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I just posted this on another MFI board and figured I might as well get the biggest bang for my six hours of writing, and post it here as well...

Hi marsh_gerda and Steve Dixon,

I just read your two terrific write-ups from April 12, 2007, on the apparent outperformance of MFI microcaps and what, if anything, to do about it.

I thought I'd post the progression of my thoughts on that subject, as they parallels yours. Until now, I sort of considered what I'm about to write as "proprietary personal knowledge," and was unwilling to share it except among a few close friends. But, as the cat is now out of the bag, what the heck? It helps my own thought process to write, and my hope is that it helps yours as well when you read it. I'll break my metamorphosis into two parts.

=======================================================================

Part 1--The Part Where I Convince Myself that Microcaps Are Best

When I first read Joel Greenblatt's The Little Book That Beats the Market in November 2005, my immediate thought about the information presented on pages 56-61 was that the performance of the microcaps ($50M - $200M) must have absolutely *demolished* the performance of the rest of the MFI universe. I wanted to estimate the degree of outperformance and came up with the following analysis:

Given:
--The largest 1,000 stocks (Mkt Cap > $1B) averaged 22.9% per year.
--The largest 2,500 stocks (Mkt Cap > $200M) averaged 23.7% per year.
--The largest 3,500 stocks (Mkt Cap > $50M) averaged 30.8% per year.

--The largest 2,500-stock universe consists of 1,000 stocks (40% of the whole) greater than $1B market cap; and 1,500 stocks (60% of the whole) in the $200M - $1B market cap range.
--The largest 3,500-stock universe consists of 1,000 stocks (28.6% of the whole) greater than $1B market cap; 1,500 stocks (42.8% of the whole) in the $200M - $1B market cap range; and 1,000 stocks (28.6% of the whole) in the $50M - $200M market cap range.

Assumption:
The Top-30 MFI stocks are evenly distributed over the entire range of market caps greater than $50M. In other words, if you sort all of the largest 3,500 companies by market cap, you will find the same number of Top-30 MFI companies in every equal-sized subset; and there would be roughly one Top-30 MFI stock in every 120-company subset.

If this assumption held true, it would mean the following:

1. When looking at the largest 2,500 stocks (Mkt Cap > $200M), roughly 12 of the Top-30 MFI stocks (40% of them) would be found in the subset greater than $1B; and roughly 18 of the Top-30 MFI stocks (60% of them) would be found in the subset between $200M and $1B.

2. When looking at the largest 3,500 stocks (Mkt Cap > $50M), roughly 8 or 9 of the Top-30 MFI stocks (28.6% of them) would be found in the subset greater than $1B; roughly 13 of the Top-30 MFI stocks (42.8% of them) would be found in the subset between $200M and $1B; and roughly 8 or 9 of the Top-30 MFI stocks (28.6% of them) would be found in the subset between $50M and $200M.

Granted, I was quite wary that such an assumption would prove to be unfounded. Certainly, some Top-30 MFI companies would be bunched closely together over the full range of market caps, and the psychology of the market might favor certain market caps at certain times; and quite different market caps at other times. History shows that the ebb and flow of business and the markets are constantly changing as the years roll by, and that the psychology of the markets changes along with it.

So, this assumption is the shakiest part of my analysis, by far. But, I at least had a place to go to test my assumption with empirical evidence under then-current market conditions. I simply looked at the market cap distribution of the Top-100 MFI stocks greater than $50M, from Greenblatt's website.

Here is that market cap distribution as of December 9, 2005:

$50M - $200M 27 stocks (27% of the whole, as compared to the predicted 28.6%)
$200M - $1B 39 stocks (39% of the whole, as compared to the predicted 42.8%)
$1B or greater 34 stocks (34% of the whole, as compared to the predicted 28.6%)

So, this made me feel a little more comfortable with my assumption--maybe too comfortable. As I write this (April 21, 2007), the market cap distribution on Greenblatt's website of the Top-100 MFI stocks greater than $50M has greatly changed, so maybe it wasn't such a hot assumption, or maybe the assumption generally holds true but at times will not--we can't say, just yet.

Here is that market cap distribution as of April 21, 2007:

$50M - $200M 13 stocks
$200M - $1B 44 stocks
$1B or greater 43 stocks

This may illustrate why many top value investors have shifted funds into larger market caps recently. In any case, encouraged by this data in December 2005, I proceeded with the logical conclusion to my analysis--some simple algebra (and you thought algebra wouldn't amount to a hill of beans in junior high).

