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T H E J O U R N A L O F

SPRING 2016 Volume 25 Number 1THEORY & PRACTICE FOR FUND MANAGERS

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The Voices of Influence | iijournals.com

SMART BETASPECIAL SECTION

The Journal of InvesTIng sprIng 2016

Nicholas aloNso

is a portfolio manager at PanAgora Asset Management in Boston, [email protected]

Mark BarNes is a director at PanAgora Asset Management in Boston, [email protected]

Efficient Smart BetaNicholas aloNso aNd Mark BarNes

When bu i ld ing equ it y portfolios that eff iciently capture factor-exposure premiums, several impor-

tant aspects must be taken into account, such as factor definition, asset selection, and asset weighting. In this article, we focus on asset weighting and show that, holding all else equal, risk balancing yields the most effi-cient factor-exposure premium capture when building factor-exposure portfolios. We find that this efficiency comes from both adequate intended factor exposure, which captures positive factor risk premiums, and reduced risk concentration in unintended factors, which comes directly from risk balancing. Other commonly used weighting schemes tend to have less eff icient factor premium capture, which is due in part to these unin-tended risk concentrations that enter the portfolio, because risk is not explicitly taken into account when weighting the assets.

WHAT IS SMART BETA?

There is considerable interest in smart beta strategies, even if there is considerable disagreement over the precise meaning of smart beta. It is unlikely that we will clarify confusion over naming conventions, but we hope to contribute to the discussion of how smart beta portfolios can be used eff iciently to achieve investor objectives.

Before undertaking this discussion, we need to take a stand in the lexicon wars and thus we are using the following definitions:

• Alternative beta portfolios use portfolio weights that are not capitalization weights.

• Smart beta portfolios seek to obtain a spe-cif ic portfolio characteristic, or factor exposure. For example, portfolios can be constructed that seek to have char-acteristics of high momentum, value, or quality. It is this type of portfolio that we discuss in the current article.

The goal of any smart beta portfolio should be the capture of the risk premium associated with the intended factor and not simply obtaining the factor exposure itself. When building a smart beta portfolio, we believe the following several steps of port-folio construction are important:

1. Factor definition: Although commonly accepted definitions of low volatility may exist, other desired characteris-tics, such as quality, need to be carefully defined.

2. Asset selection: Smart beta portfolios are likely to hold only a subset of the investable universe. For example, if an investor wants to have a high-div-idend yield portfolio, it does not make

effIcIenT smarT BeTa sprIng 2016

sense to include stocks that do not pay dividends. Generally, the portfolio is a concentrated subset of the investable universe with high exposure to the desired factor.

3. Asset weighting: Once assets are selected, the investor must decide how to weight the assets within the portfolio. Some simple alternatives are capitaliza-tion weighting and equal weighting, but there are a number of other possible weighting methods.

4. Factor combination: Some investors may be interested in investing in a number of portfolios, each having different characteristics, or in a single portfolio that has multiple characteristics. The ways in which this process deals with the aforementioned aspects can be quite tricky.

Note that although we could break the entire pro-cess into four steps, in reality these pieces can interact. For example, the process of selecting assets may interact with how the asset weighting is done and even with whether the resulting portfolio will be combined with other smart beta portfolios.

In this article, we limit our discussion to step three, asset weighting, and leave the other steps to be addressed in future research. Specif ically, we asked: Once we have selected our assets, what impact does the weighting scheme have on the portfolio’s characteristics and performance? To remove the effect of the other aspects, we use a simple framework and try to use default or noncontroversial choices when we need to make a choice. We also limit ourselves to single-factor portfolios for each of the standard Barra Global Equality Model (GEM2) (Menchero, Morozov, and Shepard [2008]) risk factors. We use the S&P 500 as the investable universe and, to remove any differentiating effects of asset selec-tion, we invest only in the top quintile of such stocks when ranked by the desired factor. To understand the effect of asset weighting, we run backtests using sev-eral weighting schemes: equal weighted, cap weighted (MSCI [2013]), factor weighted (Russell Investments [2014]), and risk-parity weighted.

