Efficient Frontier
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William J. Bernstein

Of Markets and Barbells


Iíve got a confession to make. I donít like midcap stocks. And I donít feel too bad about it, because neither do a lot of other portfolio theorists. Itís nothing personal; the problem is that theyíre neither fish nor fowl.

First, letís get some preliminaries out of the way. The Center for Research in Security Prices (CRSP) divides the investable universe into 10 size deciles, based on the approximately 1,800 stocks trading on the New York Stock Exchangeó180 NYSE stocks in each decile. The NYSE is used to demarcate the size limits in each decile for the thousands of other stocks in the NASDAQ and AMEX, most of which are quite small. So the 1st decile (largest market cap) has 212 stocks¾ 180 on the NYSE and 32 on the AMEX and NASDAQ, like Microsoft. The 10th (smallest) decile has 2,196 stocks¾ 180 on the NYSE and 2,016 on the AMEX and NASDAQ.

The original Coward's Portfolio is an extreme example of my aversion to midcaps¾ its domestic allocation is split equally between the S&P 500 and the DFA U.S. 9-10 Small Company Fund. At 1999 year-end 97.6% of the S&P 500ís cap was in deciles 1 and 2; by definition the DFA 9-10 Fund is aimed at the smallest two deciles (although in reality it also has a fair amount of 8th decile contribution as well). So splitting oneís domestic stock exposure between these two indexes produces a "barbell portfolio"¾ one which virtually ignores decile 3 through 7¾ i.e., midcaps. Using the Russell 2000, which is smeared broadly from deciles 4 through 8, instead of the 9-10, ameliorates, but does not eliminate the phenomenon.

Iím not alone in my avoidance of the middleweights. Dimensional Fund Advisors, not unsurprisingly, favors The Barbell as well. But thereís an inconsistency here. After all, DFA is the Vatican of the Efficient Market Hypothesis; I regularly genuflect in that direction as well. And if you adhere to the EMH, then you ceteris paribus believe that you must hold the entire market in cap-weighted fashion. For academic types this means the CRSP-All Index, and for the rest of us it means the Russell 3000 or the Wilshire 5000, the latter of which can be purchased as the Vanguard Total Stock Market Fund. (The stock answer from Santa Monica is that small size is yet another dimension of risk, and that holding the market portfolio does not take this into account. But that still does not explain the complete avoidance of midcaps.) So why do we violate this sacrament?

The reason is that the essence of effective portfolio construction is the combination of noncorrelating assets. Letís look at the correlations of the S&P 500 (large), S&P 400 (midcap), S&P 600 (small), and the DFA 9-10 ("microcap") indexes (monthly returns, 10 years ending 4/30/00):

S&P 500

S&P Midcap

S&P Small

DFA 9-10

S&P 500

1.00

S&P Midcap

0.87

1.00

S&P Small

0.70

0.89

1.00

DFA 9-10

0.53

0.74

0.89

1.00

Not surprisingly, the larger the difference in cap size between two indexes, the lower their correlation; notice that the lowest correlation is between the largest and microcap stocks (0.53). By adding in the small and midcap indexes you are dumping highly correlating assets into the mix, which may be counterproductive.

In order to investigate this problem I considered the 10 deciles from 1926 to 1999 as separate portfolios and optimized return/SD, rebalancing annually. It cannot be emphasized strongly enough that this is a purely theoretical exercise, as these portfolios are not actually ownable in the real world; the decile portfolios themselves are reshuffled quarterly, with very high turnover. Here is the optimization output with ascending risk:

Decile:

Return

SD

1

2

3

4

5

6

7

8

9

10

10.62%

18.86%

0.0%

79.3%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

20.7%

11.14%

20.00%

55.0%

38.1%

5.7%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

1.2%

11.74%

22.50%

32.8%

53.2%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

14.0%

12.13%

25.00%

15.4%

60.0%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

24.5%

12.39%

27.50%

1.3%

64.4%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

34.3%

12.57%

30.00%

0.0%

53.9%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

46.1%

12.67%

32.50%

0.0%

42.4%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

57.6%

12.72%

35.80%

0.0%

27.9%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

0.0%

72.1%

The first row is the minimum-variance portfolio, and the last the maximum-return portfolio. As you can see, these are in fact all barbell portfolios, consisting almost exclusively of deciles 1, 2, and 10. So, looking at the 1926-99 data, there can be no question that The Barbell beats The Market.

Next, I compared this optimized portfolio (the red curve) with three others:

As you can see, none of these portfolios has much of an efficiency advantage. Most importantly, although the market portfolio (CRSP-All) has a very different composition from the barbell/optimized portfolios, its efficiency is only slightly less. Finally, very few rational investors operate much to the right of the Market Portfolio on the risk axis¾ most folks hold some cash and bonds. So letís complete the picture by drawing a line from the riskless asset (T-bills) to the market portfolio:

As you can see, most investors would be quite well served by using the market portfolio. (And even if you were one of those truly risk adverse investors who could happily kiss goodbye 70% of their net worth from time to time, the most efficient way to obtain the best risk-adjusted return would be leveraging the market portfolio rather than attempting to travel up one of the graphís barbell-portfolio colored curves.)

Two more powerful arguments can be made against the barbell approach. The first is tracking error. No matter how rugged an individualist you are, temporarily underperforming The Market causes pain, and there can be no doubt that The Barbell does this, while offering little excess return. Second is the data-mining issue. The differences between The Market and The Barbell are so small that one cannot be sure that weíre just looking at statistical noise, even with 74 years of detailed data.

So itís hard to make a case for The Barbell on theoretical grounds. A better case can be made on current market valuation, with small stocks being considerably cheaper than large stocks by almost any parameter you look at.

And we havenít touched a much more important issue, which is the use of value exposure. In fact, adding a large value component makes a portfolio less barbell-like, since "large value" stocks have a much smaller market cap than large growth stocks ($37B for Vanguardís Value Index Fund and $5B for DFAís, versus $93B for the S&P).

Weíll save value for another day.

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