Sophisticated institutional investors have increasingly started to review factor-based equity investment strategies. For example, the parliament of Norway, which acts as a trustee for the Norwegian Oil Fund,1 commissioned a report on the investment returns of the fund. This report was requested after the fund's performance fell short of the performance of popular equity market benchmarks. The resulting report (Ang, Goetzmann and Schaefer ) showed that the returns relative to a cap-weighted benchmark of the fund's actively managed portfolio can be explained by exposure to a set of well-documented alternative risk factors. After taking into account such exposures, active management did not have any meaningful impact on the risk and return of the portfolio. The authors argue that such exposures can be obtained through purely systematic strategies without a need to rely on active management. Therefore, rather than simply observing the factor tilts brought by active managers ex-post, investors may consider which factors they wish to tilt toward and make explicit decisions on these tilts. This discussion of active managers' sources of outperformance has naturally led to factor indexes being considered as a more cost-efficient, straightforward and transparent way of implementing such factor tilts. Investors need to ask three main questions when considering such factor-based equity investing strategies.
The first question investors' face when wanting to benefit from factor investing is to determine which factors to select. To avoid the pitfalls of non-persistent factor premia and achieve robust performance, investors should keep the following checks in mind. First, they should require a sound economic rationale for the existence and persistence of a positive premium. Second, due to the risks of data-mining, investors would be well advised to stick to simple factor definitions that are widely used in the literature rather than rely on complex and proprietary factor definitions (Van Gelderen and Huij ).
However, having access to a proxy for a factor is hardly relevant if the investable proxy only gives access to a fraction of the fair reward per unit of risk to be expected from the factor exposure because of the presence of unrewarded risks—due to excessive concentration, for instance. A second relevant question is thus how to best extract the premium for a factor in an efficient way. Amenc et al. [2014a] address this question in detail. The authors present how the smart beta 2.0 approach (Amenc et al. )—the main idea of which is to apply a smart-weighting scheme to an explicit selection of stocks—allows factor indexes to be built that are not only exposed to the desired risk factors but also avoid being exposed to unrewarded risks. This approach, referred to as "smart factor indexes" can be summarised in a nutshell as follows: The explicit selection of stocks provides the desired tilt, e.g., the beta, while the smart-weighting scheme addresses concentration issues and diversifies away specific and unrewarded risks.
A third question is how to allocate across a number of different risk factors to come up with an overall allocation that suits the investor's objectives and constraints. While it is beyond the scope of this paper to provide an exhaustive framework for factor allocation, we illustrate the use of factor indexes in two different allocation contexts, one aiming at improving absolute risk-adjusted returns, and one targeting relative risk objectives.
In what follows, we provide practical illustrations of multifactor allocations drawing on smart-factor indexes, representing a set of four well-documented and popular risk factors: value; momentum; low volatility; and size. To be more specific, we will use the diversified multi-strategy approach,2 which combines five different diversification-based weighting schemes in equal proportions so as to diversify away unrewarded risks and parameter estimation errors (Kan and Zhou , Amenc et al. [2012a]).3
The rationale for multifactor allocation: why combine factor indexes?
Using smart-beta indexes as well-diversified ingredients that provide exposure to desired risk factors, we now analyse the potential benefits of combining factor tilts ("multi-beta allocations"). Many believe that multifactor allocations will tend to result in improved risk-adjusted performance. In fact, even if the factors to which the factor indexes are exposed are all positively rewarded over the long term, there is extensive evidence that they may each encounter prolonged periods of underperformance. More generally, the reward for exposure to these factors has been shown to vary over time (see, e.g., Harvey ; Asness ; Cohen, Polk and Vuolteenaho ). If this time variation in returns is not completely in sync for different factors, allocating across factors allows investors to diversify the sources of their outperformance and smooth their performance across market conditions. In short, the cyclicality of returns differs from one factor to the other, i.e. the different factors work at different times.