The general finding is that the weighting method-ology does indeed matter. Some seemingly innocuous choices about weighting can result in unintended risk profiles that affect portfolio performance. The risk parity approach, however, explicitly takes risk into account when determining portfolio weights. The results indi-cate that using a risk-balanced approach is superior to

other common alternatives. By taking the risk of the stocks into account, the portfolio reduces its unintended risk exposures while giving up very little of the desired risk factor exposure. This risk-balanced portfolio more effectively captures the premium associated with the factor in that it generally achieves higher returns with lower volatility. We further show that although each portfolio performs adequately in capturing the premium when the overall market is doing well, the outperfor-mance of the risk parity portfolio can also be attributed to its superior downside protection when the market is doing poorly.

In the following sections, we provide more details on the framework and then summarize our analysis by looking at the intended and unintended factor expo-sures, return performance, volatility, and participation ratios.

FRAMEWORK

We want to focus on the asset weighting process, and therefore we use a simple analytic framework. To reduce any distraction resulting from the choice of fac-tors, we use all of the Barra risk factors: momentum; value; growth; volatility; size; size non-linearity (mid-cap); liquidity; leverage; and one non-risk factor, divi-dend yield. For most of these factors, we build portfolios using the top quintile of scores in order to have positive exposure to the factor. For volatility, size, and leverage, we want negative exposure, so we limited the portfolio to the bottom quintile. In the case of liquidity, we were not sure which would be more informative, so we ran both low and high versions.

The basic weighting schemes we considered are straightforward: capitalization weighted, equal weighted, and factor weighted. Many smart beta portfolios use some version or combination of these simple rules. For example, the MSCI Quality Index is built using a subset of the universe with the highest factor scores, with the asset weighting being proportional to the factor score times capitalization weight. The Russell High Efficiency Factor Indexes are factor weighted. Rather than using a hybrid weighting scheme, we limited ourselves to the component basic weighting schemes to keep the results as clean as possible. Our factor weighting calculation is also simple: We set the lowest score in the target quintile to zero and renormalized the factors to obtain the weights. The negative exposure portfolios are handled inversely.


Our risk-parity portfolio approach balances risk across the most important dimension in a given uni-verse (Alonso and Barnes [2014]) and is based on the risk-balanced methodology discussed in Qian [2006]. In the S&P 500 universe, we balance risk across sector and stock. The intuition is that the investor attempts to reduce risk concentrations by moving weight away from riskier assets and toward less risky assets. This concept is important in interpreting the our results because such risk awareness naturally reduces exposure to any risk concentration. In the case of the intended exposure, we know that the proper exposure exists because the port-folio is already limited to stocks with such exposure. For the unintended exposure factors, the risk parity meth-odology ameliorates the exposure as it moves weight into less risky stocks.

The backtest period began in January 1997 and ended in December 2014. Again, to keep the analysis straightforward, we rebalanced the portfolios monthly, and performance is reported without subtracting transaction costs. We wanted to keep the framework as simple as pos-sible to highlight the patterns we see in this “frictionless” environment. A future extention of this reseach might be to determine whether adding transaction costs and rebal-ancing schedules would significantly alter the findings.

FACTOR EXPOSURES

We compared factor exposures to all of the Barra factors when building portfolios using different weighting schemes. In what follows, the strategy refers to the intended factor exposure, whereas each weighting scheme represents a different portfolio that is backtested. The weighting schemes are cap weighted (CW), equal weighted (EW), factor weighted (FACT), and risk-parity weighted (RP). We also show the benchmark exposures (SP500) for reference. Although some of these

factors may not be expected to have a factor premium, we include all of the Barra factors to show the robustness of the results and to avoid the possibility of data mining. The exhibits show the average exposure over the entire backtest. We provide detailed comments on the results for the momentum and volatility strategies to highlight some general patterns. The remaining factor results are relegated to the Appendix.

