Dec

12

Mr. Pennington’s link to Morningstar’s analysis of RSP , the S&P 500 equal-weight ETF got me to thinking… Morningstar’s conclusion was that RSP’s returns are explained by mid-cap stock returns. Stated another way, the *performance of an equal-weight large cap portfolio is explained by mid-cap performance* (?!?!?). It seems rather cavalier to dismiss a huge swath of a large-cap index and say that those are really just mid-cap stocks. It’s been a while, but I certainly don’t remember any “premium” based on size for mid-cap stocks. So what is driving the recent outperformance? Is it possible that the converse is true? Perhaps mid-cap performance is really a proxy for equal-weight portfolios regardless of size. I hypothesize it has more to do with portfolio/index construction rather than uniqueness of size. So I need to find a way to measure a portfolio’s construction and figure out if size matters.

Since I was interested in examining how the portfolio/index is weighted I took a look at S&P 500 and the S&P MidCap 400. Since both are capitalization weighted they tend to be “top heavy” in that the largest capitalization stocks get more weight in the index and subsequently have a much bigger impact on performance. But just how top heavy are they?

*S&P 500*

*S&P MidCap 400*

Top 10 Holdings of Index

19.62%

6.95%

Ratio to Equal-Weight

9.81

2.78

The S&P 500 is almost 10x top heavy relative to an equal weight portfolio. This indicates that the S&P MidCap 400, while not an equal-weight portfolio, “looks” much more like one than the S&P 500 and this could explain, in-part, the similarity between mid-cap stock performance and large-cap equal weight performance. As an aside, I thought it would be interesting to see the evolution of “top-heaviness” in the S&P 500 since I have some historical data. Using quarterly constituent data from Q2 1995 -Q3 2010 of the components of the S&P 500 I computed the weight for each stock in the index based on their market capitalization relative to the total market capitalization of the index at the beginning of each quarter. I then computed the skewness.

Back to the question at hand; I wanted to determine if size is driving the performance difference between an equal-weight and a cap-weighted portfolio or if it was due to how the portfolio/index was constructed. I decided to calculate the weighted-average correlation within a portfolio to see if there was any relationship between how “well” it was constructed. I think of this as a crude measure of how “diversified” a portfolio is, with the implication that severely skewed weightings are sub-optimal and lead to higher correlation while equal-weights by nature are more “diversified” (in a naïve sense) and that’s what is driving performance. Since I needed to look “inside” a portfolio to compute this statistic I collected the daily 100 portfolios formed on size and value from the Ken French website (it was easy and free). Using the daily data I formed non-overlapping equal-weight decile portfolios for size with break points based on both value and equal-weighting over a 62 day period. Why? Well, it’s close-ish to a quarterly period and I had to use excel so it was semi-painless and it made the weighted-average correlation calculation easier. A more careful study would actually look “inside” each of the 100 portfolios themselves. I computed the log return and the weighted average correlation within the portfolio during these periods to create a time series beginning in 1963. I report the summary statistics for the 10 decile portfolios (“quarterly”) return series.

It turns out that all of the portfolios look about the same in that the portfolio weighted average correlation and returns are clustered and there is no meaningful relationship. The one exception is the equal weight small decile which shows superior return characteristics. So to re-cap: forming a portfolio on size leads to portfolios that all look similar from both a portfolio/index construction and return perspective. Since there is no meaningful difference in returns based on size, and as noted before, the characteristics of the portfolio/index construction are similar it at least provides two data points to start questioning Morningstar’s explanation of causality. It’s not a slam dunk, but it’s a start of what could be more rigorous analysis. But wait, since I had already gone to the trouble to test “size” I thought I’d take a peek at “value”.

Lo and behold. The deeper the value proposition the lower the portfolios weighted average correlation and the higher the returns. While it’s a small sample there is clearly a strong relationship between portfolio construction (as measured by this metric) and return, certainly stronger than I would have thought ex-ante. The portfolios formed on equal weight breaks also dominate the value breakpoint formed portfolios, another piece of evidence in support of the original question. Of course on reflection this result makes intuitive sense. Growth portfolios are primarily driven by the same factors, which are largely systemic and therefore more highly correlated, whereas value portfolios tend to have more idiosyncratic risk so they should have a lower weighted average correlation within the portfolio. It is sometime easy to forget that portfolio construction is just as important, if not more so, as security selection. So now my question becomes; do the returns from value-investing accrue because it’s “value” or because they are “better” built portfolios or is it some combination of the two? Which came first, the chicken or the egg?
 


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