Assuming that the answers to life's greatest questions can be found by appealing to Google, I entered the words "equity style box" into the search box. The third "hit" directed me to About.com's Mutual Fund site (http://mutualfunds.about.com/od/mutualfunds101/fr/stylebox.htm) written by Dustin Woodard, an online marketing expert who supervises the site's career and money channels. He wrote the following:

"There are many different ways to use the style box to make your asset allocation selection. Investment professionals have different recommendations on how to use the style box. Some will recommend you purchase a fund for each category, others will recommend a single medium blend fund.

One strategy that I might suggest is going for the corners (which also happens to be a good strategy for tic-tac-toe). By going for the corners, you are making sure that your portfolio is well diversified. When you use blends and mid-caps, you have less of a grip on what allocation you are ending up with. A small blend manager may choose to buy a lot of growth stocks one year and a lot of value another."

THE FOUR-CORNERED PORTFOLIO

Obviously, opinions differ about how to use the style box, but it's interesting to see how Woodard's advice would have played out over the past five, 10 and 15 years using the performance of Russell and Wilshire style-specific indexes (see chart, "Returns From Every Box," below).

The raw performance data was extracted from the June 2005 release of Morningstar Principia.

In this table, the four "corner" indexes are highlighted in blue and the four "non-corner" indexes are colored yellow. Mid-cap blend (MB) is ignored in this comparison. Two indexes are used to represent the return of each individual style box, one from Russell and one from Wilshire. (I used two indexes because they create a more reliable indicator of the performance within each box; using only one index per box would increase the possibility of bias.)

As per Woodard's strategy, the four-corner approach avoids mid-cap funds and blend funds. "The Middle Road" table below shows the results.

Over the five-year period ending on May 31, 2005, the pretax, buy-and-hold return of the four-corner strategy (LV, LG, SV, SG) was 1.7%, compared with 4.1% for the non-corner portfolio (LB, MV, MG, SB). Performance was determined by calculating the average of the four-corner returns and the four non-corner returns, assuming a single lump-sum investment with no rebalancing.

Likewise, over a 10-year period, the four-corner strategy generated a 9.8% annual return, again underperforming the non-corner strategy, which produced an annual return of 11.3%. Over the past 15 years, the corner strategy had a 10.4% annualized return, compared with 11.7% for the non-corner strategy.

Upon closer examination, several interesting patterns emerge from the performance distribution that is shown in these tables. However, these patterns are specific to the particular time frame being studied here, and thus may not hold true going forward.

1. The non-corner strategy beat out the corner strategy each time.
2. The value indexes outperformed blend and growth in each market-cap class (large, mid and small) in all three time periods.
3. The mid-cap indexes outperformed large and small indexes in all but one case (the five-year period in which small-cap value beat mid-cap value).
4. The returns of the blend indexes were larger than those of the growth indexes, but smaller than those of the value indexes.

The fourth observation needs some qualification. The "Value Vector" table below shows that over the five-year period (ending on May 31, 2005) the average performance of the blend style (among large-, mid- and small-cap indexes) was generally halfway between the performance of the value index average and growth index average, suggesting that the composition of the blend style is a fairly equal mixture of value and growth.

However, over the past 10- and 15-year periods, the performance of the blend style has been closer to that of value, particularly among large- and mid-cap indexes. The performance of blend among small-cap U.S. equities over the past five, 10 and 15 years has been a more equal mix of value and growth performance.

Woodard's suggestion that a "small blend manager may choose to buy a lot of growth stocks one year and a lot of value another" isn't uniformly supported by recent data, but it appears to apply to some extent to the large- and mid-cap indexes.

In other words, over the past decade or so, the performance of large- and mid-blend indexes have been more closely aligned with value returns than with growth returns. This suggests the somewhat obvious observation that a blend fund is inherently subject to more changes in "tilt" over time toward either value or growth.

Perhaps the most compelling reason for advisers and investors to avoid a four-corner (or tic-tac-toe) strategy is that it effectively eliminates mid-cap funds (and mid-cap indexes) altogether. Over the past 15 years, mid-cap indexes have outperformed large- and small-cap indexes both in terms of raw return and on a risk-adjusted basis.

In the "Risky Business" chart below, we see that mid-cap value (MV) and mid-cap blend (MB) produced two of the best risk-adjusted levels of performance over the 15-year period. (Standard deviation of return is used as a surrogate for risk.)

Surprisingly, this chart also shows a negative correlation between risk and return when you look at all nine style boxes together. That is, higher risk does not always lead to higher return.

So how should you use style boxes? According to this study, at least, you wouldn't want to pick your asset allocation by looking solely at the four corners of the style box.

Shunning blend funds and/or mid-cap funds may simplify life, but may also neglect components of the Morningstar style box that have produced superior risk-adjusted returns in recent years. Simply put, a "corner-only" strategy is too restrictive. Using a corner approach to win at tic-tac-toe, however, is another matter entirely.

Craig L. Israelsen is an associate professor in the department of home and family living at Brigham Young University, where he teaches personal and family finance. His e-mail is craig_israelsen@byu.edu.