Not surprisingly, each weighting scheme has high absolute exposure to the Barra factor of the intended strategy. In fact, the targeted risk factor is the factor exposure that is largest in magnitude for each weighting scheme. For example, for the momentum strategy, all of the weighting schemes have their highest exposure to the momentum risk factor. Exhibit 1 shows all of the Barra factor exposures for each weighting scheme within the momentum strategy. The exposures to the intended factor are highlighted.

In Exhibit 1 we see some patterns in the risk factor exposures that are generally true for the four weighting schemes across the 10 strategies discussed in this article.

Benchmark Exposures

The exposure to most risk factors is very low for the S&P 500 portfolio. This is by design, as the Barra risk fac-tors are neutralized to the Barra estimation universe, which is a broad, capitalization-weighted universe of stocks. Given that the S&P 500 is also a broad, capitalization-weighted universe of stocks, we expect the risk exposures of the S&P 500 to be neutral as well. This holds true for all factors except size and dividend yield. The S&P 500 is a large-cap index, so a positive Barra size exposure is to be expected. The dividend yield is not a risk factor and is instead simply a raw dividend yield; therefore, a yield exposure of 1.82 for the S&P 500 in Exhibit 1 is the portfolio-weighted average dividend yield of the index.

e x h i B i t 1Barra Factor Exposure for Portfolios in the Momentum Strategy

Exhibits, for illustration only


Intended Factor Exposures

The highest average exposure for each of the four weighting schemes is to the desired risk factor. In Exhibit 1, all four have their highest exposure to the momentum risk factor, which is not surprising because our portfolios for the momentum strategy hold only the top quintile of stocks with the highest Barra momentum exposure.

The FACT portfolio has the highest absolute expo-sure to the intended risk factor. Given that this portfolio is factor-weighted, this outcome is expected.

The RP portfolio has slightly lower momentum exposure than the other portfolios. Given that the RP portfolio’s construction methodology mitigates risk concentration by balancing risk exposures, even risk concentration from intended factor exposure will be balanced, thus resulting in slightly lower risk exposure to that factor. This slightly lower exposure, however, is certainly not a low exposure. It should be remembered that our goal is to capture the momentum equity-risk premium efficiently and not necessarily to build a port-folio with the highest possible exposure. This finding is generally true for the other strategies considered in this article.

Unintended Factor Exposures

These strategies are designed to have greater expo-sure to a single, desired factor and lower exposure to any other factors because we are trying to capture the premium for the intended factor without the inf luence of other factor exposures. For example, in Exhibit 1, which shows factor exposures for each portfolio in the momentum strategy, all portfolios have high exposure to momentum, but only RP has relatively low exposure to volatility. The other three portfolios, therefore, have an

unintended exposure to volatility that we would prefer not to have. RP is different from the other portfolios because it explicitly takes risk into account. More gener-ally, for both intended and unintended risk factors, the RP portfolio tends to have exposures that are closer to those of the benchmark compared to the other portfo-lios. Given that the RP portfolio’s construction meth-odology mitigates risk concentrations, the mitigation of all risk concentrations, including risk concentrations due to unintended exposures, is a natural byproduct. This is an important point regarding the RP portfolio construction process because it is often unintended risk concentrations that lead to poor portfolio performance and ultimately inefficient premium capture. Because the asset selection process ensures that the portfolio contains only stocks with high exposure to the desired factor, the RP portfolio will have relatively high exposure to this factor while benefitting from RP’s reduction in the unintended factor exposures.

Size Exposures

All weighting schemes except the CW have high exposure to the size non-linearity risk factor and large negative exposure to the size risk factor. The CW weighting scheme has relatively neutral exposure to the size non-linearity factor and high exposure to the size factor because it is a capitalization-weighted portfolio of a subset of the S&P 500 Index, which itself has a strong size exposure. The size non-linearity factor mea-sures a portfolio’s exposure to mid-cap names. In these portfolios, a positive exposure to mid-cap names is a natural consequence of reducing the capital allocated to the largest names. This also explains the negative size exposure of the EW, FACT, and RP portfolios.

