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Issue 1: Modern Portfolio Theory And The Roots Of Indexing As most indexers know, modern portfolio theory was developed in the early 1950s by Harry Markowitz, who went on to share the Nobel Prize in Economics in 1990. What Markowitz did was to propose that investment strategy should be based on the notion of a portfolio of assets whose interrelationships should be considered. Markowitz defined the concept of diversification in mathematical terms, as reflected by the correlations among the assets in the portfolio. He proposed that investors who wanted to achieve the maximum ex ante satisfaction from their investments should attempt to hold only efficient portfolios, which are those that maximize expected return for a given level of risk.1 Markowitz also provided the algorithms that would identify these portfolios. Yes, I know he did a lot more, but those are the essential ideas. These results were published in his 1952 article and 1959 book.2 Shortly thereafter, three economists, William Sharpe, John Lintner and Jan Mossin, began working on the notion of what happens to markets when people behave in the manner of maximizing expected return for a given level of risk. Almost simultaneously, these three pioneers of finance found two important results. The first is that every investor would hold a portfolio that consists of all risky assets in the market, which has come to be known as the market portfolio. The second is that the expected return on an asset is given by the risk-free rate plus a premium that reflects the asset's contribution to the risk of a diversified portfolio. The appropriate measure of risk for an asset was found to be its covariance with the market portfolio, a concept that has since been dubbed beta. Of course, this model became known as the capital asset pricing model (CAPM). Sharpe published his results in 1964, Lintner in 1965 and Mossin in 1966.3 Lintner died in 1983 and Mossin in 1987. Sharpe shared the Nobel Prize in 1990 with Markowitz and Merton Miller, another well-known financial economist, though not a contributor to modern portfolio theory. As noted, an important result from CAPM is that everyone should hold the so-called market portfolio. Trying to identify over- and underpriced securities and sectors of the market would be a wasted effort. It took around 10 years for this concept to make it into practice, but John Bogle, who had written a thesis in 1951 at Princeton on the idea of a fund that would replicate a market index, created the first index fund in 1976, which came to be known as the Vanguard S&P 500 Index Fund. The fund was not too popular at the start, new and unconventional ideas nearly always being initially rejected by the masses, but the idea slowly began to take hold and the rest is, as they say, history. It is important to understand that there is nothing in the CAPM or MPT that dictates that investors should hold an index fund. The theory says that investors should buy and hold a portfolio consisting of all risky assets. That such a portfolio is represented by an index is a stretch. For one, no index can truly represent the entire universe of assets. Even if stocks and bonds were contained in an index, there would still be gold, commodities, vintage automobiles, real estate, baseball cards, comic books, fine wines, and Angelina Jolie autographs for starters. In fact, anything that one might possess that can fluctuate in value would be part of the market portfolio.4 The omission of assets from the market portfolio is often recognized as an important consideration. In his classic 1977 critique of the empirical tests of the CAPM, Richard Roll demonstrated that omitting even one asset from the empirical proxy for the market portfolio could greatly skew the results. In practice, this notion has led to the creation of indexes comprised of more and more assets. But of course, we'll never capture everything. Well, it is asking a bit much for mankind to lump all risky assets together into a single portfolio, so we'll have to let the indexers off the hook on this one. Bill Sharpe has also advanced the notion that maybe it does not really matter. The idea of a truly global market portfolio might matter to some investors but perhaps not to most. So maybe a more limited definition of the market is acceptable.5 And even if we could put all assets into a portfolio, there is no assurance that investors would buy that portfolio and hold it. In fact, I am quite confident they and their advisors would not. Trading is way too much fun and watching a static portfolio can be about as much fun as watching reruns of ''The Weather Channel.'' But it is reasonable to ask whether an index is sufficiently broad to reflect a collection of risky assets that the average investor could hold. And it is reasonable to ask whether an index that itself is dynamic in composition or is actively traded by an investor is a strategy befitting its status as a descendent of MPT and the CAPM. My point? The indexing industry has benefited from the endorsement of its products by an academic lineage going back to Markowitz's MPT. Of course, it can easily argue that academic theory is no longer needed to support an industry that has stood quite nicely on its own for many years. But by association, indexing is oftentimes treated as synonymous with the buy-and-hold-the-market portfolio strategy. We need to remember what indexing is and what it isn't. What indexing is, is a strategy for investing in a collection of assets designed by a group of human beings who have defined what assets will be contained in the index and how these assets will be weighted or combined. What indexing isn't is a strategy that assures investors that they are maximizing expected return per unit of risk. We can never be assured that we are doing just that. Markowitz, Sharpe, et al., never addressed the question of whether we can 1) measure expected returns, volatilities and correlations, and 2) measure our feelings (called preferences) about risk. While there has been much research on these subjects since that time, I am not sure we have really made much progress.6
