One of the major differences between K⁴ Fund Selection and traditional screening processes is that K⁴ allows the user to score products as well as eliminate them. The same factors can be used for either or both purposes. Generally, it’s not too hard to decide which way to go. Filters allow the user to set limits for “must-have” features while scoring allows funds displaying greater levels of desired characteristics to rank higher. Occasionally, you might want to use a factor for both purposes. For example, you might want to give more points to funds with lower expense ratios (scoring) while not even considering funds with expenses exceeding 1.5% (filtering). It may take a little thought, but setting up performance and expense factors in K⁴ is generally not very difficult. But what do you do about R-Squared?

If investment evaluation models focused solely on return, R-Squared wouldn’t be an issue in K⁴. However, any model using factors such as Beta, Alpha, or their derivatives (e.g., Information Ratio) should also include R-Squared. But is it a scoring factor, a filter, or both? K⁴ users seem to be divided on this, often using the roles interchangeably. While there’s no absolute “right” or “wrong” way to use this particular factor, it really does make a difference in the scenario. So users are correct in identifying R-Squared as an important factor (especially if they use other Modern Portfolio Theory statistics as other factors), but they may benefit by putting a little more thought into its role in their scenarios.

Statistics such as Alpha and Beta drawn from Modern Portfolio Theory (MPT) are based on linear regressions of the investment returns versus those of the appropriate market benchmark. The stronger the relationship between the two sets of returns, the more meaningful the MPT statistics. R-Squared measures the strength of the relationship and can run from 0 to 100.

Consider, for example, two funds, A and B. Both have the same Alpha (0.5%) and the same Beta (1.4) relative to the benchmark index. Their regression analyses are shown on Charts A and B. The red lines are the regression lines, representing the “best fit” between all the dots. Although their regression lines are virtually identical, the data that generates them are quite different. Each dot on the charts represents a return for the index (plotted on the vertical axis) and the return for the fund (plotted on the vertical axis) for the corresponding period. Fund A’s line touches almost all the dots while B’s only crosses two. Many of the dots on B’s chart aren’t even close to the regression line.

Fund A	Fund B

If just two or three dots were moved only slightly on Chart B, the regression line would look quite different. This isn’t true for Chart A, where the points that don’t actually fall on the line are very close to the line. This is why B’s R-Squared is only 0.39 while A’s is 0.98. In other words, there is a much stronger relationship between A’s returns and those of the benchmark than between B’s and the benchmark's. Although their regression lines are almost identical now, that could be more coincidence than actual correlation. The relationship between B and the index is so tenuous, its regression line could look quite different as time passes and more data points are added to the chart.

The fact that you can find a regression line doesn’t guarantee that the resultant MPT statistics are truly meaningful. When the relationship (as measured by R-Squared) is weak, the regression line and MPT statistics can change considerably over even short periods of time and are said to lack statistical significance. On the other hand, if there is a strong relationship between the investment and the benchmark (and a high R-Squared), the MPT statistics are much more reliable. That’s why it’s important to pay attention to R-Squared when using MPT statistics in a fund evaluation model.

Most K⁴ users are aware of its importance and include R-Squared in their models. Those with a screening background will often use R-Squared along with other critical characteristics as a scoring factor. This rewards funds with higher R-Squareds.

This may be appropriate if you’re seeking index funds or funds that closely track the benchmark. You might do this if you use indexes to construct asset allocation models and want to implement those models using funds that trade like the representative indexes. Or you might seek actively managed funds that follow the benchmarks but also offer the opportunity to incrementally outperform over time.

But in most other instances, you don’t want to use R-Squared as a scoring factor. Do you really want to give funds more points if they behave like the benchmark? Are you really looking for closet indexers? In most cases, the answer to these questions is probably “No.” Models are typically designed to find funds that are the “best,” meaning they somehow outperform their benchmark and peers. In order to do this, they have to differ from the index, not mirror it.

While you’d probably want to give more points to a fund that has an R-Squared of 0.98 than one with 0.39, does it really matter when the two values are 0.98 and 0.93, or 0.39 and 0.35? It’s not the actual value that’s so critical but whether it’s high enough to assure that the fund’s MPT statistics are statistically significant. In other words, when seeking the best actively managed funds rather than the best fit to the index, you want to make sure that R-Squared is above a specific threshold, and that suggests it should be used as a filter.

Filters are used in the K⁴ Decision Tools to eliminate products that don’t meet specific “must have” features. For example, you might only want to consider funds with positive 5-year Alphas or with Expense Ratios below 1.5%. In these instances, you’d use filters with a minimum of 0.01% for 5-year Alpha and a maximum of 1.5% for Expense Ratio. You can set filters for R-Squared levels, too.

Generally, an R-Squared above 0.75 is considered indicative of a “strong” relationship. Analysts set their filters at different levels, but the minimums usually fall in the 0.70 – 0.85 range. This assures that the MPT statistics for all survivors are statistically significant. It doesn’t matter if the R-Squared is 0.99 or just barely above the cutoff; no additional points are earned for degrees of strength above the minimum. It is important, however, that the minimum level be attained. Setting a filter for R-Squared in K⁴ provides a way to find funds that differ from the index on certain key factors, yet assures this minimum level of reliability for the statistics you are using.

Weighted factor models have numerous advantages over simple screening in fund evaluation, offering superior analysis as well as time savings. Even so, certain factors are often more appropriately used as screens and R-Squared is an example of this. While there can be instances when it is appropriate to use it as a factor for scoring, it is generally best used as a filter to assure statistical significance of other factors. Part of the power of K⁴ is that it allows you, the user, to have best of both worlds — the superior analysis and time savings of models plus screening for the “must have” limits on certain characteristics.