factor efficiency - hsbc · volatility times correlation, msci barra research. 4 ... for a...

Factor Efficiency

Date: November 2015

Quantitative Equity Research

2 | HSBC Global Asset Management

Factor EfficiencyExecutive Summary

This note sets out the premise behind our views on

efficient beta investing and describes a method of

identifying the most ‘efficient’ factor driven strategies.

Smart beta indexes and Exchange Traded Funds (ETFs)

have become increasingly popular, with many providers

offering a broad suite of such strategies. Most are

based on well recognised risk premium factors such as

value, small cap, momentum, low volatility and quality.

However, many such indexes have unintended risks

and additional exposure to untargeted factors because

of their construction methodology. We investigate a

method of determining the efficiency of a factor index

and apply it to our smart beta investment solutions. By

showing that pure indexes have larger factor efficiency,

we can conclude that they are relatively efficient: they

have a larger portion of active risk attributed to the

targeted factor.

HSBC Global Asset Management | 3

IntroductionThe appeal behind smart beta indexes is that they are

systematic and transparent, rendering them easy to construct

and rebalance. Smart beta indexes are also a low cost way

for an investor to obtain exposure to factors which they might

be lacking within their portfolios. Many smart beta indexes

tend to be constructed with an emphasis on simplicity,

often using simple sorting and weighting techniques based

on either a single factor (e.g. book-to-price) or a composite

score (e.g. value). Some smart beta indexes are constructed

to maximise investability, combining factor tilts with market

cap weighting. Unfortunately, even though this sort of

construction technique tends to result in higher factor

exposures, there are usually few restrictions on other style

characteristics. This leads to unintended factor exposures

and thus undesired risk.

The inspiration for this paper comes from a recently

published paper by Hunstad and Dekhayser1, where they

introduce a new measure called the factor efficiency ratio.

Much of the debate on smart beta index construction stems

from unintended factor exposures. These are usually the

result of conforming to the requirements of transparency,

simplicity and investability. Indexes are constructed from

stocks ranked by factor of interest (e.g. factor indexes

sold by FTSE, MSCI and Russell). There is evidence that

simple minimum variance optimisation, a common smart

beta strategy, results in time-varying factor exposures2.

Goldberg et al. suggest that it is important to be aware of

these exposures and highlight the benefits of targeting pure

exposures when building such indexes.

In what follows we describe how the factor efficiency

ratio is calculated, how it should be interpreted and

relevant applications.

1 Hunstad and Dekhayser (2014) – Evaluating the Efficiency of ‘Smart Beta’ Indexes, Working Paper.

2 Goldberg, Leshem and Geddes (2013) – Restoring Value to Minimum Variance, Forthcoming in Jour-nal of Investment Management Davis and Menchero (2010) – Risk Contribution is Exposure times Volatility times Correlation, MSCI Barra Research.


MethodologyThe factor efficiency ratio is defined as the ratio of tracking

error from the desired factor(s) to the total tracking error.

It follows that this can be used to measure the efficiency

of an index, i.e. the ratio of desired to undesired active risk.

Formally, it is constructed as follows:

Factor Efficiency Ratio =∑ARD

AR - ∑ARD

∑ARD is the sum of active risk contributions of the desired

factors while AR is the total active risk of the portfolio. Here

we look at active risk contribution as opposed to absolute risk

contribution: the purpose of index is to add exposure beyond

that of a specified benchmark (i.e. we look at active style

exposures). For a single-factor smart beta value index,

the factor efficiency ratio is calculated as follows:

Factor Efficiency RatioValue =∑ARValue

AR - ∑ARValue

Ex-ante active risk can be decomposed as follows

(this is discussed in detail in Davis, Menchero3:

AR = Var(RA) = ∑x σFi ρFi,R

A + ∑w σuk ρuk,RA

where σFValueρFValue RA is otherwise equivalent to the

marginal contribution to risk of the value factor.