Intuitively, we would expect pronounced allocation benefits across factors that have low correlation with each other. As shown in Figure 1, the correlation of the relative returns of the four smart-factor indexes over the cap-weighted benchmark is far below 1. This entails in particular that a combination of these indexes would lower the overall tracking error of the portfolio significantly. On a side note, the same analysis done conditionally for either bull or bear market regimes leads to similar results. More generally, in an asset allocation context, Ilmanen and Kizer  have showed that factor diversification was more effective than the traditional asset-class diversification method, and that the benefits of factor diversification are still very meaningful for long-only investors.
Moreover, investors may benefit from allocating across factors in terms of implementation. Some of the trades necessary to pursue exposure to different factors may actually cancel each other out. Consider the example of an investor who pursues an allocation across a value and a momentum tilt. If some of the low-valuation stocks with high weights in the value strategy start to rally, their weight in the momentum-tilted portfolio will tend to increase at the same time as their weight in the value-tilted portfolio will tend to decrease. The effects will not cancel out completely, but some reduction in turnover can be expected through such natural crossing effects.
We now turn to a detailed analysis of the two key benefits of multifactor allocations; namely, the performance benefits and the implementation benefits.
Performance Benefits Of Allocating Across Factors
Investors may use allocation across factor tilts to target an absolute (Sharpe ratio, volatility) or relative (information ratio, tracking error with respect to broad cap-weighted index) risk objective. We show in Figure 2 the performance and risk characteristics of two multi-beta allocations in the U.S. stock market over a 40-year track record and in the developed excluding U.S. universe over the last 10 years. The first one is an equal-weight allocation of the four smart-factor indexes (low volatility; midcap; value; and momentum). This allocation is an example of a simple and robust allocation to smart factors, which is efficient in terms of absolute risk. The second one combines the four smart-factor indexes so as to obtain equal contributions (see Maillard et al. ) to the tracking error risk from each component index. This approach is an example allocation with a relative risk objective consistent with risk-parity investing.4 Both multi-beta allocations are rebalanced quarterly. Of course, the multi-beta multi-strategy equal weight (EW) and equal risk contribution (ERC) indexes are starting points in smart-factor allocation. More sophisticated allocation approaches (e.g., conditional strategies, or strategies that are not agnostic on the rewards of the different smart-factor indexes) can be deployed using smart-factor indexes as ingredients to reach more specific investment objectives (see Amenc et al. [2014b]).
Figure 2 shows that both the multi-beta multi-strategy EW and ERC indexes present returns that are close to the average returns of the constituents but lower absolute and relative risk than the average constituent index. Both allocations thus deliver improvements in risk-adjusted returns compared to the average constituent index. One should note that the EW allocation delivers the highest Sharpe ratio (0.52 in the U.S., 0.56 in the developed universe) which, compared to the broad cap-weighted reference (0.24 in the U.S., and 0.36 in developed universe), represents a relative Sharpe ratio gain vof 115 percent in the U.S. data and more than 50 percent in the developed universe. One can also note that the allocation across several smart-factor indexes allows the tracking error to be reduced with respect to the cap-weighted reference index. Indeed, one witnesses impressive improvements for the multifactor allocations compared to the average of their component indexes in terms of relative risk, where both in the U.S. and in the developed universe, the reduction in the tracking error is around 0.70 percent for the EW allocation and 1 percent for the ERC allocation (which represent a risk reduction of about 11.5 percent for the EW allocation and more than 16 percent for the ERC allocation relative to the average tracking error of the component indexes in the U.S. case). This tracking error reduction yields an increase in the information ratios to levels of 0.76 and 0.77 from an average information ratio for the constituent indexes of 0.67 in the U.S., while in the developed region the average constituent information ratio is 0.78 and the multi-beta indexes deliver even higher information ratios, of 0.98 and 1.05, respectively, for the EW and ERC allocations. Such improvements in the information ratio, of 26 percent and 35 percent for the EW and ERC allocations, respectively, in the developed universe, are considerable and support the idea of diversification between smart factors. Moreover, compared to the average of their constituent indexes, the multi-beta multi-strategy indexes also exhibit significantly lower extreme relative risk (95 percent tracking error and maximum relative drawdown). In the developed universe, the maximum relative drawdowns of the multi-beta indexes are actually lower than those of any of the constituent indexes. It is noteworthy that—due to its focus on balancing relative risk contributions of constituents—the ERC allocation provides greater reductions in the relative risk measures such as the tracking error and the extreme tracking error risk.
