Professors successfully apply statistical technique to picking mutual funds.

Five for five. That's the heady batting average of a new, if not experimental, mutual fund selection technique that began predicting outperformers last year. Its recommended portfolios have beaten the Wilshire 5000 by an average of about 300 basis points, risk adjusted, in each of the last five quarters (ignoring load fees).

What does the model use to forecast fund performance? "Just historical returns, nothing else," says Matthew Spiegel, a professor of finance at the Yale School of Management who developed the approach with Harry Mamaysky, a former Yale assistant professor who is now a vice president at Morgan Stanley, and Hong Zhang, an assistant finance professor at INSEAD in Singapore. "How can we do what we're doing? We use a different model than others have in the past," Spiegel says.

In Search Of Alpha

To understand the new model, a brief review of investment basics is necessary. You probably know that the 90-day Treasury bill yield is considered investing's risk-free rate. Stocks, of course, since they carry risk, are expected to return more-i.e., a market premium, or excess return. A statistic called alpha indicates a stock or fund's excess return on a risk-adjusted basis.

The adjustment for risk is made with the beta statistic. It is constructed so that a value of 1.0 denotes average market risk, while a beta above or below that figure indicates, respectively, above- or below-average risk relative to the overall stock market. Take a fund with a beta of 1.25. If equities are expected to return 4% above T-bills, then this fund would be expected to generate a 5% excess return (4% expected market premium times 1.25 fund beta). After all, if the fund is 25% riskier than the norm, its rewards should be that much greater, too.

Suppose the fund actually earns 6% above the risk-free rate. Then its alpha is 1% (6% actual excess return minus 5% expected risk-adjusted return). The goal of the mutual fund manager is to buy stocks with high current alphas-that is, ones expected to outperform the market. Likewise, investors seek to buy funds that own high-alpha stocks and therefore have high alphas themselves.

Against that background, the new model advanced by Spiegel and his colleagues makes some important assumptions that depart from previous work in the field. The first is intuitive: Fund managers trade their portfolios based on a signal received from the investment environment. The signal could be macroeconomic data, company earnings projections, actual or forecasted changes in interest rates-who knows what the information is? And that's the point. Investors can't see the signal, yet presumably a fund manager follows some beacon to his investment decisions. Isn't that why managers who sit on conference panels are routinely asked about their buy and sell disciplines?

Paradigm Shift

The other assumptions are more novel. The researchers contend that the signal from the investment environment varies in strength, so that a manager may possess valuable information at some points in time but not others. "Above-market returns are achieved only when a manager has valuable information at the moment," Spiegel asserts. In other words, not only does a fund's expected alpha depend on a signal that cannot be seen by investors, the signal may or may not have value at any given time. Alpha thus changes over time, Spiegel says. "Previous empirical studies of mutual fund performance assume that the ability to beat the market sticks with the manager, that if he can beat the market by 40 basis points in one year, he can do it every year"-a static alpha. "Our view was that that didn't make sense," Spiegel says.

He also observes that a fund's beta changes, even though theories heretofore have considered it to be constant. Clearly, though, as a manager trades the portfolio's risk profile changes, morphing beta. Properly gauging beta is important because an inaccurate estimate of it leads to misestimating alpha. By assuming that a fund's alpha and beta parameters are both in motion, "our model has a lot of flexibility," Spiegel says.

The model is described in Estimating the Dynamics of Mutual Fund Alphas and Betas, a 2003 Yale International Center for Finance working paper now making the rounds in academic circles. The model was developed in hopes that it could identify mutual funds that are poised to outperform-that currently have high expected alphas. But how do you calculate alpha if it is a function of something unseen?

With the Kalman filter, an obscure statistical technique used to solve signal extraction problems, where "you have data that's noisy about some signal and you're trying to figure out what the signal is," says Spiegel. The technique was originally used by the Navy to track submarines-you know they're moving, but you don't know where to, or why. Or consider an engineer reading Geiger counter data: He's getting a noisy signal about what he would like to get.

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.