Issue 2: Market Value Weightings Recent debates have questioned whether market value weighting, or cap weighting as it is often called, is a good strategy. Let's see where that idea comes from. Assume that stock A goes up by 10 percent to $44 and stock B goes down by 5 percent to $28.50. Then company A is worth $4,400 and company B is worth $5,700. Thus, the stocks are now worth $10,100. The weight of A is now 43.56 percent and the weight of B is now 56.44 percent. A is now more weighted than before and B is less weighted. While some may disagree, the essential argument against market value weighting is this: A is now more expensive than before and B is now less expensive than before. Therefore, investing according to market value weights means to commit relatively more money (than previously) to more-expensive stocks and relatively less money (than previously) to less-expensive stocks. Some have even referred to market value weighting as essentially buying high and selling low. But the basic idea is that stocks that have gone up are ''expensive'' and stocks that have gone down are ''cheap.'' Therefore, such a strategy presumably makes little sense. That is absurd. Investing according to market value weighting is nothing more than going along with what other investors believe. In our example, A has become relatively more expensive than B because investors increased the price of A and decreased the price of B and did so for a reason. A is now worth more because investors are more optimistic about the future prospects of A and less so about the future prospects of B. To disagree with the beliefs of the majority of investors is not necessarily an unreasonable strategy. But to do so arbitrarily, mechanically and as an ongoing strategy is equivalent to following a continuous contrarian strategy. While we are all contrarians on occasion, outright rejection of market value weighting is simply saying, ''Sell what everyone else is buying and buy what everyone else is selling.'' I believe that history has proven time and again that in financial markets, the majority tends to be right more often than wrong. And even when it's not right, there is at least some comfort in being collectively wrong.7
Issue 3: Fundamental Indexing Fundamental analysis has some elements of a science. Financial analysts compute ratios, forecast dividends and growth rates, plug them in to formulas and come up with precise numbers. Then they go on CNBC and tell Maria Bartiromo things like, ''I see that stock hitting $75, maybe $80 a share in the next 12 months.'' Realistically, no one really has a clue. Fundamental analysis is as much of an art as it is a science. The ability to judge the quality of a company's management, surely an art form, is as important as the analyst's shot-in-the-dark estimate of future growth. But it's all fuzzy. No one can really identify the fundamental value of a company. But those who do well, such as Warren Buffett, will likely be good at identifying the overpriced and underpriced stocks. Buffett may not be able to tell you the true value of the company, but he seems able to often identify whether that value is higher or lower than the current price. That leads us to the notion of fundamental indexing. The fundamental indexers are basically telling us that they can identify overvalued and undervalued stocks and sectors. Their rules are often simple and sometimes easily replicated. They might pick high-dividend-paying stocks, or they might pick those stocks with the strongest earnings growth in the last year. Value and growth stock indexes are elements of fundamental indexing. Their compositions change based on the notion of whether a stock's price is high (growth) or low (value) relative to fundamental value. Fundamental indexers will often tell you that market value weightings are biased toward growth stocks. They reason that market value weightings, which tilt a portfolio toward higher-valued companies, therefore favor growth stocks and disfavor value stocks. But this notion is correct only if by definition value stocks are ones with lower market values. That might sometimes be the case, but surely not always. Investing cannot be as simple as preferring stocks with relatively low weights and eschewing stocks with relatively high weights.9 Fundamental indexing is a form of active trading in which the index creator pronounces that it will create and actively manage an index. Change ''an index'' to ''a portfolio'' and you have precisely the same thing. Of course, calling this ''indexing'' gives it a certain blessing; one whose origins are in MPT, CAPM, Markowitz and all that good stuff as I previously discussed. I have no problem with fundamental indexing—or, call it what it is, active trading—a point I will discuss in the next section. And I really have no problem with calling it ''indexing,'' because I can tell the difference between that and a strategy of buying and holding a broadly diversified portfolio. I'm not so sure, however, that everyone notices that difference.