Conclusion:
1. Question--On average, what is the annual return (R1) of Top-30 MFI stocks with a market cap in the $200M - $1B range?

Using the above data in the "Given" section, along with my "Assumption," I came up with the following algebraic formula to illustrate the market cap breakdown of returns from the 2,500-stock universe:

(0.4 x 1.229) + (0.6 x R1) = 1.237

In other words, using the 2,500-stock universe, if 40% of the Top-30 MFI stocks (those greater than $1B market cap) generated a 22.9% return, while 100% of the Top-30 MFI stocks (those greater than $200M market cap) generated a 23.7% return, then solving for R1 in the equation would tell us what the 60% of Top-30 MFI stocks (those in the $200M - $1B range) returned, on average.

Answer--R1 = 1.242, so the $200M - $1B market cap range performed to the tune of 24.2% per year, on average.

2. Question--This question is really the information that I was after. On average, what is the annual return (R2) of Top-30 MFI stocks with a market cap in the $50M - $200M range?

Using the above data in the "Given" section, along with my "Assumption," as well as my above calculation for R1, I came up with the following algebraic formula to illustrate the market cap breakdown of returns from the 3,500-stock universe:

(0.286 x 1.229) + (0.428 x 1.242) + (0.286 x R2) = 1.308

In other words, using the 3,500-stock universe, if 28.6% of the Top-30 MFI stocks (those greater than $1B market cap) generated a 22.9% return; and 42.8% of the Top-30 MFI stocks (those in the $200M - $1B market cap range) generated a 24.2% return; and 100% of the Top-30 MFI stocks (those greater than $50M market cap) generated a 30.8% return, then solving for R2 in the equation would tell us what the 28.6% of Top-30 MFI stocks (those in the $50M - $200M range) returned, on average.

Answer--R2 = 1.486, so the $50M - $200M market cap range performed to the tune of 48.6% per year, on average.

My immediate reaction was a phrase often exclaimed by Frank Barone in one of my favorite TV shows, Everybody Loves Raymond--"Holy crap!" I felt like Ponce de Leon discovering the Fountain of Youth; or Indiana Jones discovering the Holy Grail. My much-sought-after path to riches was ensured!

Uhh, not so fast.

=======================================================================

Part 2--The Part Where I Convince Myself that Largest Universe Is Best, Regardless of Market Cap

My initial investment strategy was going to focus exclusively on that microcap range of $50M - $200M, or even as little as $1M - $200M. It took me until my fifth reading of the Little Book in roughly July 2006 (that's right, fifth; apparently, I'm not such a fast learner) to come to a different theory, as you two have also done.

Because my future wealth would depend on my then-current line of reasoning (as long as I stuck with a strategy based on that reasoning), I attempted to shoot holes in my theory. Could I be wrong? Could the apparent outperformance of the microcaps be a mirage, masking a different truth? If so, what might that truth be? I was stymied until I came to the table on page 64 of the Little Book. That table flicked on a light switch in my head, by demonstrating a vital MFI characteristic in two similar ways:

1. The table demonstrates that grouping the 2,500-stock universe into deciles, as ranked by the MFI system, resulted in a perfect step function of investment returns. The best-ranked decile (Group 1) had the highest investment performance. The second-best-ranked decile (Group 2) had the second-best performance. The worst-ranked decile (Group 10) had the worst performance. As you walked along the continuum of MFI deciles, proceeding from best-ranked to worst-ranked decile, each lower-ranked decile took you perfectly down one step on the performance staircase--with no missteps. As Greenblatt said, "The magic formula appears to work in order." This demonstrates the simple fact that, as you move from a group of higher-ranked stocks to a group of lower-ranked stocks, your performance will degrade, on average.

2. The table also demonstrates that, even within a single decile, moving from a group of higher-ranked stocks to a group of lower-ranked stocks will reduce your performance, on average. Let's take a look at Group 1 in the table on page 64, keeping in mind that this table shows the results of the 2,500-stock universe, broken into ten 250-stock deciles:

Group 1 earned a 17.9% average annual return.

Group 1 can be broken into two subsets: the Top-30 MFI stock subset (stocks ranked 1-30), along with its associated results as given on page 60; and the subset made up of the remaining stocks in Group 1 (ranked 31-250):

The Top-30 MFI stock subset earned a 23.7% average annual return, as shown on page 60.

Using more algebra, we can arrive at the average annual investment return for the subset of stocks ranked 31-250 within Group 1 by the following formula, noting that 30 stocks make up 12% of the 250-stock decile (30/250 = 0.12):

(0.12 x 1.237) + (0.88 x P) = 1.179

Solving for P, we get the following result:

The subset of stocks ranked 31-250 within Group 1 earned a 17.1% average annual return.

