Interest in passive investing has risen in recent years. Many investors, increasingly cost-sensitive in the wake of the financial crisis, are not convinced that active management will deliver excess returns, net of fees, over their benchmarks. Passive investing has traditionally focused on replicating cap-weighted benchmark indexes, either through index mutual funds, exchange traded funds (ETFs) or the creation of matching in-house portfolios. Cap-weighted indexes provide cost-effective exposure to various segments of the equity market with a high degree of liquidity and capacity. This assures investors of a return that closely tracks the broad equity market at a low cost.

Parallel to investors’ increased interest in passive investing has been the growth in numbers of indexes based on strategies that depart from those of cap-weighted indexes. These new indexes aim to incorporate exposures or strategies that typically are not available in cap-weighted indexes. Variously termed “strategy indexes,” “smart beta indexes” or “alternative indexes,” they make up a middle ground between the traditional opposites of passive and active investing. They are attractive for their low cost compared to actively managed funds, and for their ability to customize exposures and incorporate specific strategies, options that are generally not possible in traditional passive investing.

Among the most innovative of these smart beta strategy indexes are “fundamentally weighted indexes” (see Arnott, Hsu and Moore [2005]). The Russell Fundamental Index® methodology, which Russell developed in collaboration with Research Affiliates®, weights stocks by accounting measures such as sales revenue, cash flow and dividends. The key characteristic of these weights is that the size of a company is measured without any direct link to current market price (see Russell [2012] for the precise construction methodology). This stands in sharp contrast to the standard practice of weighting the stocks in an index by their capitalization as measured by current market price – i.e., cap weighting. As we shall see, fundamental indexes have a value tilt, but because the weights are divorced from current market prices, the result is a time-varying value strategy that is distinct from those characterizing traditional cap-weighted value indexes. This provides a complementarity investors can exploit to diversify their existing equity portfolios.

This paper explores how an investor might combine cap-weighted and fundamental indexes to shape factor exposures that have historically improved the risk/return profile of the whole portfolio. Our emphasis is on exploration, with no intention of arriving at a single “optimal” portfolio. To make the analysis more clear, we look at a hypothetical passive investor in U.S. equities who uses the Russell 3000 all-cap U.S. index as a benchmark. This investor is convinced by the extensive literature on the subject that there are long-term rewards to be gained by tilting portfolios to value and small cap factors (Fama and French [1992]). The traditional approach to incorporating these views is to allocate portions of the portfolio to cap-weighted value and cap-weighted small cap indexes. This paper uses a factor analysis to show how, historically, Russell Fundamental Index strategies would have added new dimensions of diversification for our hypothetical investor.

**The Fama-French-Carhart four-factor model **

The Fama-French-Carhart four-factor model is a workhorse in academic research. Fama and French (1992) extended the single-factor CAPM of Sharpe (1964) to include factors for both value and small cap. Carhart (1997) showed that a fourth factor - momentum - was an important explanation of stock returns as well.

The complete model is expressed as

*Index-rf=a+b∙(Market-rf)+c∙SMB+d∙HML+e∙MOM+error, *(1)

where *rf *is the “risk-free” rate of financial theory, proxied by the one-month T-bill. *Market *is the cap-weighted return of all the stocks on the NYSE, AMEX and NASDAQ exchanges. *SMB *(small minus big) is the return to a portfolio of small cap stocks minus the return to a portfolio of large cap stocks, and thus is an estimate of how well the market rewards a tilt to small cap stocks. Likewise, *HML *(high minus low) is the return to a portfolio of stocks with high book/price ratios minus the return to a portfolio of stocks with low book/price ratios. This too is an estimate of how well the market rewards a tilt to value stocks (see Fama and French [1993] for a detailed description of how the factors are constructed). *MOM *(momentum) is the return to a portfolio holding many of the previous 12 months’ best-performing stocks minus the return to a portfolio holding many of the previous 12 months’ worst-performing stocks (see Carhart [1997] for details). The coefficients *b, c, d *and *e *measure the exposures of the index to each factor. The contribution of the factor to the index return would then be the exposure times the market or factor rewards: *b∙(Market-rf),c∙SMB*, etc.