Issue 4: Active Trading Now let us assume that through countless conferences, innumerable books, and the tireless classroom and research efforts of business school professors like myself, the next generation is firmly convinced that indexing and by that I mean buying and holding a broadly diversified portfolio is the way to go. Let's think about what would happen. With everyone solidly committed to indexing, there would be no technology and health care analysts.10 Information about the relative worth of the technology and health care sectors would be of little use because everyone indexes. Thus, the overvaluation of one sector is offset by the undervaluation of the other. Who cares if technology is overpriced and health care underpriced? We all buy and hold a proxy for the market portfolio. I'll tell you who ought to care. We all ought to care a lot! The firms in overpriced sectors will have relatively lower costs of capital, while the firms in underpriced sectors will have relatively higher costs of capital. This means that overpriced firms will be able to invest in more projects, while underpriced firms will be unable to invest in some otherwise attractive projects. Thus, capital is being allocated inefficiently. We can even carry the argument a degree further. Suppose the advocates of indexing notice that the sectors are frequently mispriced. Seeing an opportunity, they create indexes on the sectors. Now there is a whole new, or at least revived, profession of sector analysts processing information. Then we are likely to get more accurately priced sectors, but what about the component stocks? No one is following stocks, because everyone either holds the overall market index or the sector indexes. So now individual stocks become mispriced. Microsoft might then have access to inordinately cheap capital with which it can continue to grind out infinitesimally ''improved'' versions of Windows, while Eli Lilly, on the verge of curing ALS, has a cost of capital so high that it cannot sink any more money into R&D unless the disease becomes sufficiently widespread that it can sell enough of the drug to justify the investment. That's great. Our PCs still turn into the infamous ''blue screen of death'' and we have to hope more people get ALS. How depressing. Thus, with regard to active trading, I will just quote Martha Stewart, usually talking about something she made out of pine cones, ''It's a good thing.''11 This justifiable pursuit of alpha by large, sophisticated and low-cost investors who can afford it benefits us all. But most investors do not have the kinds of resources required to actively trade at a low enough cost with a reasonable expectation of generating alpha, so they ought to be content to index, knowing that they reap the benefits of efficient capital allocation in the economy.
Issue 5: Alpha First, it is extremely important to understand that alpha is not a measure of market- or sector-timing ability. It is a measure of selectivity that indicates the performance of a stock or sector relative to its benchmark or expected performance. Consider two investors, one an optimist who invests 100 percent of his money in an index fund and the other a pessimist who invests 100 percent of her money in cash, which earns 4 percent. In accordance with MPT, the index fund has a beta of 1.0, so the optimist has a beta of 1.0 and the pessimist has a beta of 0.0. Let's say the index earns 10 percent. The benchmark return of the optimist is: Optimist: 4% + (10% - 4%)1.0 = 10%. The benchmark return of the pessimist is: Pessimist: 4% + (10% - 4%)0.0 = 4%. The alpha of the optimist is: Alpha (optimist): 10% - 10% = 0% The alpha of the pessimist is: Alpha (pessimist): 4% - 4% = 0%. Thus, both optimist and pessimist have alphas of zero. But the market outperformed cash and the optimist was in the market. The optimist made the right call, and the pessimist made the wrong call. What gives? Well, what gives is that alpha does not measure timing; that is, the act of being in or out of a market or sector at the right time. In the example above, you can change the return on the index to anything you want and you will get the same result. Alpha will not distinguish two investors, one of whom makes the right market or sector call and the other of whom makes the wrong one. But to fully appreciate this issue, we need to distinguish timing from selectivity. Isn't one just a form of the other? For example, let's go back to our market with two sectors, technology and health care. Assume there are no individual stocks, just sectors. These could be two enormous holding companies that have bought up all of the component stocks so you can only buy the sectors through buying the holding companies. Let us assume one sector is undervalued and one is overvalued. The objective should be to buy the undervalued sector and sell the overvalued sector. If the investor does so successfully, it generates an alpha. But we have to be very careful in recognizing what alpha is. Alpha is the excess return earned from taking on risk that is not rewarded. In the MPT-CAPM world, an investor cannot expect a premium from investing in sectors and individual assets. That risk is diversifiable, and diversifiable risk does not qualify for a risk premium.12 Alpha is earned from taking on a degree of this type of risk that goes beyond the market value weightings. In practice, whether alpha can be earned from identifying mispriced sectors depends on whether there is a risk premium from investing in a sector, knowing that sector risk can be eliminated by diversifying across sectors. The CAPM says that there is no sector risk