When Three Is not a Crowd or When Three Indexes Are Better than One

Three's Good Company: How passive fund investors can create the best equity market proxy

he "active investing versus passive investing" debate will outlast us all. In the meantime, passive investors might consider such "fine-tuning" issues as how many index funds provide a true representation of the U.S. equity market. More specifically, if the goal is to capture the aggregate return of U.S. stocks, is it better to own one total market index or several different indexes?

To answer this question, one could analyze the Dow Jones Wilshire 5000 or Standard & Poor's 500. However, since investors can't actually buy raw indexes, this study used the Vanguard Total Stock Index, which tracks the Dow Jones Wilshire 5000 Index, as the proxy for the U.S. equity market.

The study compared the performance of the Vanguard Total Stock Index to the aggregate performance of three separate index funds-the Vanguard 500 Index, the Dreyfus Mid Cap Index, and the Vanguard Small Cap Index-which represent the large-, mid-, and small-cap components of the Dow Jones Wilshire 5000. When combined into a single portfolio, these three funds seek to accomplish, at least in theory, the same goal as the Total Stock Index.

The time frame for the comparison was limited by the life of the Vanguard Total Stock Index fund, (which started in April 1992) to the 12-year period from January 1, 1993 to December 31, 2004. The data used in this study were extracted from Morningstar Principia.

When each funds' annual returns were measured separately, (Figure 1) the Dreyfus Mid Cap Index had the highest annualized returns with the lowest standard deviation, while the Vanguard Total Stock Index had the lowest return and the second-highest volatility.

But where it gets interesting is the comparison between the Total Stock Index and the three indexes combined into one portfolio. Figure 2 shows the pre-tax results of making a lump sum investment of $1,000 into each of the three separate index funds (Vanguard 500 Index, Dreyfus Mid Cap Index, Vanguard Small Cap Index) on January 1, 1993. At the same time, $3,000 was invested into the Vanguard Total Stock Index fund. By the end of 2004, the combined account value of the three-fund portfolio was $11,809 compared with $10,116 for the Total Stock Index fund-a $1,693 advantage for the three index-fund approach.

So, if the Total Stock Index incorporates large-, mid-, and small-cap stocks, why did the three-index fund portfolio outperform? The short answer is that the Total Stock Index is really a large-cap index rather than a representation of the whole equity market. Even a fund that attempts to be a broad market index by holding literally thousands of securities-most of them small or mid cap-can't escape the impact of market-cap weighting. Any portfolio in which the stocks are weighted according to their market capitalization will be most affected by the performance of the holdings with the largest market cap.

There's plenty of evidence that the three-funds alternative offers greater diversification. Even though the majority of stocks in the Vanguard Total Stock Index are small and midcap, its annual returns are almost the same as those of the Vanguard 500 Index (see Figure 1). The 10-year correlation in annual return between the two is .98, nearly a perfect match. By comparison, the 10-year correlation between the Vanguard Total Stock Index and the Dreyfus Mid Cap Index (as of 12/31/04) was .91 and the correlation with the Vanguard Small Cap Index was .83. The Dow Jones Wilshire 5000 Index is comprised of about 750 large stocks, roughly 1,750 small stocks, and approximately 2,500 micro cap stocks. Nevertheless, according to Morningstar calculations, less than 10% of the market capitalization of the Vanguard Total Stock Index is attributable to small and micro cap stocks. Thus, roughly 90% of the market cap (and therefore return) of the Wilshire 5000 (i.e. Vanguard Total Stock Index) is generated by large cap stocks, which represent only about 15% of the 5000 holdings in the portfolio.

A closer look at Figure 2 shows how the two different approaches performed over the 12 years. In 1998 and 1999, the cumulative account value of the Total Stock Index fund beat that of the three-index fund portfolio by $766 and $1,309, respectively. But when the market began tanking in 2000, the Total Stock Index plummeted faster than the three-index fund portfolio. In 2000, the former lost $1,151, while the latter even eked out a small gain of $76. In 2001, the Total Stock Index gave up $1,067, while the three-fund portfolio lost only $380. Diversification across three distinct indexes, made a big difference when the market turned down. When large caps took a beating in 2001, mid-cap stocks were flat, and small caps were slightly positive, buffering the poor performance of the three-index portfolio's large-cap stock component. By the end of 2001, the three-index portfolio account value was just over $600 larger than the total stock index and by the end of 2004 nearly $1,700 larger. So far, the study only reflects a buy-and-hold strategy, however. Figure 3 shows several other management options that could be used with a three-index portfolio. For example, rebalancing equally among the three index funds at the end of each year generated only a slight improvement in the 12-year annualized return compared with a buy-and-hold approach (12.21% vs. 12.10%).

When the portfolio was annually rebalanced so that one of the three indexes was over-weighted at 50% of the portfolio (with the remaining two indexes being weighted at 25% each) the results were not dramatically improved. In fact, over-weighting the large-cap index (Vanguard 500 Index) led to a lower return and higher volatility compared with both the buy-and-hold approach and equal annual rebalancing. The results of over-weighting the small-cap index were comparable to the buy-and-hold strategy. However, over-weighting the mid-cap index improved the 12-year annualized return by 47 basis points and lowered the volatility by 51 basis points compared with a buy-and-hold approach using three indexes.

Significantly, over this particular 12-year period, each of the five portfolio management strategies generated a higher return, with lower volatility of return, than a buy-and-hold approach using the Vanguard Total Stock index.

It's instructive to look at this performance using rolling three-year returns, which not only minimize the effect of the first and last years' returns, but also capture the dynamic nature of the returns as they occurred. The figure for 1995 (the first row in Figure 4) represents the three-year annualized return from 1993-1995. The next three-year rolling return adds the annual performance of 1996 and drops the 1993 return.

There were 10 three-year rolling returns in the 12-year period. Overall, the over-weighted mid-cap index had the highest average rolling return and the second-lowest standard deviation of rolling returns. But all the average three-year rolling returns of the three index funds were superior to the Total Stock Index in every other management strategy. Even more dramatic was the reduction in the standard deviation of the three-fund approach versus the Total Stock Index fund. Returns for the Total Stock Index accelerated more quickly in the late 1990s and then plunged more drastically as the market cooled in 2000. The rolling return data in Figure 4 are displayed graphically in Figure 5.

Advisers have to be aware that most total stock index funds, like the Vanguard Total Stock Index, accurately reflect a capitalization-weighted equity market. When the performance of a portfolio is weighted according to the market capitalization of the holdings, large-cap stocks will always dominate the performance. If that is the goal, go for it. But, if the goal is to gain exposure to the unique return patterns of large-, mid-, and small-cap U.S. stocks, creating a three-index fund portfolio is clearly a better approach.

Three's not always a crowd.

Figure 1. Annual Returns

Figure 2. Account Balances for Three Indexes vs. Total Stock Index

Figure 3. 12 Year Results

Figure 4. Three-Year Rolling Returns

Figure 5. Three-year Rolling Returns

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Craig L. Israelsen, Ph.D. is an associate professor at Brigham Young University. He teaches family finance in the Department of Home and Family Living. His research interests include mutual fund analysis. He writes monthly for Financial Planning magazine.