August 2016

**In Brief**

**Adoption and sophistication increases**— Investors are increasingly incorporating factor-based strategies into their portfolio mix and becoming more sophisticated —*e.g.*, by employing multiple smart beta strategies and expressing interest in multifactor applications — in part because single factors have had periods of underperformance.**Combining factors**— Combination factor portfolios usually outperform single factors. The simple combination of factor-based strategies in the equity market,*i.e.*, an asset allocation approach, can add value by reducing portfolio volatility and increasing average returns. Combining those factors cross-sectionally, forming portfolios of stocks that score well on multiple factors, further improves portfolio performance relative to the asset allocation approach.**Optimized factor combinations**— Some form of optimization can provide additional value when factors are combined, again primarily through volatility reduction. Here also, cross-sectional combinations (bottom-up) of factors have provided higher return with lower volatility than asset allocation (top-down) type approaches.**Active management**— Smart beta strategies can be combined, or better yet, based on a signal composed of several factors. As they progress along this spectrum, they begin to look more like quantitatively based active investment strategies that may have a more developed underlying approach and proven track records.

Asset owners are increasingly using smart beta strategies, also known as factors or factor-based strategies, in their equity investment portfolios. In doing so, they are looking beyond asset classes to examine factors — the broad, persistent drivers of risk and return that underlie all assets — and determine how best to capture the risk premia associated with them.^{1}

In thinking about factors such as value, quality and size, one might consider the following analogy: In the same way that protein, fat and carbohydrates are the underlying constituents of a hamburger and fries, factors are the building blocks of asset classes. Even if we are focused on the protein and carbohydrates in the hamburger and fries (the asset class), the fat (the factor) is still part of the meal. Factors are part and parcel of what drives risk and returns in investment strategies, whether they are explicitly identified or not.

Investors in securities essentially take two forms of risk: systematic factor risk and idiosyncratic security-specific risk. It is the former that can be isolated and targeted in specific investment strategies. While some individual factors have shown persistence and produced positive returns over time, they have also been shown to have periods of relative underperformance. This has led to an interest in understanding the merits of employing multiple factor strategies.

In this paper, we present research focused on factor portfolios invested in global equities, and make four key points. The first point is that factor investing continues to gain momentum. The second is that multifactor models tend to outperform single factors over time. The third is that when combining factors, it is generally more efficient, both in terms of average return and risk-adjusted return, to do so cross-sectionally through a multifactor model, rather than via asset allocation. An asset allocation approach makes portfolio allocations individually to each of the factors, while a cross-sectional approach allocates based on an aggregation of factor rankings. For example, in this case, the cross-sectional forms its portfolio by ranking the universe by each factor, then combining those ranks and taking the top 20% of the average rank. The asset allocation approach forms separate factor portfolios and then combines the portfolios each month. The fourth is that using optimization-based tools that weight factors in a composite based on those factors’ returns, correlations and volatilities can help improve the investment returns of the composite, mainly by reducing the volatility of its returns. (See the Methodology on page 8 for further details.)

These last two return-enhancing steps, combining factors in the cross section and via optimization-based methods, begin to blur the line between smart beta and quantitative investing, in which well-developed investment processes and long track records are the norm. To provide some context before delving into the key points mentioned above, we have included some data on the current adoption of equity factor strategies among institutional investors.

### Factors: State of play

Investing in equity factors is gaining traction across the globe and particularly in Europe. Almost three-quarters (72%) of over 250 asset owners in Europe, North America and Asia surveyed in a recently published FTSE Russell study indicated they have implemented or are actively evaluating equity factor strategies, up from 44% last year and double the percentage reported in 2014 (see Exhibit 1).2 The proportion of asset owners reporting they have not evaluated factor investing has dropped from 40% in 2014 to 12% in 2016.

