 May 2003 A Tip of the Cap
What happened? Why isn't this quant portfolio working? It's natural to question the portfolio and the underlying theory that created it, but in this case, there's also good reason to question the benchmark. While this may look like a really bad form of data mining (If the model fails against the benchmark, change the benchmark.), it really isn't. To see why, you have to understand the composition of both P5 and the benchmark S&P 1500 Super Composite. Caps and BoxesPortfolio 5 was designed to track (and hopefully exceed) the return of the broad equity market. This includes large, mid, and small company stocks as well as growth, value, and core issues. There are nine permutations of these cap and style types (e.g. large cap growth, mid cap core, small cap value, etc.). We nicknamed this the "Stylebox" Portfolio since it mirrors the nine sections of the Morningstar stylebox.
The portfolio itself doesn't hold individual stocks, but rather exchange traded funds (ETFs) representing the nine stylebox categories. Every three months we rebalance the holdings to optimize expected performance. (For more details, click here). Since P5 spans all market capitalizations and all equity styles, we thought it fitting that it have a broad market index as its benchmark. In creating the portfolio, we utilized nine ETFs that track the various S&P capitalization and style indexes so it stood to reason that we would compare the
Many investors are familiar with the S&P 500 and the S&P/Barra Growth and Value Indexes, but haven't heard of the S&P 1500 Super Composite. As the name implies, it's the combination of the S&P 500 (large cap) Index, the S&P 400 (mid cap) Index, and the S&P 600 (small cap) index. Like each of the other S&P indexes, the 1500 is capitalization weighted. This means the S&P indexes aren't just simple averages like the Dow Jones Industrials, but rather are adjusted by weighting each company in the index by the number of shares outstanding. Many investors prefer this approach since they feel it more accurately reflects the price behavior of the overall market. One of the consequences of cap weighting is that the performance of larger company stocks has a greater bearing on the overall index return. To get a sense of this, take a look at Chart 2. There you'll notice that small stocks (defined for our purposes as those with market capitalizations up to $1.5 billion) represent more than half of the 1500 constituent stocks, but only 5.8% of the index' market cap. On the other hand, there are only 223 stocks with market caps over $7.5 billion, but they represent over 77% of that of the index. Giving Equal Weight
To a degree, P5 is market weighted, too. Since its potential constituent ETFs represent the value, growth, or core components of the various market weighted S&P indexes, it's also market weighted within each capitalization. But that's not the same as being a market weighted portfolio. Each quarter when we optimize portfolio holdings, we compare large, mid, and small cap index performance on an equal weighted basis. If our optimization procedure says to favor mid caps over large caps, we add additional weighting to the former at the expense of the latter. That's not what happens with the 1500 though. Given it's over dependence on the handful of companies with the largest market caps, even if mid caps outperform by a considerable margin, it will still trade more in line with large caps. This is illustrated in Charts 3 and 4. Chart 3 shows the annual relative performance of the 1500 and the market cap indexes. Notice how closely it
Chart 4 again shows the annual performance of the 1500, but it also shows what it would have looked like if it were equal weighted between the three market cap indexes. Notice how performance of the Equal Weight Index trails the 1500 in the late '90s when large stocks dominated, and how the trend is reversed when large caps began their correction in mid-2000. We also considered the performance of the Wilshire 5000, another broad-based market index. As its name implies, it's composed 5000 widely traded domestic stocks. It, too, is market weighted, so it's not too much of a surprise to find it tracking much closer to the 1500 than our Equal Weight Index. When It's Good, It's Good;
So does the market weighting of the S&P 1500 pose a problem for using it as the benchmark for Portfolio 5? Perhaps so.
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O DOUBT ABOUT IT, PORTFOLIO 5 hasn't fared too well versus it's benchmark. Early on it behaved much better, exceeding the S&P 1500 Super Composite by as much as 4.86% on May 15, 2002. But lately, it's fallen well behind, trailing by as much as 4.33% as recently as March 17, 2003.
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Chart 5 Small Stocks Relative to Large Stocks January 2002 - March 2003 |
 Source: Ibbotson Associates |
Take a look back at Chart 1. Recall that P5 moved well ahead of both the S&P 500 and 1500 when large stocks underperformed smaller ones. This pattern reversed itself when large company stocks again took the lead.
Now consider Chart 5. It shows the relative performance of the S&P 600 (small caps) vs. the S&P 500 (large caps). Again notice how small stocks outperformed until May 2002. At that point, their lead diminished through October 2002. No rocket science here, that's how the indexes traded. Chart
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Where it gets interesting, though, is the period from October 2002-March 2003. Chart 5 indicates smaller stocks and larger stocks effectively traded together. Small stocks' relative performance moved in a relatively tight range between 4-6%, and ended the period in roughly the same position as they started.
But this is the period in which P5 loses ground to the benchmarks. Certainly P5's component style weightings have something to do with this. During that time, it was emphasizing mid cap value and large cap growth. The latter was the best performing asset class while the former lagged. That could explain some of the underperformance.
Nevertheless, we'd suggest there's more at work here. Large caps were represented in P5 yet it underperformed considerably. We would submit that any time large caps outperform and P5 is not 100% invested in them, it will fall behind the S&P 1500 rather substantially. This again, is the effect of the benchmark's market weighting.
Conversely, when large caps lag and P5 emphasizes other capitalizations, it should experience outsize gains versus the S&P 1500. In other words, when it's good it's good; when it's bad, it's real bad.
To be sure, P5 hasn't always made the correct market and style call. Even so, the effect of market weighting on the benchmark warrants watching.
There aren't but so many broad market indexes available, and the most well known ones (the Wilshire 5000 and the S&P 1500) are market weighted. For lack of better alternatives, we'll continue to measure P5 against the 1500 but we'll keep a close eye on the market weighting effect.
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