades of risks which benefit both sides of the trade. Many academic theorists say that this is in fact what efficient markets are all about.

This is an almost trivial observation. These allocation strategies don’t come “in pairs”. Maybe if one presupposes everyone does indeed start with the total market, then they can arrive at their desired holdings by executing a series of pairwise trades in individual assets amongst themselves, without affecting the total market.

In the case of equal-weighting countries, people who believe that markets are efficient counter by noticing once again that if the cap-weighted international market percentage for some country is, for example, 15%, and if some behavioral analyst says that the proper weighting is some other percentage, say 10% or 20%, then the question to ask the analyst is “The international market thinks the proper weighting for this country is 15%, but you disagree – what do you know about this country’s prospects that the international market does not already know?” To an efficient market believer, equal-weighting countries or regions in international investing makes no more sense than equal-weighting sectors, styles, or even individual stocks in US investing. None of these equal-weighting strategies have anything at all to recommend themselves if markets are efficient.

Besides all the reasons prior, there are additional reasons to believe international capitalization weighting is not a priori reasonable. For one, global capital flow is far from liquid. Capital is often country-bound and filtered through currency exchange barriers and currency risk, especially in the emerging market. Some people just don’t have the choice of investing in certain markets, not because they would not like to. Secondly, information flow about global markets is not efficient. Thirdly, the objective of the investor in one country is likely to be far different from the objective of those in other countries or the country in which the capital project is taking place.

It isn’t bad to start with the total market if one is forced to be able to do only a few rough modifications to it (in a limited funds situation). However, why bother with this belief in efficiency based on the wrong assumptions, when one can pick a few assets (or asset classes as reasonable) and run optimization to find an efficient portfolio for the risk to be taken? One may need to track efficiency over time. Why deviate from the market? Because the market isn’t run by one investor like you and it isn’t going to be efficient for you or for anybody in particular. Not being able to exploit inefficiencies within the market doesn’t mean holding the market as a portfolio is efficient — those are two separate issues.