While growth has been flat over the past two years, just under half of asset owners with $10 billion or more in assets under management (AUM) have a factor allocation. Growth in factor adoption has been strongest among asset owners with under $1 billion in AUM: In 2016, just over a quarter have a factor allocation, up from 9% in 2014.

Europe continues to lead North America and Asia in adopting equity factor strategies (see Exhibit 2). Among adopters, the share of equity portfolio AUM devoted to factor strategies has increased: Those with over 20% of assets in factor strategies has grown from 18% in 2014 to 39% in 2016 (see Exhibit 3).

There is a diversity of opinion and practices in factor investing. Among institutional investors employing equity factor-based strategies, more than two-thirds are using two or more factor strategies (see Exhibit 4). However, usage is dispersed with fat tails: 31% use a single strategy, while 21% use five or more.3 On average, four strategies are being evaluated by asset owners (among both users’ factor strategies and those who do not use them)^{4}.

Having established the trend toward greater use and sophistication vis-à-vis smart beta investing, we delve into our first two points: 1) combination factor portfolios usually outperform single factors; and 2) combining factors in the cross section has historically been more effective than combining factors through asset allocation.

## Technical definitions

**Factors **— Broad, persistent drivers of risk and return that underlie all assets.

**Smart beta **— Typically, rules-based strategies that screen a broad group of securities to target one or more factors in an attempt to deliver higher returns or reduced risk relative to a traditional index.

**Asset allocation approach **— In this context, an asset allocation approach makes portfolio allocations individually to each of the factors on a top-down equal-weighted basis or based on some other fixed weighting schema.

**Cross-sectional approach **— Adopts a security-level bottom-up approach and makes portfolio allocations based on an aggregation of factor rankings.

**Portfolio optimization **— A formal mathematical approach to making investment decisions across a collection of financial instruments or assets in such a way as to make the portfolio better than any other according to some criterion.

## Combining smart beta strategies

To examine the merits of combining factors, we looked at the historical returns of six common smart beta strategies, as well as the best possible equal-weighted combinations of those strategies.^{5} The strategies are: high price momentum (momentum), low volatility, high return on equity (ROE), low price-to-book or high book-to-price (B/P), high dividend yield (yield) and low price-to-earnings or high earnings yield (E/P).

We represent these smart beta strategies using the MSCI World Universe.^{6} For each strategy, at each month-end, beginning December 31, 1997,^{7} we ranked all the stocks in the universe by the factor in question and then formed an equal-weighted portfolio from the top 20% of stocks. We held this portfolio for a month, observed its return, and then rebalanced. For more on the details of this process, please refer to the Methodology section at the end of the paper.

Exhibit 5 shows that these strategies have had average returns of between 79 bps/month (low volatility) and 100 bps per month (E/P). The volatility of monthly returns has varied considerably, ranging from 3.32% to 6.47%, the standard deviation calculated for the low volatility and book-to-price (B/P) portfolios, respectively.

To illustrate the benefits of combining strategies, in Exhibit 6 below we summarize the monthly returns to combinations of different numbers of these smart beta strategies, starting with a combination of two strategies, then looking at three strategies, and so forth.

For each number of factors used, we chose the equal-weighted combination of factors with the highest ratio of mean monthly return to volatility of return. For example, of the 15 possible combinations of two of the six factors, the one with the best average return relative to volatility of return was momentum plus low volatility.

We show returns to two types of factor combinations. The first, labeled “XS” for cross-sectional (bottom-up), forms its portfolio by ranking the universe by each factor and then combining those ranks and taking the top 20% of the average rank. The second, labeled “AA” for asset allocation (top-down), forms separate factor portfolios and then combines the portfolios each month. For each approach to factor combination, we chose the set of factors with the best mean return to volatility ratio, i.e., the best XS and AA combination.