One strategy for which the risk factor exposures are slightly different is volatility. In Exhibit 2, we show

e x h i B i t 2Barra Factor Exposure for Portfolios in the Low-Volatility Strategy



the Barra risk factor exposures for each weighting scheme in the volatility strategy, in which we attempt to have low volatility exposure. Exhibit 2 shows many of the same patterns previously discussed, with a couple of exceptions:

1. In the case of the volatility strategy, the exposure to the volatility risk factor is negative because the strategy focuses on low volatility, which is where we expect a premium.

2. For the value, growth, and liquidity factor expo-sures, the CW, EW, and FACT portfolios gener-ally have higher exposures than the RP portfolio. These higher exposures are unintended given that this is a volatility strategy, and may lead to relatively inefficient premium capture from these weighting schemes.

For the sake of brevity, all other risk factor expo-sure exhibits are shown in the Appendix. The patterns discussed for the momentum and volatility strategies are generally repeated for the other factor strategies.

RISK DECOMPOSITION

In the previous section we looked at the ability of different portfolios to obtain desired factor exposures. In this section, we consider the contribution to total portfolio risk coming from each factor, which is argu-ably more informative than the exposures alone. Our approach is to use the risk of the portfolios calculated using the Barra risk model and isolate each risk fac-tor’s contribution to portfolio risk. As expected, most of the risk comes from the world beta and sector factors, but here we look at just the risk index factors. Specifi-cally, we calculate the risk stemming from each factor in isolation as a percentage of total portfolio risk. As in

the previous sections, we use an example to illustrate some common trends. Details of the calculation and the remaining results are in the Appendix.

In Exhibit 3 we see again that for the portfolios in the momentum strategy, a relatively large percentage of the total portfolio risk is derived from the momentum factor, which is the intended exposure. The RP port-folio tends to have some of the lowest risk contributions from the other unintended exposures. One interesting observation concerns the risk contribution from the size risk factor: Although the RP portfolio has the highest percentage risk contribution from size, this portfolio also has the lowest total exposure to size, as explained in the previous section. This occurs because risk con-tributions are independent of the portfolio exposure’s sign and thus both pieces of information (exposure and risk contribution) are important in understanding a risk factor’s impact on portfolio risk.

The patterns of risk contributions, in which the RP portfolio generally has lower unintended but adequately high intended risk contributions, are very similar for the other strategies and can be found in the Appendix.

EFFICIENT CAPTURE

In the previous two sections, we discussed factor exposures and made the point that our goal is to capture the equity premium associated with a given factor expo-sure as efficiently as possible. To measure this, we looked at portfolio performance in backtests for each weighting scheme and across all 10 strategies. The exhibits in the following sections show the average return for each weighting scheme in each strategy, again with com-parisons to the S&P 500 Index.

All backtests cover the period from January 1997 to December 2014. The average returns are geometrically

e x h i B i t 3Barra Factor Risk Decomposition Momentum Strategy



eight of the 10 strategies, with volatility and low liquidity being the exceptions. In the case of low liquidity, RP is second best, but the difference between its return/risk ratio and that of the EW portfolio is very small. In the case of the volatility strategy, RP is the third best behind both the FACT and EW portfolios. Although each portfolio return played a part, most of the increased return/risk ratio for the FACT and EW portfolios is due to their reduced volatility, which is likely the result of these portfolios’ higher exposure to the volatility risk factor coupled with the persistence of volatility at the stock level in this backtest period.

Value-Added Performance

Exhibit 7 shows the value-added return relative to the S&P 500 Index for each weighting scheme and across

linked and annualized. All reported standard deviations are also annualized. The highest return for each strategy is highlighted.