The intercept of equation (1), *a*, plays an interesting role in this model. It is a systematic return that cannot be explained by the four factors. This could be due to value added or subtracted from the way the exposures change over time, or to exposures that are not in the model. Academic researchers call it “alpha” or “abnormal return,” but practitioners tend to think of true alpha as being an additional return from active stock-picking insights, which cannot be indexed. For lack of a better term, we will call it “alpha” as well, but the reader should keep in mind that it is more realistically thought of as being a return that cannot be explained by the included factors.

All four factors are derived by use of cap-weighted methodologies, so we expect that they cannot capture all of the return variation in a Fundamental Index investment. This might show up in the estimated intercept as well as in a lower R-squared. In our analysis, that turns out to be the case. But before we get into the empirical results, a brief digression on the relationship between the Fundamental Index concept and traditional value indexes is in order.

**The Fundamental Index approach and traditional value indexes **

One of the knocks on the Fundamental Index construct is that it is just “old wine in a new bottle,” i.e., merely a value index with a new name (Asness [2006]). To illustrate the logic behind this argument, we look at a very simple version of a fundamental index, one weighted solely by book value._{1}

The exact relationship between the fundamentals weight and the market cap weight of a particular stock produces

*W*i,F=*W*i,C *(B*i*/P*i*)/(B*m*/P*m *), *(2)

where Wi,F is the fundamentals weight on stock *i*, Wi,C is the market cap weight on stock *i, B*i */P*i is the book/price ratio of stock *i, *and *B*m*/P*m is the book/price ratio of the cap-weighted market.2 Equation (2) shows that a stock will have a greater weight in a fundamental index than in the cap-weighted market if it has a high book/price ratio relative to the market cap-weighted average book/price ratio. Since stocks with above-average book/price ratios are also classified as value stocks, it is clear that the fundamental index has a value tilt.

However, if the book value of the stock rises and the price does not move, then the fundamentals weight will rise, but the cap weight will not. Conversely, if the market price of the stock rises, but the book value stays the same, then the cap weight will rise while the fundamentals weight will not budge.3 Traditional value indexes select a subset of stocks based on price ratios such as book/price and then cap-weight that subset of value stocks (see Russell [2013] for the construction methodology of all of the cap-weighted indexes in this paper). We can see that while it’s true that a fundamental index has a value tilt, it’s also true that a value index has a tilt toward fundamental index characteristics. The point is that even though they are correlated, they are not the same, and they may exhibit different behaviors over market cycles. As we will see, combining these differing behaviors would have presented diversification opportunities for our hypothetical investor.

**Factor model estimates of large cap value and fundamental indexes **

We start in the large cap space and look at factor exposure estimates over a long period before we look at how those exposures might vary over time. The Russell Fundamental U.S. Large Company Index (FDM LC) has the largest 87.5% of U.S. stocks as measured by a composite score of sales adjusted for leverage, retained cash flow and dividends plus buybacks. The Russell 1000® Value Index (R1000V) is a cap-weighted subset of the Russell 1000® Index (the largest 1,000 U.S. stocks by cap weight), which has an above-average book/price ratio, among other characteristics. Thus, because our hypothetical investor wants exposure to value, we do not consider the Russell 1000. Table 1 shows the exposure estimates of the R1000V Index and the FDM LC indexes.4

By comparing the estimates in Table 1, one can see that both indexes had negative exposures to the small cap factor (SMB), which is to be expected from a large company index; and that both indexes had significant exposures to the value factor (HML), which is also to be expected. The only noteworthy difference between the two is that the alpha estimate for the Russell 1000 Value was negative and statistically significant at the 5% level._{5}

One might conclude, if Table 1 were the only evidence, that the two indexes aren’t much different. But these estimates were averages over many years, and there is no indication of how they might vary over time. Rolling 36-month Fama-French regressions were run to examine this aspect. Figure 1 shows rolling 36-month exposures to the value factor HML. The actual HML returns are also displayed. The series are centered in the middle of their 36-month windows to visually pinpoint the timing.

Figure 1 shows that the exposure to HML was time-varying for both the R1000V and the FDM LC, but the volatility of the FDM LC exposure was 62% higher than the volatility of the R1000V exposure. An important feature is that while both indexes always maintain a value exposure, the dynamic range of exposures was wider for the FDM LC. This more pronounced dynamic is a consequence of weighting by non-price measures of size. In a paper on style timing, Asness, Friedman, Krail and Liew (2000) show that “value spreads… are important indicators of the attractiveness of value over growth.” The range of value spreads is greater with fundamental indexes than with traditional cap-weighted value indexes, which may offer additional predictive power.