We can make a few statements about the results in Exhibits 5 and 6:

**Combination factor portfolios outperform single factors**— Investing in a combination of factors yields an improved return profile, relative to single factors, due to diversification. For example, the asset allocation combination of momentum and low volatility has returned, on average, 84 bps per month, the average of the two individual strategies’ returns of 79 and 88 bps per month. However, the volatility of the combined portfolio is 3.85%, which is less than the average of the two strategies’ volatility, i.e., 4.07%.

**Bottom-up/cross-sectional outperformed top-down/asset allocation**— For each number of factors combined, a multifactor model or cross-sectional combination of factors has been more effective than an asset allocation approach. In each multifactor combination, the XS row has a higher mean return and higher return per unit of risk than the AA row.^{8}

**No single number of factors outperform**— While there are clear benefits to combining multiple strategies, there is no single number of factors that is clearly more beneficial than the others (at least among these six factors). For example, the best three-factor model’s top quintile portfolio has about the same mean return and return-to-risk ratio as the best five-factor model. This is partly because these factor combinations are equal-weighted and do not take advantage of factor correlation structure.

The exhibits illustrate the value added over time of making simple combinations of smart beta strategies, particularly at the security level (as opposed to the factor portfolio level). The next section of the paper looks at the benefit of accounting for relationships between factors in such combinations.

## Factor correlation structure

The six factors shown in Exhibit 5 are not independent. For example, book-to-price and earnings-to-price have historically been positively correlated: Stocks that tend to trade cheap relative to their book value also tend to trade cheap to their earnings. Both factors tend to be negatively correlated with price momentum, since stocks that have been outperforming their peers are often more expensive on a valuation basis than those peers. It is also true that over time different portfolios designed to capture these factors will exhibit different behavior.

These correlations, along with information about factors’ average returns and their return volatility, can be important inputs in deciding how to weight factors in a composite model, or how to weight factor portfolios in a combined portfolio.

Exhibits 7 and 8 below summarize the time series and average cross-sectional correlations of these factors.

Exhibit 7 confirms that book/price and earnings/price have historically been positively correlated, i.e., stocks that trade cheap to book have also traded cheap to earnings. Both factors are also positively correlated with dividend yield. Momentum is negatively correlated with all three factors, reflecting the fact that high-momentum stocks are often not value stocks. One can observe other relationships as well. For example, the fact that historically book/price has been negatively correlated with high return on equity (ROE).

The time series return correlations in Exhibit 8 show that these factors often have return dynamics similar to their factor correlations, as one might expect. Momentum, for example, is negatively correlated with book-to-price, dividend yield and earnings-to-price, indicating that the momentum factor has outperformed when value factors have underperformed and vice versa.

## Value of optimization

These correlation structures, combined with the differing factor signal strengths and return volatilities shown in Exhibit 5, indicate that it is possible to improve on the average and risk-adjusted returns of the equally weighted models shown in Exhibit 6. We illustrate this in Exhibit 9 below, which summarizes the returns to equal-weighted and optimized asset allocation and cross-sectional models. To give the optimization methodologies the most opportunity to add value, we focus on models that combine all six factors.

In the case of the optimized asset allocation model, we use mean-variance optimization. This approach allocates weight to factor portfolios based on their average historical return, the volatility of those returns, and their return correlation. All else being equal, it will allocate more weight to factors with better signal strength, lower return volatility and returns that are less correlated with other factors.

In the case of the optimized cross-sectional model, we use panel data regression. This approach sets factor weights based on each factor’s historical signal strength and its cross-sectional correlation with other factors. All else being equal, it will allocate more weight to factors with better signal strength and lower correlation with other factors. Please refer to the Methodology at the end of the paper for further details on these techniques.