Absolute Performance

In Exhibit 4, we can see that the RP portfolio is often the best-performing portfolio among those tested; at worst, it is the second-best portfolio. The RP portfolio beats the other portfolios in six of the 10 strategies shown in Exhibit 4. The EW portfolio, on the other hand, has the highest return in the vola-tility and low liquidity strategies. In both of these cases, the RP portfolio has the second-highest return, which is very close to that of the EW portfolio. The FACT weighting scheme has the highest return in the size and high liquidity strategies. In both cases, the RP portfolio has the second-highest return; in the size strategy, the return of the RP portfolio is very similar to that of the FACT portfolio.

Exhibit 5 shows the portfolio standard deviations for each weighting scheme and across each strategy. The RP portfolio delivers the lowest portfolio risk in eight out of 10 cases. The FACT portfolio yields the lowest volatility in the volatility strategy, which is not sur-prising given that the strategy is to obtain a low volatility portfolio and FACT is factor weighted. The CW port-folio yields the lowest portfolio risk in the low-liquidity strategy, but it is not much lower than the RP portfolio, which is the second lowest.

Exhibit 6 shows the return/risk ratios for each weighting scheme and across each strategy. The RP portfolio again delivers the highest return/risk ratios in

e x h i B i t 4Portfolio Annualized Returns

e x h i B i t 5Portfolio Annualized Standard Deviations

e x h i B i t 6Portfolio Return/Risk Ratios



deliver a lower tracking error than in the RP, and in that case the difference is very small. Generally speaking, however, the CW portfolio has the lowest tracking error after the RP portfolio.

Finally, Exhibit 9 shows the information ratio (IR), which is the ratio of value-added return over portfolio tracking error, for each weighting scheme and across each strategy. The RP portfolio delivers the highest IR in eight of the 10 cases, with the volatility and low liquidity strategies being the exceptions. In both of these cases the RP portfolio is a close second behind the EW.

PARTICIPATION RATIOS

In this section, we look at participation ratios to help understand what is driving performance patterns. Participation ratio analysis focuses on the portfolio’s co-movement with either the market or the factor premium to understand how the portfolio behaves in different environments and how that behavior contributes to overall performance. For more on participation ratios, see Qian [2015].

We start by looking at each portfolio’s perfor-mance relative to the S&P 500, conditional on the sign of the S&P 500’s return. We define the upside participa-tion ratio as the average return of the portfolio over the average return of the S&P 500 during periods when the S&P 500’s return is positive. This statistic tells us what percentage of the S&P 500’s return is captured in up markets. A similar statistic is the downside participation, which tells us the percentage of the S&P 500’s return

each strategy. The RP portfolio delivers the highest value-added return in six of the 10 cases, which is not surprising as Exhibit 4 shows a similar pattern for the portfolio’s absolute returns.

Exhibit 8 shows the tracking error for each weighting scheme and across each strategy. In this example, the RP portfolio delivers the lowest tracking error to the S&P 500 in nine of the 10 cases. At first glance, these results may seem surprising given that one of the portfolios considered is CW, which uses the same weighting scheme as the index to which it is being com-pared, albeit only on a subset of the index’s constituents. One explanation for this apparent discrepancy may be that the CW portfolio tends to have unintended risk concentration that which drives the portfolio’s perfor-mance away from the benchmark at different times. Only in the low liquidity case does the CW portfolio

e x h i B i t 7Value-Added Returns

e x h i B i t 8Tracking Error

e x h i B i t 9Information Ratio



that is captured in down markets. Finally, we define the participation ratio advantage (PRA) as the difference between the upside participation ratio and the downside participation ratio. Strategies with positive participation ratio advantages are considered superior to those with negative participation ratio advantages.

Exhibit 10 shows the participation ratios and PRAs for each weighting scheme across each strategy. The results are shaded to show which portfolio has the greatest participation advantage. The RP portfolio always yields a positive PRA, and in seven out of 10 cases it has the highest PRA, with volatility, high liquidity, and low liquidity being the exceptions. In both liquidity cases, the RP portfolio always has at least the second-highest PRA, and the difference between the PRAs is small. With the exception of the yield and volatility strategies, the RP portfolio always has the lowest down-side participation ratios but not always the lowest upside participation.