The factor efficiency ratio is therefore by construction

an ex-ante ratio which decomposes the risk the portfolio

expects to deliver into desirable and undesirable active risk.

iiA

KA

The variables above can be estimated using a factor risk

model. We use our internal factor risk model which is broadly

similar to the commercially available alternatives from Barra,

Axioma and Bloomberg. It is a cross-sectional risk model

that decomposes systematic market risk into 10 broad style

factors and industry, country and currency factors. The

cross-sectional variance-covariance matrix is built using

10 years of weekly data and covariance shrinkage.

DataWe first obtains the smart beta index constituents and

weights through time for the indexes, the MSCI style indexes

and the RAFI indexes. We care about changes over time as

the calculated factor efficiency is time-varying. Next, we

construct the factor risk model specific to the investment

universe, in this case the MSCI World. We extract factor

exposures and factor returns from the risk model, which

we use to calculate marginal active contributions to risk.

Finally, we calculate the factor efficiency ratio for each of

pure indexes (value, momentum, small cap, low volatility and

quality) and compare them to their closest competitors.

Total Active Risk

Sysrematic Active Risk

SystematicActive Risk

IndustryGroup

Style

Country

Currency

Total Active Risk Specific

Active Risk

Figure 1: Decomposition of total active risk in cross-sectional factor risk model

3 Davis and Menchero (2010) – Risk Contribution is Exposure times Volatility times Correlation, MSCI Barra Research.

i


Results

As of March 2015

Hunstad and Dekhayser highlight the disparity between

active exposure and factor efficiency. An index with high

exposure to a particular factor will not necessarily have high

factor efficiency. For example, a simple ranking of value

stocks often has significant small-cap exposure. If we were

to buy the top quintile of value names, we would anticipate a

high exposure to both value and small cap factors. We would

prefer an efficient beta index to have a large proportion of

active risk driven by the targeted style factor and minimal

active risk contributions from the other factors.

From the results we can demonstrate that pure indexes

are indeed relatively ‘efficient’ from a factor efficiency ratio

perspective. This is not surprising as HSBC’s index construction

process aims to minimise unwanted factor exposures as well as

broad active risk due to its active weight constraints.

In Figure 2 we show the factor efficiency ratios for pure indexes.

Figure 2: Factor efficiency ratios Factor Efficiency Ratios as of March 2015

0.0

0.3

0.6

0.9

1.2

1.5

Momentum Quality Small Cap

Value Low Volatility

As can be seen from Figure 2, high factor exposure does

not directly correlate with factor efficiency. For example, the

momentum index has the lowest factor exposure at 0.47 but

a high factor efficiency ratio of 1.40. This is understandable

as momentum is a more volatile factor with a higher active

risk contribution. Looking at the desired factor’s exposures

alone might be misleading. Factor exposures fail to take

into account the risks from exposure to other potentially

undesirable factors.

Concentrating on active risk contribution also connects back

to the general debate on risk premia factors. There is a degree

of risk in investing in factors and their returns are time-varying.

Note that indices with the same factor exposures may

have different active risks based on the nature of the factor.

An index that is factor efficient has less contribution from

undesired risks. The key point is that we are only taking a risk

on the factors that we choose to invest in.

Total Active Risk (%)Factor Contribution to Active Risk (%)

Proportion of Factor Contribution to Active Risk (%)

Factor Efficiency Ratio

Exposure

Momentum 2.15 1.25 58.4 1.40 0.47

Quality 1.42 0.19 13.1 0.15 0.76

Small Cap 3.38 0.85 25.1 0.34 1.37

Value 2.3 0.54 23.3 0.30 0.91

Low Volatility 2.47 0.99 40.2 0.67 0.45

Source (for both the table and chart): Factset, Worldscope, Thomson Reuters, MSCI.


Figure 3 is the decomposition of active risk for value pure index as of March 2015. This is a common risk attribution output from

portfolio attribution packages. As is evident from both the factor efficiency ratio and the breakdown (Figure 3), the active risk

contribution from value is significantly larger than most other active risk components. This is indeed what we expect to see from

an “efficient” index.