Another interesting aspect of Figure 1 is the differences in timing across style cycles. The exposures to both indexes would have risen dramatically in tandem during the late 1990s, just before the dot-com collapse with its resurgence of value returns. But the exposure of the Fundamental Index would have dropped sharply in the run-up to the recent financial crisis, while the exposure of value remained steady until the actual financial crisis. Since the crisis, the HML exposure of the Russell Fundamental Index has remained much reduced compared to the value index; this would have provided a tailwind, as value has underperformed growth for much of the post-2008 period. Overall, the differing dynamics of the two indexes was best illustrated by how the value exposure of the Fundamental Index would have taken a deeper dip ahead of value underperformance.

**The Fundamental Index approach and traditional small cap indexes **

Next, we turn to our investor’s goal of obtaining an exposure to small cap. The usual suspect would be an allocation to the Russell 2000® (R2000), as that is the most heavily invested index of small cap U.S. stocks6. The R2000 is made up of the smallest 2,000 stocks of the Russell 3000® all-cap benchmark (the R1000 makes up the largest 1,000 stocks of the R3000). The R2000 covers around 8% of the total capitalization of the market. The investor might also be interested in the Russell 2000 Value (R2000V) index, as it combines both desired exposures, size and value, by selecting a subset of the R2000 that has a high book/price ratio, among other characteristics.

As an additional source of exposures, the investor might consider the Russell Fundamental U.S. Small Company Index (FDM SC). It includes the bottom 12.5% of stocks ranked by composite scores of accounting measures of size. As with the FDM LC, the FDM SC has a value tilt.

Table 2 displays the results for the three small cap/small company indexes. History for the FDM SC is only available from 1996:07, so all estimates are made from that date to ensure an apples-to-apples comparison. All three indexes would have had significant small cap exposure, with the R2000 showing the most; the R2000V would have followed, and then the FDM SC. All three would also have shown a value tilt, with the R2000V having the largest tilt, which is expected.

Differences between the three indexes would have arisen with alpha and momentum. The FDM SC would have had an alpha over this period of 2%; the two cap-weighted indexes would have had negative alphas. On the other hand, the FDM SC would have had a negative exposure to momentum (anti-momentum) , while the two cap-weighted indexes would have had small momentum exposures. These complementary differences could have proven useful in the construction of portfolios, as we will see below.

Figure 2 shows rolling 36-month exposures to the small cap factor SMB. The actual SMB returns are also displayed. The series are centered in the middle of their 36-month windows to visually pinpoint the timing. The SMB exposure in the R2000 would have shown the least volatility of the three, and would have been consistently larger. This makes sense, as the subset of stocks in the R2000V tends to be the relatively larger companies within the R2000; and the FDM SC index includes the bottom 12.5% of the market by accounting measures, while the R2000 includes the bottom 8% by cap weight.

Looking at the time variation of the exposures, we can see that they all would have jumped in the aftermath of the bursting of the dot-com bubble. We can also see that an upward trend would have occurred in exposures to the SMB factor, especially with FDM SC. Since the financial crisis, the FDM SC would have had exposures close to, and at times larger than, those of the R2000, but has trended downward recently. This shows that Fundamental gives an investor a different small cap dynamic than a traditional small cap index.

**Portfolios of indexes for large and small cap segments **

The preceding analysis of the characteristics of Russell Fundamental Index strategies and cap-weighted indexes leads us to consider how our hypothetical investor might have combined the indexes to produce a portfolio with a desirable set of exposures.

We start with the large cap segment of the investor’s portfolio. Given our hypothetical investor’s belief in a value premium, a good place to start building a passive portfolio might be the Russell 1000 Value (R1000V) Index. The factor exposure estimates in Table 1 and Figure 1 suggest that the R1000V would have delivered substantial value exposures, which is the primary goal. But it is useful to get a clearer picture of other factors that would have contributed positively to returns, and of those that would have detracted. Figure 3 multiplies the rolling exposure estimates with three-year average factor returns to get smoothed cumulative returns to each of the factors, shown as the growth of a dollar. This amounts to a kind of factor-based performance attribution.