It is worth dwelling on the intuition of these results for a moment. Participation analysis considers the comovement of the portfolio with the benchmark.

Although this is similar to standard capital asset pricing model beta analysis, by splitting the backtest into periods when the market is up or down, we seek asym-metries in the comovement. If the portfolio’s response to the market were strictly linear, we would then expect the upside and downside participation ratios to be the same, and thus no participation advantage would exist. The fact that we do see some asymmetries, however, implies that there something else is affecting the por-folio’s response to the market movement. In the case of an RP portfolio, we interpret this difference to be due to its lack of risk concentrations or simply better diversification.

Our second view into participation ratios is aimed at understanding how the portfolios pay off when the factor itself does or does not pay off. Standard calcula-tions of factor returns are usually based on long–short portfolios in which investors go long the top quintile (or decile) of stocks and short the bottom quintile (or decile) of stocks, with equal-weighted portfolios in both cases. However, because we are confining our analysis to long-only portfolios, we are not interested in the

e x h i B i t 1 0Participation Ratios vs. the S&P 500 Index



behavior of the short side of the factor return, and it is possible that asymmetries mean that the short side behaves quite differently from the long side. To avoid this problem, we used the equal-weighted return of the top quintile of stocks as a proxy for the long-only com-ponent of the factor return. Obviously, this is identical to the EW portfolio in our analysis, and as such, the EW portfolio can be considered the base case in the following results.

Exhibit 11 shows the participation ratios and PRAs for each weighting scheme across each strategy relative to the EW portfolio. The results for the EW portfolio are all equal to one for the upside and downside because, as discussed, it is being measured against itself. The results are shaded to show the portfolio with the highest partici-pation ratio advantage. In this case, the RP portfolio has a higher PRA in nine out of the 10 cases, with volatility being the only exception.

Our interpretation of the results is similar to the benchmark participation ratio analysis shown in Exhibit 11. For example, looking at the FACT port-folio, we see that in all strategies but volatility and low

liquidity, upside and downside participation ratios are both greater than one. This makes sense because, rela-tive to the equal-weighted baseline, the FACT portfolio loads up on the stocks with the most exposure to this factor. The participation advantage for FACT, however, is generally close to zero, which implies that not much asymmetry in the portfolios response to the factor return exists; in other words, the factor return seems to be driving the FACT performance.

By comparison, the RP portfolio generally has an upside participation ratio less than one, which implies that it does not have the full exposure to the factor that the baseline equal-weighted portfolio has. This is as expected given that the RP’s risk balancing will shift weight away from all risk concentrations, including the desired factor. Similarly, RP tends to have a downside participation ratio of less than one. The RP portfolio does, however, tend to have a large participation ratio advantage, which implies that important asymmetries exist in the portfolio response to the factor return. We interpret this as we did previously: Exposure to the factor drives the upside participation, but diversification

e x h i B i t 1 1Participation Ratios Relative to the EW Portfolio



mitigates some of the exposure to the factor when the factor has a negative return. That the RP portfolio has a large participation ratio in eight of the 10 strategies suggests that this effect is not spurious.

CONCLUSION

The idea of a smart beta portfolio is an attrac-tive one: It offers the idea of being able to invest in a transparent investment that cleanly obtains exposure to a desired factor. Seemingly innocuous decisions about how to weight the assets within the portfolio, how-ever, can have important implications for the portfolio’s characteristics and how they affect the capture of the desired factor premium. For example, cap weighting the stocks can result in unintended size exposures. Factor weighting effectively doubles down on the factor by amplifying the factor exposures obtained through the asset selection process. Even equal weighting, which may seem like the most neutral of weighting choices, can result in unintended factor exposures. Our analysis shows that it is imperative to take into account risk itself when weighting the assets in order to avoid unintended factor exposures. Although this strategy may result in a slightly lower desired factor exposure, the portfolio

e x h i B i t a 1Factor Exposures

benefits from having more neutral unintended factor exposures, which ultimately lead to a more eff icient capture of the factor premium. It must be remembered that the goal is to capture the premium efficiently and not to obtain the highest factor exposure. By building a portfolio that is risk diversif ied, investors can take advantage of both the factor premium when a positive payoff to the factor results and the diversification of the portfolio when a negative payoff to the factor results.