Figure 3: Decomposition of total active risk (31 March 2015) Pure Value Enhanced Value

When comparing this to the MSCI World Enhanced Value Index (MSCI’s high exposure version of a value index), we can see how

different the index is in terms of factor efficiency ratios. The factor efficiency ratio of the MSCI World Enhanced Value Index at

the same point in time is 0.09, compared to figure of 0.30. This implies that index takes on approximately 5 times as much value-

related active risk than the MSCI World Enhanced Value Index per 1% of non-value active risk. At the same time, it has a similar

active exposure to value as the MSCI World Enhanced Value (High Exposure) index (0.91 vs 0.84). Thus, in a sense, the Pure

Value index manages to provide equally high exposure to the value factor coupled with lower active risk from other exposures.

Looking at the decomposition of style active risk for the MSCI index on Figure 4, we can see that even though the biggest

component of active risk is indeed value, there are still significant active risk contributions from size, growth and momentum.

A significant portion of its active risk comes from country active risk. A closer look at the breakdown shows that the majority

of this comes from active exposure to Japan. This does not appear to be consistent with an “index” strategy.

Figure 4: Decomposition of style active risk Pure Value Enhanced Value

0%

20%

40%

60%

80%

100%

10%

30%

50%

70%

90%

Style Countries Industries Currencies Non-Factor0%

20%

40%

60%

80%

100%

10%

30%

50%

70%

90%

Style Countries Industries Currencies Non-Factor

Contribution Positive Contribution Negative Total

0%

5%

10%

15%

20%

25%

Volatility

Value

Trading Activity

Size

Profitability

Mom

entum

Leverage

Grow

th

Earnings Variability

Dividend Yield

Volatility

Value

Trading Activity

Size

Profitability

Mom

entum

Leverage

Grow

th

Earnings Variability

Dividend Yield

0%

4%

8%

12%

16%

18%

Contribution Positive Contribution Negative

Source: Factset, Worldscope, Thomson Reuters, MSCI.



To extend the comparison between the funds with other style indexes, we look at the two ranges of MSCI factor indexes:

their high exposure range as well as their high capacity range. The latter impose tilts on the cap-weighted index to increase

investability. In terms of factor efficiency ratios, as of the end of March 2015 the pure indexes appear to be more ‘efficient’

than both ranges. They also exhibit consistently higher exposures than the tilt range.

Figure 5: Comparison of factor efficiency ratios Factor Efficiency Ratios as of March 2015

Figure 6: Comparison of active exposures Active Exposures as of March 2015

MSCI High Exposure

Total Active Risk (%)

Factor Contribution to Active Risk (%)

Proportion of Factor Contribution to Active Risk (%)

Factor Efficiency Ratio

Exposure

MSCI Momentum 4.01 1.12 27.9 0.39 0.46

MSCI Quality 2.9 0.10 3.4 0.04 1.02

MSCI Equal Weighted 2.52 0.33 13.1 0.15 0.94

MSCI Enhanced Value 3.69 0.30 8.2 0.09 0.84

MSCI Minimum Vol 3.94 0.78 19.7 0.25 0.33

0.0

0.3

0.6

0.9

1.2

1.5

Momentum Quality Small Cap Value Low Volatility

HSBC’s Pure Factors MSCI Tilt MSCI High Exposure

0.0

0.3

0.6

0.9

1.2

1.5

HSBC’s Pure Factors MSCI Tilt MSCI High Exposure

QualityMomentum Small Cap Value Low Volatility




Figure 7: 12 month rolling factor efficiency ratios

Note that momentum and low volatility have the highest

variability in factor efficiency ratios. Ex-ante active risk is a

product of exposure, factor volatility and correlations, so any

of these can drive fluctuations in active risk composition.

Quality has the lowest average factor efficiency ratio through

time. This suggests that there are other active risks we

might wish to consider when constructing a quality index.

Quality might be harder to capture as a pure factor because

it is naturally skewed in terms of exposures to countries and

industries. We examined this by looking at snapshots of the

quality index active risk decomposition at different points in

time. A substantial part of active risk appears to come from

countries in both 2009 and 2015.

Time seriesNext we examine the changes in factor efficiency over

time using indexes, for which we have full constituent

and weighting data. We are unable to do the same for our

competitors’ indexes due to the lack of data. Instead we look

at annual snapshots of the indexes as far as they are available.