We chose these two methods to indicate the potential value added of optimization because each uses the information readily available to those employing both the cross-sectional, multifactor modeling approach and the asset allocation, time series approach. When building a portfolio based on a multifactor ranking of characteristics, two key pieces of available data are the historical signal strength of the factors and their cross-sectional correlations over time. When building a time series model for allocating to factor portfolios, key data available are the average returns of each factor, their volatilities and return correlations. While we use different optimization methodologies for the cross sectional and asset allocation approaches, our results are broadly the same if we apply the same set of optimized weights (for example the mean-variance weights) to the asset allocation and cross sectional approaches. It should be noted that the optimized results are in-sample and thus reflect the upper bound of the potential value added by optimizing weights.^{9}

In both the cross-sectional and time series cases, optimized models achieve better risk adjusted returns than their equal weighted counterparts, primarily by reducing return volatility. This reflects the benefits of combining factors with an eye to their correlations and volatilities. The optimized cross-sectional model outperforms both its equal-weighted peer and both time series models, primarily by virtue of combining factors at the security, rather than the portfolio, level.

While the summary table in Exhibit 9 can provide an overview to differences in model performance, a chart of compounded returns can show the implication of these differences over time. Exhibit 10 shows that the cross-sectional portfolios have had materially larger compounded returns over time. For example, a $100 million invested at the end of 1997 compounds to $728 million based on the cross-sectional optimized model, while for the optimized asset allocation model that value is $542 million, a difference of $186 million.

Given the points made, it is little surprise that multifactor combination strategies are on many investors’ radar. Just under half of the respondents in the FTSE Russell 2016 study are evaluating multifactor smart beta strategies, while close to 40% are evaluating low volatility strategies (see Exhibit 11).

In our view, it can be helpful to complement factor-based investment approaches with fundamental inputs as a way to capture qualitative analysis in a way that purely quantitative methodologies are not always able to do as effectively. Adding a complementary independent source of information may also improve risk-adjusted returns by increasing diversification.

## Conclusion

Our research shows that combination factor portfolios outperform single factor strategies. Moreover, multifactor models have outperformed a top-down asset allocation approach. Optimized models have achieved better risk-adjusted returns than their equal-weighted counterparts, primarily by reducing return volatility.

In our view, the analysis presented shows that harnessing systematic factor returns over time requires the ability to employ a multifactor approach along with other portfolio management tools such as optimization. As more sophisticated smart beta approaches are used, the more they begin to look like quantitatively-based active investment strategies that, like MFS, typically have a well-developed underlying approach and proven track records.

When investment strategies are predicated on more complex quantitative models, it is important to bear in mind that models have limitations, and these need to be thoughtfully taken into account. We suggest that complementing a factor-based approach with a fundamental signal — what we term a “blended” approach — may be beneficial in some cases.

## In Summary

- Interest in factor investing is growing in the market along with a greater level of sophistication.
- Multifactor portfolios have outperformed single-factor portfolios over time.
- In multifactor portfolios, a cross-sectional bottom-up approach is more efficient than a top-down asset-allocation approach.
- Optimized portfolios have achieved better risk-adjusted returns than their equal-weighted counterparts, primarily by reducing return volatility.
- As they become more sophisticated, multifactor portfolios begin to look like active quantitative strategies, which have incorporated multifactor capabilities for several decades.
- Fundamental analysis may provide a complementary independent investment signal to quantitative portfolio construction methods, which by design look to the past to predict the future, improving diversification and potentially improving risk-adjusted returns in the process.

## Methodology Notes

**Universe**: constituents of the MSCI World Index, observed monthly from 31 December 1997 through 31 December 2015.

**Data**: Fundamental data, *e.g.*, earnings per share or return on equity, is sourced from Compustat for US stocks, and the Worldscope database for international stocks. All fundamental data is lagged by three months to reflect a reporting lag. Pricing data, used to calculate price momentum, stock level volatility and forward returns, is provided by FactSet Historical Prices. Forward returns are trimmed at +/- 75% to limit the influence of outliers.

