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RESEARCHERS at Yale appear to have solved a big problem for mutual fund rating systems. In doing so, the research team may have also found a better way to pick winning stock funds.
--- The New York Times


The Kalman filter: could it be the Holy Grail?
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Benchmarks

Professor Matthew Spiegel
February 21, 2005

You go from your house to a store ten miles away. It takes you 20 minutes. Did you get there quickly? The answer depends on your options. If walking was your only alternative then you arrived incredibly quickly. However, if you could have driven by car over a major highway then 20 minutes is actually quite slow. A particular mode of transportation is only fast or slow when compared to some alternative mode of transportation. When it comes a portfolio's returns the same general concept holds. A portfolio's return is good or bad only when compared to some alternative benchmark portfolio.

For most people the natural benchmark portfolio is a broad market index like the Russell 3000 or the Wilshire 5000 (both of which are used by Alpha Investment Opportunities (AIO) to judge our model portfolio's returns). The returns on these two indices represent what the average dollar invested in the stock market earns. This is a particularly useful measure since the average dollar in the whole market must earn the same return as, well, the average dollar invested. (Pretty deep, no?) Thus, if your portfolio has a return above the return of either of these indices you did better than the typical investor. That is, in fact, pretty good. Unlike the movies in real about life half the people earn less than average. So, if you earn more than these indices your portfolio's returns must put you in the top half of the population.

Broad indices like the Russell 3000 and Wilshire 5000 not only allow you to calculate the average invested dollar's return but they also tell you how you would have done using a simple and effective investment strategy that you can easily carry out. An accounting identity plus some financial analysis reveals why holding these portfolios cannot be too bad of an idea. At the end of every single day, every single security must have one and only one home. There are no unloved securities lying around the floor of the stock exchange waiting (yea hoping) for somebody to pick them up and carry them home. Similarly, there are no securities that can be called the "darlings of Wall Street" over which investors threaten violence should they be inhibited from their ownership. Instead security prices adjust so that one and only one person wants to hold each and every one at every moment in time. This is nothing more than an accounting identity (like one equals one). The collective holdings of all investors must add up exactly to the set of all available securities.

Since prices adjust to ensure that collectively society owns all of the available securities then this must be a pretty good portfolio to own. Why? If this portfolio has some obvious flaws then collectively society would not own it. For example, imagine that everybody knows that the returns on stock "A" are expected to be relatively poor. Then people would try to unload it. That in turn will drive down its price and increase its future expected return until investors no longer believed that shares of A have a particularly good or bad return. (The realized return on an asset equals the future payoff divided by price at which you purchased the asset. If the price goes down but the future payoff does not, then your expected return goes up.) Thus, so long as every asset has one and only one home the portfolio of all assets must be something investors collectively believe has a pretty good return. In fact, this portfolio is so important in finance that it has a special name, the market portfolio.

At first glance you might believe the market portfolio is easy to beat. After all how hard can it be to do better than average? To begin with, as noted above, half of all portfolios earn less then the market so right there your odds of beating it are at best 50-50. Another item to note is that anyone holding the market portfolio incurs very few transactions costs. The market portfolio is a value weighted index and thus requires very little trading. Furthermore, it is easy to own. You do not need to do any research or give it any thought. Just buy the portfolio that contains everything. All of this means that the vast majority of mutual funds underperform the market index. This happens in part because most fund managers trade a lot (thus incurring transactions costs) and charge a lot for their services (thus reducing their investor's returns). Because of these expenses a fund manager's investors will only receive an above market return if that manager earns enough to more than cover these transactions costs and other fees. That is not an easy task and it is why most funds underperform the market portfolio. Of course, not every fund underperforms the market portfolio and this is where the Alpha Investment Opportunity newsletter comes in. Our newsletter is designed to help you locate those managers that are more likely to produce returns that are above those you can earn by investing in the market portfolio. As of the date of that I am writing this, the recommended model portfolio has never underperformed the market portfolio over any quarter.

Beyond the market portfolio there are many, many other benchmarks. As noted above a good benchmark should provide you with a way to measure returns from a strategy that can reasonably substitute from the one you might otherwise employ. Because mutual funds vary in their restrictions a good manager might underperform any one benchmark. Consider a fund L that is required to hold only large capitalization stocks. If overall large capitalization stocks underperform small capitalization stocks then even if L's manager is talented his fund's returns may fall below that of the market portfolio. For fund L a more reasonable comparison would be with a portfolio that contains the securities the manager was allowed to chose from. In this case a better benchmark would be the S&P 500 since it tells you how the shares of the country's largest companies fared. In general, if you want to see if a particular manager has done well for his investors you should use a benchmark that contains the securities that manager was allowed to hold. You can find a number of useful benchmarks at Yahoo! as well as other web sites devoted to finance.


©Matthew Spiegel
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