Mutual fund investing is similarly shrouded, Spiegel argues. "I can't see the information that the managers have, but I know they're taking action based on it. The Kalman filter estimates the unobservable variable's location, then tries to guess its trajectory and where it will be next," he says. The filter's two sets of equations, along with some matrix algebra, attempt to mathematically separate the noise from the true signal in the input data. The algorithm's goal is to find a best-fit function-specifically, the function that maximizes the likelihood that its estimate of the unseen signal would have produced the input data.
Spiegel and colleagues tested this approach on fund return data from the Center for Research on Stock Prices. They used the Kalman filter to simulate predictions of funds' alphas and betas for various periods between 1993 and 2000. Funds with the highest expected alphas were then combined in a portfolio whose ensuing performance was compared to that of a portfolio constructed with a traditional static-alpha model. The Kalman filter portfolio, rebalanced every three to six months with the model's latest picks, did better. "By assuming that an unobservable variable with a known stochastic process drives portfolio holdings, past changes in a fund's alpha and beta"-which the Kalman filter can extract from historical return data - "can be used to predict their values in the future," the researchers concluded, although the predictive power seems to fade within six months (which accounts for their frequent rebalancing). To employ the model in real life, Spiegel says, you'd have to move in and out of funds every few months, probably in a tax-deferred account.
Going Public
It's one thing to simulate predictions that could have been made in the past and then reconstruct history to see if they would have worked. It's quite another to predict in real time. Yet since last year, Spiegel has been doing just that on his Web site, http://som.yale.edu/~spiegel.
At the beginning of each quarter, Spiegel runs his Kalman filter model on Morningstar data to produce current expected alphas for more than 6,000 U.S. equity funds. Spiegel declares the five highest-ranked funds as his model's portfolio. A new portfolio is created quarterly since the model's predictive power appears to be short-lived. (In practice, the predictions aren't posted until a few weeks into the quarter, when Spiegel finds the time. "I'm not getting paid to do this," he says.)
The Big Question
When the quarter ends, the model portfolio's return is calculated. For five consecutive quarters dating back to the beginning of last year, the Kalman filter portfolio has outperformed the Wilshire 5000. It seems the filter may have honed in on the signal that fund managers use to guide their investment decisions. So, what information do they key on? "We don't know," says Spiegel. "All the Kalman filter provides is an estimate of how good the signal is at the moment"-in other words, the estimated current value of a manager's research-"without telling you what information he actually has."
Despite this unsettling agnosticism (or perhaps because of it), it's interesting to note that some of the model portfolios have had themes. In the fourth quarter, for instance, the picks had a decidedly small-cap flavor. In another quarter, Spiegel neglected to screen out non-U.S. equity and the model tapped three emerging markets funds. In cases such as these, says Spiegel, "the model may be picking up something about the sector. If there is something to be known in a subarea, it is reasonable to expect that several smart people working in that area would all know it." Presumably, that's the knowledge investors are hoping to access when they choose actively managed funds.
But why does the model sometimes select index or other passive funds? The answer is actually the same, according to Spiegel. With no manager between the stocks and the model, "it is picking up on things underlying that sector." In other words, the Kalman filter is picking stocks in that sector-could it be the Holy Grail?
"Certain companies' managements may know that their industry is about to ramp up, so they invest in production and assets, and the model might be able to detect that in advance to give you an idea of which stocks to be in," Spiegel says, extending his theory of a black-box of information from funds to companies. Like a mutual fund's unseen (to investors) research, which may or may not be valuable at any given time, sometimes a firm has many good investment opportunities that it is prepared to take advantage of, and sometimes not. An outsider can't tell which is the case, Spiegel says. "Stock investors try to extract a signal regarding the firm's investment opportunities. Because that's not very different from what a mutual fund manager is presumably trying to do, we suspect the Kalman filter might work for picking individual stocks, too, not just funds." But that research is a few years down the road, Spiegel says.