Briefly stated, the multi-beta allocations provide the average level of returns of their component indexes. However, factor diversification leads to a risk reduction that is particularly strong in relative terms, which eventually results in risk-adjusted performance that is well above average. Additionally, the benefits of allocation across different factors can be seen in the probability of outperformance, which is the historical frequency with which the index will outperform its cap-weighted reference index for a given investment horizon. The results in Figure 2 suggest that the probability of outperformance increases substantially for the multi-beta indexes compared with the average across component indexes, especially at short horizons. The higher probabilities of outperformance reflect the smoother and more robust outperformance resulting from the combination of different rewarded factors within a multi-beta index. The outperformance of multifactor allocations is further analysed in Figures 3, 4 and 5.
In Figure 3, the graphs on the right-hand side display the accumulated wealth (i.e., cumulative total index returns) since the beginning of the 40-year period for the SciBeta Long-Term US Multi-beta Multi-strategy (MBMS) EW together with its cap-weighted reference index in the top panel, and the SciBeta Developed MBMS ERC and the SciBeta Broad Cap-Weighted Index in the bottom panel. On the left-hand side, the graphs show the corresponding wealth ratio, i.e., the ratio of the wealth level of the MBMS index over the wealth level in the cap-weighted reference. If the wealth ratio goes up, it means the MBMS index is over performing the cap-weighted index, and conversely, if it goes down, it is underperforming. We can see that over the 40-year U.S. track record, there was only one period where the MBMS EW index suffered relatively long underperformance—in the late 1990s. If one looks at the factor returns over this period, when there was the build-up of the technology bubble, the cap-weighted index performed quite well, as it was quite concentrated in technology stocks. Of course, over a short time period, it can happen that this concentration actually pays off relative to the factors used in the multi-beta allocation, as large, high-beta and growth stocks fared better during that period than small, low-risk or value stocks. Apart from that period when most of the factors did not pay off, the performance was quite steady over time. Similarly, one can link the periods of relative drawdown in the last 10 years in the developed universe to short time spans where the factors happened not to work. However, as the multi-beta allocations diversify the sources of return, such periods are rare and relatively short.
Bearing in mind that the rewarded factors yield positive premia in the long term in exchange for risks that can lead to considerable underperformance or relative drawdowns in shorter periods, it is important to analyse the robustness of the performance and its dependence on the market and economic conditions. One approach is to use the NBER definition of business cycles5 to break down the analysis into alternating sub-periods of "contraction" and "expansion" phases. Figure 4 shows annualised excess returns of the four multi-strategy factor indexes over the broad CW index throughout different economic cycles. The Mid Cap Multi-strategy Index has outperformed by a larger margin in expansion phases, while the Low Volatility Multi-strategy Index has a bias toward contraction phases. The difference across each multi-strategy factor index can be big, and presents opportunities for diversification across factors. The multi-beta allocations present less extreme variations throughout the different economic phases as they exploit the asynchronous movements of the different smart-factor indexes.