Asset weighting is one of several important steps in building smart beta portfolios. In ongoing research, we are also analyzing the importance of asset selection when building a portfolio. Extending the finding that portfolio diversif ication is important when obtaining factor exposure, preliminary research suggests that it is important to choose a sufficiently diversified subset of stocks in the asset selection step. In a second research project, we examine a combination of smart beta port-folios. We find that naively combining factor portfo-lios often fails to deliver the desired factor exposure or the associated factor premiums capture because of the interaction of the factors. Our research suggests that it is important to understand the interactions before choosing and weighting the assets within a portfolio. These are areas for future research.

a p p e N d i x

Factor exposures

(continued)



e x h i B i t a 1 (continued)Factor Exposures

RISK DECOMPOSITIONS

To decompose risk into its constituents, we followed a methodology similar to that employed by Barra. We report the percentage of portfolio standard deviation coming from each of the Barra risk factors independent of the risk that can be attributed to world beta, industries, and currencies.

Formulaically, our calculation of risk decomposition is as follows:

RC

X d

p

# (X d# (X d( )X d( )X d g X( )g X t( )t# (( )# (X d# (X d( )X d# (X dia# (ia( )ia# (iag X# (g X( )g X# (g Xiag Xia# (iag Xia( )iag Xia# (iag Xiag X)g X( )g X)g X=

( )Σ ∗( )g X( )g XΣ ∗g X( )g X)( ))Σ ∗)( ))g X)g X( )g X)g XΣ ∗g X)g X( )g X)g X

σ(A-1)



e x h i B i t a 2Barra Factor Risk Decomposition for Various Strategies

(continued)



e x h i B i t a 2 (continued)Barra Factor Risk Decomposition for Various Strategies

where RC is an F×1 vector of percentage risk contributions from each factor; X is an F×1 factor exposure vector; diag(S) is the F×F factor covariance matrix in which all of the off-diagonal covariance terms have been set to 0; σp is the portfolio’s total risk measured in standard deviation; # is the element-wise multiplication operator; and Ones is an F×1 vector of ones.

Given that the independent risk contributions do not explain all of the portfolio risk (i.e., Onest *

tGiven that the independent risk contributions do not

tGiven that the independent risk contributions do not

( )( )X d( )X dia( )iag X( )g Xiag Xia( )iag Xia t( )t( )Σ ∗( )g X( )g XΣ ∗g X( )g X( )#(( )X d( )X d#(X d( )X d( )( )( )g X( )g X( )g X( )g X( )Σ ∗( )( )( )Σ ∗( )g X( )g XΣ ∗g X( )g X( )g X( )g XΣ ∗g X( )g X( ))( ) ≠ σp and therefore onest * RC ≠ 1), there is an additional catch-all term that we do not report but which can be thought of as the effect on risk due to the interaction of risk factors.

REFERENCES

Alonso, N., and M. Barnes. “Dimensions of Diversification in the Emerging Markets.” Investment Insight, PanAgora Asset Management, September 2014.

Menchero, J., A. Morozov, and P. Shepard. “The Barra Global Equity Model (GEM2).” Research notes, MSCI/Barra, 2008.

“MSCI Quality Indices Methodology.” Internal publication, MSCI, 2013.

Qian, E. “On the Financial Interpretation of Risk Contribu-tion: Risk Budgets do Add Up.” Journal of Investment Manage-ment, Vol. 4, No. 4 (2006), pp. 41-51.

——. “On the Holy Grail of ‘Upside Participation and Downside Protection’.” The Journal of Portfolio Management, Winter 2015, pp. 11-22.

“Smart Beta Guidebook: An Overview of Russell Smart Beta Indexes.” Internal publication, Russell Investments, 2014.

