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William F. Sharpe, the 1990 Nobel laureate in economics, once put forth a very simple premise for investors called the “Arithmetic of Active Management” that, while difficult to refute, is often ignored by most investors. By using simple arithmetic, he explained why the great bulk of investors never earn returns near the market’s average returns. Furthermore, this explanation gives us an insight into why most investors should prefer to invest in passive indexes rather than search for market beating performance. The first part of his premise is that, before costs, the returns on all actively managed dollars invested in the stock market equal the returns of all average passively managed dollars invested in the stock market. The second part of his premise, and one you need to spend some time thinking about, is that, after costs, the return on the average actively managed dollar must be less than the return on the average passively managed dollar. How did he come to these conclusions? He applied logic and used a little simple arithmetic. Consider the stock market as whole. The value of every stock or bond within this market is determined by its market capitalization. The market capitalization is simply the number of shares or bonds outstanding, multiplied by their current market price. So, the U.S. stock market, with a current value of close to $15 trillion, represents the total investment of all U.S. equities. It must be logically concluded from this that all investors taken as a group must earn whatever rate of return the market earns. For example, if the market earns 20 percent for the current year, then all investors, taken as a collective group, must have earned 20 percent. This return is less any expenses or costs they incurred in the investment process. The amount of costs incurred in obtaining returns becomes a direct deduction from the market return. Arithmetic tells us that the more costs we incur, collectively, the further the difference from market averages that our collective returns will fall. Passive managers who charge low fees, and not all of them do, deliver market-like returns to their investors at a very low cost. This strategy is most commonly thought of as an index strategy. Active investors as a class must also earn returns equal to the market’s return less their costs. Over long periods of time, all investors will earn a return that is a weighted average of the returns on the securities within the market, minus their cost. Passive strategies are very low-cost; there’s no need to pay for research. This is one of the reasons their returns are so close to market averages. Active strategies, on the other hand, tend to be expensive. Trying to obtain an informational advantage over all of the participants in the market can be a very costly undertaking. Since active and passive returns have to be equal before costs, it has to be true that the average actively managed funds must have returns that are lower than the passively managed funds. Simple arithmetic tells us that the only way that managers can attempt to have market-beating returns, is to have a portfolio that looks significantly different than the market portfolio. Some stocks, some segments, or some asset classes can be over weighted in an attempt to have returns greater than the market. This is where active managers justify their fees; they believe they have better insight into the process than the next manager. But the problem with this is that, taken as a whole, they must earn the market return less their fees. We can demonstrate the validity of this premise by using simple direct comparisons of active and passive investment returns. The Journal of Indexes uses Morningstar and Standard and Poor’s data to regularly report on how well active managers are doing versus their comparable indexes, which is called their benchmark. By comparing three well-known indexes to active managers who are benchmarked to them we can get a clear idea of how well this premise holds up to scrutiny. First, let’s take a look at the Standard and Poor’s 500 and the active managers who compare themselves to it. This index represents around 70 percent of the U.S. stock market capitalization and is the de facto benchmark for the market. The results are really quite startling. Over the past five years ending Dec 31, 2006, the Standard and Poor’ 500 index, when passively held, outperformed 71 percent of all large-cap funds. This means, that if you were a large-cap investor, by simply holding a passive index in the S&P 500, you would have earned returns that would have put you in the top 30 percent of all investors. This does not only hold true for large capitalization stocks. When we compare the S&P Mid-Cap 400 with actively managed funds who are benchmarked to this index, we find that the index outperformed 79 percent of all actively managed funds. The results are similar when we use the S&P Small-Cap 600. This index outperformed 77 percent of all actively managed funds that compare themselves to this index. Does this prove Sharpe’s theory? Yes, these are exactly the results that can be predicted. The total returns for all investors have to be the returns earned in the market less their costs. Does this mean that we shouldn’t use active managers to run our investments? Not necessarily. It would depend upon how confident you were in your ability to select managers that can consistently produce superior returns. Some managers have demonstrated the ability to achieve superior returns after costs, but on the whole, the returns of all active managers must equal the market returns less the costs. These comparisons of active managers with their respective passive indexes prove that the great majority of managers fall short of their benchmarks. While this is does not always true over the short run, there can be many hot hands; over the long run arithmetic requires it to be proven. Many investors believe that it is well worth the time and effort necessary to try to find out who the good managers are. If, however, you believe that you would be satisfied having your results fall in the top twenty or thirty per cent of all investors you should use a low-cost, passive investment strategy and ignore trying to pick the best funds or managers. You can then shift your investment efforts from trying to find the best investment, where the odds are against you, to the management of the investment process where your efforts can have large positive impacts. If you would like to chart a middle ground between passive and active investing approaches, simply follow the course that many large pensions use with a core and explore approach. With this method the bulk of your investible assets, say 80 to 90 percent are invested in a low-cost passive core. Then, the remainders, of your monies are invested in what you consider to be the very best ideas to add value to your portfolio. This type of strategy assures you of having a decent return; you are rewarded for the market risk you take, while allowing you to speculate on any unique insights you have. Whatever approach you take, there are additional factors that add value to the investment process that don’t involve investment selection. Making sure that you have a portfolio suitably designed for your specific need is the first step. Next, focus your efforts on factors that you can control. Efficient tax management, periodic rebalancing, and cost-minimization all have incredible long-term benefits for your portfolio’s health. Unlike trying to beat the market, which simple arithmetic tells us is extremely difficult, efforts should be focused on techniques that we know will bring positive results. I certainly won’t suggest to you that you cannot find the next hot stock or the next hot manager. All I am sure of is what the past data tells us. The great majority of active managers have failed to match their appropriate benchmarks over long periods of time. You can have a very satisfactory investment experience, among the top of all investors, by simply having a passive investment strategy and working to maximize the details. After all, isn’t that what you are really interested in? WILLIAM Z. SUPLEE IV is the president of Structured Asset Management Inc., a financial planning and investment advisory firm located in Paoli, Pa. He may be reached at 610-648-0700 or [email protected].

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