premium, but there are some who believe otherwise. Thus, in a loose sense, timing and selectivity can be viewed as similar, but there is a clear difference. Timing is buying an asset class that commands a risk premium before that asset class outperforms a different asset class, and selling the asset class before it is outperformed by a different asset class. Because that asset class commands a risk premium, quality timing is not reflected in alpha. Measuring timing performance requires something other than alpha, a topic we do not get in to here. Investing in an asset class that does not command a risk premium, on the other hand, can generate alpha. Hence, one can view an individual stock as a tiny asset class. Buying it in such a weight that more is held than dictated by a benchmark can lead to alpha, if you're good. Thus, we have to be clear on what an alpha is: earning a return from an asset that does not command a risk premium. Of course, using alpha assumes that we can adequately measure alpha, and that is an even more important question. But the editors would kill me if I got started on that issue. Maybe another time.
Issue 6: Stocks, Bonds And Long-Term Investing I have no problem with this argument. Stocks have indeed been the best long-term investment in the past. But some people mistake that notion for the idea that stocks are best for the long run because they diversify your risk across time. And they believe that because stocks have been the best long-term historical investment in the past, the same will carry over to the future. Let us take a look at what these views mean. The first idea is the notion of time diversification, which must be contrasted sharply with portfolio diversification. In the latter case, assets are combined in such a manner that their relative behaviors provided something of a canceling or offsetting effect. If well diversified, an investor will be unlikely to find that all assets will go down at once. Likewise, all assets will rarely go up at once. This is the notion of diversification that is the basis for buying and holding the market portfolio. Time diversification, on the other hand, is the idea that if you remain invested for a long enough period of time, bad performance in some periods will be more than offset by good performance in other periods. In contrast, if you are invested for only a short period and that period happens to have bad performance, you have no opportunity to recover in later periods. So the argument goes: Be in it for the long haul. This is a misleading view and arises from thinking of long-term market history as a large number of short subhistories rather than just a single period of long history. Consider Siegel's annual return data from 1802–2006, a period of 204 years. How do you view it? Is it one period of 204 years, or 204 periods of one year? If it's the latter, why not view it as 408 periods of six months, or 2,448 twelve-month periods, or so on? The finer we divide time, the more it appears that we have more experience than we really have. In fact, what we have is one period of 204 years, a time over which stocks outperformed bonds and earned a compound annual return of 8.3 percent. The next 204 years could be different. That market history is not an agglomeration of subhistories is easy to verify with a market simulator. While I will not take you through the details, consider a computer program generating random numbers indexed to have the characteristic of the same average return, 9.7 percent, and standard deviation, 17.5 percent, as stocks did over the 1802–2006 period. Each time you run the simulation, it generates a series of prices that represent a possible long-term history of the market. Each series will have come from a process with the correct annual return and standard deviation, but some realizations of that process will go up and some will go down. This means that it is quite possible that investing in the stock market for the 204 years since 1802 would have been a losing proposition. We have lived through only one 204-year period since 1802, and it happened to be a good one.14 Whether stocks will be a good long-term investment in the future is not really much related to the fact that they have been a good long-term investment in the past. But the two important issues are whether stocks will outperform cash; that is, whether there is a positive return to bearing the risk that stocks have, and whether stocks will deliver a compound return of 8–10 percent as they have in the past over the long run. Should stocks beat cash in the long run? They should. Except for inflation, stocks have risk that cash does not. If investors do not perceive that stocks will beat cash, they will sell stocks. In fact, that is pretty much what makes stocks go down as investors take money out of the stock market and put it into cash and other markets. The loss in stock prices makes stocks have higher expected returns, as investors pay less for stocks. This process continues until stocks have prices that are sufficiently low to imply high enough expected returns so that there is a premium expected for bearing risk. Therefore, it is extremely unlikely that stocks will not outperform cash and all other investment avenues that bear less risk in the long run. But it is unclear exactly how far into the future one must look to define the long run. Clearly stocks are sometimes outperformed by cash. In fact, there have been two four- and two five-year periods in the history of U.S. markets in which cash outperformed stocks. I don't know about you, but I would probably be getting impatient had I been around at that time.