To order reprints of this article, please contact Dewey Palmieri at [email protected] or 212-224-3675.


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The opinions expressed in this article represent the current, good faith views of the author(s) at the time of publication, are provided for limited purposes, are not definitive investment advice, and should not be relied on as such. The information presented in this article has been developed internally and/or obtained from sources believed to be reliable; however, PanAgora does not guarantee the accuracy, adequacy or completeness of such information. Predictions, opinions, and other information contained in this article are subject to change continually and without notice of any kind and may no longer be true after the date indicated. The views expressed represent the current, good faith views of the author(s) at the time of publication. Any forward-looking statements speak only as of the date they are made, and PanAgora assumes no duty to and does not undertake to update forward-looking statements. Forward-looking statements are subject to numerous assumptions, risks and uncertainties, which change over time. Actual results could differ materially from those anticipated in forward-looking statements. HYPOTHETICAL PERFORMANCE RESULTS HAVE MANY INHERENT LIMITATIONS, SOME OF WHICH ARE DESCRIBED BELOW. NO REPRESENTATION IS BEING MADE THAT ANY ACCOUNT WILL OR IS LIKELY TO ACHIEVE PROFITS OR LOSSES SIMILAR TO THOSE SHOWN. IN FACT, THERE ARE FREQUENTLY SHARP DIFFERENCES BETWEEN HYPOTHETICAL PERFORMANCE RESULTS AND THE ACTUAL RESULTS SUBSEQUENTLY ACHIEVED BY ANY PARTICULAR INVESTMENT PROGRAM. ONE OF THE LIMITATIONS OF HYPOTHETICAL PERFORMANCE RESULTS IS THAT THEY ARE GENERALLY PREPARED WITH THE BENEFIT OF HINDSIGHT. IN ADDITION, HYPOTHETICAL TRADING DOES NOT INVOLVE FINANCIAL RISK, AND NO HYPOTHETICAL TRADING RECORD CAN COMPLETELY ACCOUNT FOR THE IMPACT OF FINANCIAL RISK IN ACTUAL TRADING. FOR EXAMPLE, THE ABILITY TO WITHSTAND LOSSES OR TO ADHERE TO A PARTICULAR INVESTMENT PROGRAM IN SPITE OF TRADING LOSSES ARE MATERIAL POINTS WHICH CAN ALSO ADVERSELY AFFECT ACTUAL TRADING RESULTS. THERE ARE NUMEROUS OTHER FACTORS RELATED TO THE MARKETS IN GENERAL OR TO THE IMPLEMENTATION OF ANY SPECIFIC INVESTMENT PROGRAM WHICH CANNOT BE FULLY ACCOUNTED FOR IN THE PREPARATION OF HYPOTHETICAL PERFORMANCE RESULTS AND ALL OF WHICH CAN ADVERSELY AFFECT ACTUAL TRADING RESULTS.

The S&P 500 Index is an unmanaged list of common stocks that is frequently used as a general measure of U.S. stock market performance.

RISK CONSIDERATIONSInternational investing involves certain risks, such as currency fluctuations, economic instability, and political developments. Additional risks may be associated with emerging market securities,including illiquidity and volatility. Active currency management, like any other investment strategy, involves risk, including market risk and event risk, and the risk of loss of principal amount invested.

Derivative instruments may at times be illiquid, subject to wide swings in prices, difficult to value accurately and subject to default by the issuer. Strategies that use leverage extensively to gain exposure to various markets may not be suitable for all investors. Any use of leverage exposes the strategy to risk of loss. In some cases the risk may be substantial.

This material is directed exclusively at investment professionals. Any investments to which this material relates are available only to or will be engaged in only with investment professionals. Past performance is no guarantee of future results. PanAgora is exempt from the requirement to hold an Australian financial services license under the Corporations Act 2001 in respect of the financial services. PanAgora is regulated by the SEC under US laws, which differ from Australian laws.

smart beta - iinews.com · many smart beta portfolios use some version or combination of these...

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