Furthermore, market conditions such as bullish or bearish markets may have a substantial impact on how different portfolio strategies perform. Amenc et al. [2012b] show considerable variation in the performance of some popular smart-beta strategies in different sub-periods, revealing the pitfalls of aggregate performance analysis based on long periods. Separating bull and bear market periods to evaluate performance has been proposed by various authors such as Levy , Turner, Starz and Nelson  and Faber . Ferson and Qian  note that an unconditional evaluation made, for example, during bearish markets, will not be a meaningful estimation of forward performance if the next period were to be bullish. We thus divide the 40-year period into two regimes: quarters with positive return for the broad CW index comprise bull market periods, and the rest constitute bear markets. Figure 5 shows that the performance of multi-strategy factor indexes depends on market conditions. For example, the U.S. Long-Term Mid Cap Multi-strategy Index posts much higher outperformance in bull markets (+5.37 percent) than in bear markets (+3.02 percent). The opposite is true for the U.S. Long-Term Low Volatility Multi-strategy Index, which underperforms by 0.81 percent in bull markets and outperforms by 7.33 percent in bear markets. If one combines the individual factor tilts, the dependency on the market regime is reduced for the multi-beta allocations compared to the constituent indexes. Indeed, in terms of information ratio, the performance of the multi-beta allocations is roughly the same between bull and bear markets. In terms of returns, both the EW and ERC multi-beta allocations remain defensive diversification strategies, as they outperform by a larger amount in bear regimes than in bull markets. In the end, the multi-beta allocations on the smart-factor indexes allow the premia from multiple sources to be harvested while producing more effective diversification, as they achieve a smoother outperformance across the economic cycles and bull/bear market regimes.
Aimplementation Benefits Of Allocating Across Factors
The multi-beta indexes analysed above were designed not only to provide efficient management of risk and return but also for genuine investability. Each of the smart-factor indexes has a target of 30 percent annual one-way turnover, which is set through optimal control of rebalancing (with the notable exception of the momentum tilt, which has a minimal target of 60 percent turnover). In addition, the stock selections used to tilt the indexes implement buffer rules in order to reduce unproductive turnover due to small changes in stock characteristics. The component indexes also apply weight and trading constraints relative to market-cap weights so as to ensure high capacity. Finally, these indexes offer an optional high-liquidity feature, which allows investors to reduce the application of the smart-factor index methodology to the most liquid stocks in the reference universe. Amenc et al. [2014a] present a more detailed explanation on how including carefully designed rules at different stages of the index-design process eases implementation of investments in smart-beta indexes.
In addition to these implementation rules, which are applied at the level of each smart-factor index, the multi-beta allocations provide a reduction in turnover (and hence of transaction costs) compared to a separate investment in each of the smart-factor indexes. This reduction in turnover arises from different sources. First, when the renewal of the underlying stock selections takes place, it can happen that a stock being dropped from the universe of one smart-factor index is being simultaneously added to the universe of another smart-factor index. Second, for constituents that are common to several smart-factor indexes, the trades to rebalance the weight of a stock in the different indexes to the respective target weight may partly offset each other.
Figure 6 displays statistics relative to the investability of the multi-beta equal-weight and relative ERC allocations along with the average of the midcap, momentum, low-volatility and value smart-factor indexes. For comparison, we also show the same analytics for their highly liquid counterparts. We see that the turnover of multi-beta indexes is very reasonable. In fact, managing a mandate on each smart-factor index separately would yield a turnover that is higher than the average turnover across the smart-factor indexes. This is due to the fact that rebalancing each component index to the allocation target would induce extra turnover. However, implementing the multi-beta index in a single mandate exploits the benefits of natural crossing arising across the different component indexes and actually reduces the turnover below the average level observed for component indexes. We provide in the table for each multi-beta allocation the amount of turnover that is internally crossed in multi-beta indexes as compared to managing the same allocations separately. We see that about 6 percent turnover is internally crossed by the EW allocation and that the ERC allocation that tends to generate more turnover also exploits natural crossing effects more than the EW allocation (around 7.8 percent is crossed internally). These cancelling trades result in an average one-way annual turnover that can be even lower than for the EW allocation, as is the case in the developed universe.
