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Where the Kalman Filter Rankings Come From
To understand the origin of the Kalman filter model it helps to understand what somebody should look for in a mutual fund. Imagine that the market goes up 10% this month. If a fund returns 8% for the month is that good or bad? An 8% return over one month looks pretty good but it is below average. How do you know that? The "market" return is defined as the average return across all stocks so if the market returned 10% then the average stock portfolio did so too. Does this mean 12% is good? Again that depends. Suppose a fund buys securities that are especially sensitive to market moves. For example, a fund might purchase the stock of a nearly bankrupt firm called The Distressed Company (TDC) at $1 per share. Because the company is nearly bankrupt any small change in its fortunes will have a tremendous impact on its stock price. If the economy does better than expected the stock could easily go to $2 (a 100% return), and if the economy does poorly to 0 (a -100% return). If the market returns 10% in a month (a great performance) then a fund holding TDC would be expected to return 100% that month. If in fact the fund held a number of stocks like TDC and earned "only" 90% that would be indicative of poor managerial ability despite the eye popping return. An average manager holding similarly distressed firms should have earned 100%.
As the above examples indicate a manager's performance can only be determined relative to the overall market and an expectation regarding how the stocks held by the fund should perform relative to the market portfolio. A fund manager has done well if his holdings do better than expected given the market's return. This leads to two Greek letters that are famous, at least among financial academics, α (pronounced alpha) and ß (pronounced beta). A fund's beta measures its sensitivity to moves in the overall market. By definition a fund with a beta of one should be expected to produce the same average return above short term treasuries as the market. (The short term treasury rate is typically taken as the current yield on the one year Treasury bill.) A fund with a beta of 1.1 would move 110% as much as the market (both up and down), while one with a beta of .8 should only move 80% as much. The other letter, alpha, is potentially more interesting to investors as it measures "managerial talent." A manager that has no particular ability to select stocks should produce an alpha of zero, or perhaps one that is even slightly negative due to the fee's and transactions costs incurred by the fund. The goal is to find funds with positive alphas.
The Kalman filter model is a statistical device designed to help locate funds that have potentially positive alphas over the next investment period. The model is based upon the underlying principle that funds can only produce positive alphas if they are run by talented people and those people happen to have valuable information at the moment. While talent may remain constant from period to period it is unlikely that information does as well. It seems a lot more likely that fund managers come across useful information only sporadically and that over time the value of this information ebbs and flows producing some periods of above market and others of ordinary returns. This differs from most other models that simply assume talented people will produce the same "bonus return" period after period.
By comparing a fund's past returns to those of the market (known as looking at market adjusted returns) the Kalman filter model tries to estimate both a manager's talent and the likelihood that he has information at any point in time. As to the latter, the statistical model is also flexible enough to recognize that some managers are able to acquire information with a longer useful life than others. This is one reason some funds will appear at the top of the rankings for longer periods of time than others.
To produce the rankings each month the Kalman filter model is run on every single fund in our database that has at least 80% of its money currently invested in stocks and at least a 61 month track record. The model first projects each fund's alpha and beta for the previous month using the returns up to but not including the last month. This projection is then compared with how the fund did last month. If the model got it right, in that a fund with a positive predicted alpha in fact produced a positive market adjusted return the fund is put in the active pool. Funds in the active pool then have their alphas estimated once again but this time with the most recent 60 months of data. Finally, funds are eliminated if their estimated alpha or beta seems unreasonable which we define to be an alpha above 2% per month or below -2% per month or a beta below 0 or above 2. The tables list the remaining funds by their forecasted alpha.
The academic research that produced our fund ranking technique indicates that a portfolio holding the up to the top 20% of all ranked mutual funds will yield an overall alpha that is positive. The funds in the top 10% are rated Buy, and those in the next 10% Buy-. These groups are separated out since tests showed that the higher decile funds produce higher average returns. Not too surprisingly the research also showed that a portfolio invested in the top 10 funds does better yet, and thus these are listed as Buy++ funds. Holding the top 20 funds does nearly as well as the top 10 and thus funds 11 through 20 are rated Buy+. At the other end of the spectrum the bottom funds are rated Sell since our tests indicate that they can be expected to produce negative market adjusted returns on average.
While the Kalman filter rankings are a potentially useful investment tool just as important is what does not go into them. We do not interview managers, or check their credentials. The rankings are derived only on the basis of reported returns for each fund during the previous five year period. Additionally, we do not check to see if a fund's manager has changed recently. Thus, it is possible that a fund will score highly because a talented manager ran it for the past five years, and that manager may now be gone. Finally, the rankings are not magic. While the portfolios recommended by the Kalman filter have done very well in the past, there will almost certainly come a time where they will not. This is due at least in part to the fact that stock returns are mostly unpredictable and every now and then the "roll of the dice" will go against any particular strategy. Despite all of the above qualifications tests using historical data have shown that an investor using the Kalman filter model to select mutual funds would typically outperform the market as a whole.
If you are interested in additional information there are several sources on the web. A somewhat more detailed explanation of the Kalman filter and how the ranks are produced can be found at Professor Matthew Spiegel's web page http://som.yale.edu/~spiegel. Go to the section on current mutual fund performance and forecasts and then follow the link to the "less detailed explanation." Another source is the original paper "Improved Forecasts of Mutual Fund Alphas and Betas" which can be downloaded at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=567284.
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