Again, we see that as you move from a group of higher-ranked stocks (the Top-30 MFI stocks which achieved a 23.7% return) to a group of lower-ranked stocks (stocks ranked 31-250 which achieved a 17.1% return), your performance will degrade, on average. This characteristic of the MFI strategy is vital to the argument I will make below.

=================

Imagine the Top-30 MFI stocks as sorted by the MFI ranking system from best to worst, displayed from top to bottom in a vertical layout. Using the 1,000-stock universe (Mkt Cap > $1B), suppose we call that universe's Top-30 MFI stocks A1 through A30, and arrange them vertically with A1 at the top through A30 at the bottom. Simple enough.

Now, imagining the 2,500-stock universe (Mkt Cap > $200M), suppose we call that universe's Top-30 MFI stocks B1 through B30, and arrange them vertically with B1 at the top through B30 at the bottom. Consider the make-up of this group of 30 stocks. Using my "Assumption" from Part 1 above, these 30 stocks will contain 12 stocks (40% of the total) with market caps greater than $1B; and 18 stocks (60% of the total) with market caps in the $200M - $1B range. Thus, stocks B1 through B30 will contain only stocks A1 through A12 from the (greater than $1B) market cap range discussed in the preceding paragraph. Stocks A13 through A30 will have been ranked so low in this larger universe as to push them all down the list, and out of the 2,500-stock universe's Top-30 MFI group. This does not tell us where in the new Top-30 MFI group stocks A1 through A12 will fall; only that they will be interspersed throughout the group of 30, amongst their 18 smaller cousins. More importantly, because we know that groups of higher-ranked stocks outperform groups of lower-ranked stocks, it stands to reason that the group of 30 stocks consisting of B1 through B30 will outperform the group of 18 stocks consisting of A13 through A30, which got pushed further down in the rankings by the inclusion of additional stocks in the universe.

Finally, imagining the 3,500-stock universe (Mkt Cap > $50M), suppose we call that universe's Top-30 MFI stocks C1 through C30, and arrange them vertically with C1 at the top through C30 at the bottom. Consider the make-up of this group of 30 stocks. Again, using my "Assumption" from Part 1 above, these 30 stocks will contain about 9 stocks (28.6% of the total) with market caps greater than $1B; 13 stocks (42.8% of the total) with market caps in the $200M - $1B range; and about 8 stocks (28.6% of the total) with market caps in the $50M - $200M range. Thus, stocks C1 through C30 will contain only stocks A1 through A9 from the (greater than $1B) market cap range discussed two paragraphs above; and only stocks B1 through B13 from the ($200M - $1B) market cap range discussed in the preceding paragraph. Stocks A10 through A30, as well as stocks B14 through B30, will have been ranked so low in this larger universe as to push them all down the list, and out of the 3,500-stock universe's Top-30 MFI group. This does not tell us where in the new Top-30 MFI group stocks A1 through A9, and B1 through B13, will fall--only that they will be interspersed throughout the group of 30, amongst their 8 microcap cousins from the $50M - $200M range. Most importantly, because we know that groups of higher-ranked stocks outperform groups of lower-ranked stocks, it stands to reason that the group of 30 stocks consisting of C1 through C30 will outperform the group of 38 stocks consisting of A10 through A30 and B14 through B30, all of which got pushed further down in the rankings by the inclusion of additional stocks in the universe.

=================

My conclusion from Part 1 above was that:

--The largest 1,000 stocks (Mkt Cap > $1B) averaged 22.9% per year.
--The next-largest 1,500 stocks ($200M - $1B) averaged 24.2% per year.
--The smallest 1,000 stocks ($50M - $200M) averaged 48.6% per year.

Based on that conclusion, I thought it best to invest in the micro cap group only, shunning stocks greater than $200M.

I now change my conclusion to the following:

The greater returns achieved from the largest (3,500) stock universe did not arise because of the addition of smaller caps, per se, but because the universe was simply larger, causing the Top-30 MFI stocks to be of higher overall quality, as ranked by the MFI's goodness and cheapness parameters.

I now think it best to cast the widest net possible, opting for a universe consisting of market caps greater than or equal to $1M, and gravitating toward the top 25 before looking at the top 50 or top 100 on Greenblatt's website, ignoring any steering toward a particular market cap group. I am leery of relying on my 48.6% performance estimate for the smallest 1,000 group of stocks.

Lincoln Minor
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