In addition to turnover, Figure 6 shows the average capacity of the indexes in terms of the weighted average market cap of stocks in the portfolio. This index-capacity measure indicates very decent levels, with an average market cap of around $10 billion for the multi-beta index, while the highly liquid version further increases capacity to levels exceeding $15 billion in the case of the U.S. long-term track records. In the case of the developed universe, the weighted average market caps are higher, as the period under scrutiny is more recent (last 10 years)—around $16.3 billion for the standard indexes and $23 billion for the highly liquid ones. In both regions, we provide an estimate of the time that would be necessary to set up an initial investment (i.e., full weights) of $1 billion AUM in the indexes, assuming the average daily dollar traded volume can be traded (100 percent participation rate) and that the number of days required grows linearly with the fund size.6 Overall, this does highlight the ease of implementation of the multi-beta indexes and the effectiveness of the highly liquid option. Indeed, the DTT required for the initial investment on U.S. indexes are very manageable (about 0.12 days for the standard multi-beta indexes, and 0.07 days with the highly liquid feature). Even in the developed universe, the highly liquid multi-beta indexes would require about 0.09 days of trading. In addition, one should keep in mind that the number of days needed to rebalance the indexes (i.e., trade the weight change rather than the full weight on each stock) would be much lower. Even though the excess return is reduced by a few basis points, which can be explained by a potential illiquidity premium, it should be noted that the highly liquid multi-beta indexes do maintain the level of relative risk-adjusted performance (information ratio) of the standard multi-beta indexes in the U.S. case, and it provides even stronger information ratios in the developed universe. Finally, even when assuming unrealistically high levels of transaction costs, all the smart-factor indexes deliver strong outperformance (from 2 to 3.69 percent) net of costs in both regions. Compared with the average stand-alone investment in a smart-factor index, the multi-beta indexes almost always result in higher average returns net of costs due to the turnover reduction through natural crossing effects across its component smart-factor indexes.
Multi-Smart Beta Allocation: Toward A New Source Of Value Added In Investment Management
While in practice, investors may select among various ways of combining smart-factor indexes in order to account for their investment beliefs, objectives and constraints, the cases of an equal-weighted allocation, and a (relative) equal-risk contribution allocation to four smart-factor indexes seeking exposure to the main consensual factors (notably value, momentum, low volatility and size) provide evidence that the benefits of multifactor allocations are sizable. In particular, exposure to various factors whose premia behave differently over time and across market conditions provides for smoother outperformance. Moreover, natural crossing benefits reduce turnover of multifactor mandates relative to separate single-factor mandates. Investors and asset managers may thus be well advised to further explore the potential of multifactor allocations in a variety of investment contexts.
- See Chambers, Dimson and Ilmanen  for more details about the "Norway model" and Koedijk, Slager and Stork  on how to address practical challenges that institutional investors face to integrate factor investing in their investment process.
- Diversified multistrategy weighting is an equal-weighted combination of the following five weighting schemes: maximum deconcentration, diversified risk weighted, maximum decorrelation, efficient minimum volatility and efficient maximum Sharpe ratio (see Gonzalez and Thabault ).
- To make a popular analogy, one can think of the diversified multistrategy approach as exploiting an effect similar to Surowiecki 's wisdom-of-crowds effect by taking into account the "collective opinion" of a group of strategies rather than relying on a single strategy.
- Maillard et al.  discuss a weighting scheme that equalises each asset's contribution to absolute risk, i.e., portfolio volatility. It is straightforward to extend their approach by applying it to relative returns with respect to a cap-weighted reference index. In this case, the objective is to equalise the contribution of each constituent to the overall relative risk (tracking error) with respect to the chosen reference index.
- The NBER defines a recession as "a significant decline in economic activity spread across the economy, lasting more than a few months, normally visible in real GDP, real income, employment, industrial production, and wholesale-retail sales." See: http://www.nber.org/cycles/cyclesmain.html.
- The days to trade (DTT) measure is computed for all stocks at each rebalancing in the last 10 years (40 quarters). Based on the estimated DTT for all constituents of a given index, we can derive an estimate of the required DTT for the index itself, by using, for example, extreme quantiles of the DTT distribution over time and constituents, such as the 95th percentile that we report.
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