So I am just not quite sure how long the long run is. As the Eagles sing, Well, we won't find out. But maybe our children's children will. Keep reading for more on this.
Some Final Thoughts What will investing be like? I will venture a prediction that indexing will go in and out in waves. At times, the industry will market indexing as a new invention and people will see indexes on everything from the latest hot stocks to the latest cold stocks to stocks predicted by Nostradamus to outperform in the 22nd century. At other times, indexing will be outré, and individual stocks possibly even poorly diversified portfolios will be touted as the only reasonable means of achieving true long-run wealth. Doctoral dissertations will be written on the good, the bad and the ugly of indexing and other forms of investing. There will be 1 million mutual funds but, because of mergers and failures, only a few more publicly traded companies than there are today. But one thing is for sure: People will still expect to earn a higher return for taking more risk in the long run. And they'll still be wondering just how long this long run really is. _____________________________ The author acknowledges helpful comments from Al Neubert. 1 . Note that I emphasize the Latin words ex ante. Markowitz said nothing about whether investors would realize ex post satisfaction. In other words, he did not collect any data and examine whether the ex ante measures of risk and return proved to be good measures of ex post results. That's another story, a part of which I take up as the 6th issue. 2. Harry Markowitz, ''Portfolio Selection,'' The Journal of Finance, Vol. 7, 1952, pp. 77-91 and Portfolio Selection: Efficient Diversification of Investments, 1959, New Haven: Yale University Press. 3. William F. Sharpe, ''Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk,'' The Journal of Finance, Vol. 19, 1964, pp. 425-442; John Lintner, ''The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets,'' Review of Economics and Statistics, Vol. 47, 1965, pp. 13-37; Jan Mossin, ''Equilibrium in a Capital Asset Market,'' Econometrica, Vol. 34, 1966, pp. 768-783. Interestingly, Sharpe and Mossin used the term ''capital asset'' followed by either ''prices'' or ''markets,'' while Lintner did not use the term at all. None used the term ''Capital Asset Pricing Model.'' Eugene Fama, another of the pioneers of the model, was not noted for using the term, seeming to prefer ''two-parameter model.'' Frankly, it is not clear who gave the model the name it is so commonly referred to, though the term was used in 1972 by Fischer Black, Michael C. Jensen, and Myron Scholes in their article, ''The Capital Asset Pricing Model: Some Empirical Tests,'' in Studies in the Theory of Capital Markets, ed. Michael C. Jensen, 1972, New York: Praeger Press. 4. The remarkable success of online auctions further complicates the issue of identifying the market portfolio. Thanks to eBay, we now know that people possess an incredible amount of marketable junk that may well constitute its own asset class, what with rates of return, standard deviations, etc. 5. http://www.stanford.edu/~wfsharpe/art/talks/indexed_investing.htm 6. Just to show you how little we know about risk preferences, take note that economists believe they have learned a great deal about this subject by studying game shows, as if people act normally on national television risking money that wasn't theirs when the show started. 7. Unless, of course, you are a politician or CEO, where you are expected to be correct and in agreement with your constituents 100 percent of the time. 8. See Robert D. Arnott, Jason C. Hsu, and Philip Moore, ''Fundamental Indexation,'' Financial Analysts Journal, Vol. 61, March/April 2005, pp. 83–89. 9. If my explanation isn't good enough for you, see André F. Perold, ''Fundamentally Flawed Indexing,'' Financial Analysts Journal, Vol. 63, November/December 2007, pp. 31-37. |
Ah indexing. What a fascinating and contentious subject. At the almost innumerable indexing conferences and on the pages of this journal and elsewhere, we hear nearly endless debate on the critical issues of the times in the riveting world of indexing. As an observer of this industry, I find these issues fascinating, not always for what we hear, but oftentimes for what we don't hear. I think it is worthwhile on occasion to take an objective look at this debate. So in this article, I intend to visit six of the key issues in indexing. I will outline each issue and tell you what I think is really going on.