**Factor definitions**:

- Momentum: Trailing 12 month total return, less the most recent month’s return
- Volatility (used for the low volatility factor): The standard deviation of the last two years’ monthly returns. The underlying monthly returns are capped at +/- 100% to limit the influence of outliers
- Return on Equity: Trailing twelve months net income divided by average total equity
- Book/price: Most recent book value per share divided by price per share
- Earnings/price: Trailing twelve months earnings per share/price
- Yield: For US stocks, dividend yield is primarily a projected annual per share dividend payment, based on the most recent dividend paid (excluding extra or special dividends). For international stocks, where reporting frequencies are more variable, dividend yield is primarily based on dividends paid over the last twelve months

**Optimization**:

- Mean-variance optimization: Factor portfolio weights are optimized to maximize an objective function that seeks to maximize the weighted return of the factor portfolios and minimize the weighted covariance of the factor portfolios. The returns underlying the optimization are the total returns of factor top quintile portfolios. Weights are constrained to be greater than or equal to zero. The factor covariance matrix is “shrunk,” in that sample correlations and volatilities are regressed toward the mean correlation and volatility for the set of factors. This shrinking is done to limit the effect of noise and create more intuitive weights
- Panel data regression: The dataset used in this study is a history of monthly cross sections. Each monthly dataset can be envisioned as a spreadsheet of data, with individual stocks in each row, and characteristics or factor exposures (
*e.g.*, momentum, book/price) in each column. To create the independent variables used in the regression, each month’s factor exposures are stacked on top of each other, creating one matrix of six columns and several hundred thousand rows (roughly: 12 months x 18 years x 1500 stocks). Similarly, each month’s forward return data is stacked to create a vector of the same length. Forward returns are then regressed onto the factor exposures. The resulting set of betas is scaled so that it sums to 100 to provide the cross- sectional model weights.

## Endnotes

^{1}In this paper, factor-based strategies and smart beta are used synonymously, referring to rules-based strategies that screen a broad group of securities to target one or morefactors in an attempt to deliver higher returns or reduced risk relative to a traditional index. Risk premium is the return in excess of the risk-free rate of return that an investment is expected to yield.

^{2}FTSE Russell: Smart Beta: 2016 Global Survey Findings from Asset Owners. This is the third year FTSE Russell has conducted this study. The number of asset owners participating in the study was: 181 in 2014; 214 in 2015; and 253 in 2016. It was conducted in Jan and Feb 2016.

^{3}Ibid.

^{4}FTSE Russell Insights: Combining Factors, February 2016.

^{5}While the insight that multifactor models have outperformed an asset allocation approach is something we have seen in our own research and portfolio management experience, in writing this paper we acknowledge the contributions of Roger Clarke, Harindra de Silva, and Steven Thorley, “Factor Portfolios and Efficient Factor Investing”, June 30, 2015.

^{6}The MSCI World Index captures large and mid cap representation across 23 developed market countries. It currently has 1,645 constituents, covering approximately 85% of the free float-adjusted market capitalization in each country.

^{7}Data for the analysis was available from this date.

^{8}For examples of use of similar smart beta strategies in recent literature see: “Alternatively Weighted and Factor Indexes”, FTSE Russell, February 2016; “Smart Beta: 2016 Global Survey Findings from Asset Owners”, FTSE Russell, 2016 (cited elsewhere in paper); Rob Arnott, Noah Beck, Vitali Kalesnik, Ph.D., and John West, CFA, “How Can ‘Smart Beta’ Go Horribly Wrong?”, Research Affiliates, February 2016.

^{9}In both approaches, one can definitely improve over the simple, backward-looking averages used to fit these models. For example, one can develop forward-looking forecasts for factor returns, applicable in either the multifactor modeling or asset allocation approach. However, the two approaches used here are equally simplified given their input data. It is also important to point out that the returns to these optimized models are completely in-sample. In other words, model returns are calculated over the same sample set for which models are fit. In this sense, these model returns represent the best-case improvement in model performance possible through optimization. In reality, researchers commonly see that when used out-of-sample, i.e., applied to new data, models do not perform as well as they do over the data to which they are fit.

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