The charts in Figure 7 show that factor efficiency ratios

vary over time and are dependent on the active risk of the

targeted factor relative to the other factors. However, we

expect the factor efficiency ratio of pure indexes to be higher

over time. This is because the evaluation of active risk is a

product of exposure and marginal contribution to risk. Pure

indexes explicitly target exposure to other style factors so

the risk contribution of the main factor of interest should be

proportionally higher.

0.0

0.5

1.0

1.5

2.0

0.0

0.2

0.4

0.6

11/201211/2010 11/201311/2011 11/2014

Fact

or E

ffici

ency

Rat

io

Momentum Quality

Fact

or E

ffici

ency

Rat

io

0.0

0.5

1.0

1.5

0.5

1.0

1.5

Fact

or E

ffici

ency

Rat

io

0.0

Small Cap Value

Fact

or E

ffici

ency

Rat

io

0.5

1.0

1.5

2.0

0.0

Low Volatility

Fact

or E

ffici

ency

Rat

io

11/201211/2010 11/201311/2011 11/2014

11/201211/2010 11/201311/2011 11/2014 11/201211/2010 11/201311/2011 11/2014 11/201211/2010 11/201311/2011 11/2014

0.0

0.5

1.0

1.5

2.0

0.0

0.2

0.4

0.6

11/201211/2010 11/201311/2011 11/2014

Fact

or E

ffici

ency

Rat

io

Momentum Quality

Fact

or E

ffici

ency

Rat

io

0.0

0.5

1.0

1.5

0.5

1.0

1.5

Fact

or E

ffici

ency

Rat

io

0.0

Small Cap Value

Fact

or E

ffici

ency

Rat

io

0.5

1.0

1.5

2.0

0.0

Low Volatility

Fact

or E

ffici

ency

Rat

io

11/201211/2010 11/201311/2011 11/2014

11/201211/2010 11/201311/2011 11/2014 11/201211/2010 11/201311/2011 11/2014 11/201211/2010 11/201311/2011 11/2014

Source: Factset, Worldscope, Thomson Reuters, MSCI: Nov 2010 to April 2015.


Figure 8: Pure quality index active risk decomposition

Thus a potential improvement for quality indexes would be through the direct control of country and industry exposures.

However this would inevitably reduce exposure to quality as the additional constraints would shrink the feasible set of solutions.

Figures 9 and 10 chart the changes in factor efficiency ratios over time for different indexes. They imply that if the index

construction process does not change over time, factor efficiency ratios should stay within an expected range.

Figure 9: Comparison of factor efficiency ratios for value indexes

Figure 10: Comparison of factor efficiency ratios for quality indexes

0%

20%

40%

60%

80%

100%

10%

30%

50%

70%

90%

Style Countries Industries Currencies Non-Factor0%

20%

40%

60%

80%

100%

10%

30%

50%

70%

90%

Style Countries Industries Currencies Non-Factor

Contribution Positive Contribution Negative Total

0.0

0.2

0.4

0.6

0.8

1.0

2012 2013 2014 2015

AMG Pure Value MSCI Value Tilt

0.00

0.05

0.10

0.15

0.20

2012 2013 2014 2015

AMG Pure Quality MSCI World Quality

0.0

0.5

1.0

1.5

2.0

2.5

20122011 2013 2014 2015

AMG Pure Low Volatility MSCI World Minimum Volatility

0.0

0.2

0.4

0.6

0.8

1.0

2012 2013 2014 2015


0.00

0.05

0.10

0.15

0.20

2012 2013 2014 2015


0.0

0.5

1.0

1.5

2.0

2.5

20122011 2013 2014 2015


0.0

0.2

0.4

0.6

0.8

1.0

2012 2013 2014 2015


0.00

0.05

0.10

0.15

0.20

2012 2013 2014 2015


0.0

0.5

1.0

1.5

2.0

2.5

20122011 2013 2014 2015


Figure 11: Comparison of factor efficiency ratios for low volatility indexes

The difference of factor efficiency

ratios is the result based on the

analysis above, it is natural to conclude

that the pure indexes appear to be

more efficient than the series of MSCI

indexes. This is a result of the index

construction process minimising

exposures to other factors, indirectly

causing a decrease in active risk

contribution from styles.

Figures 9, 10 & 11 Source: Factset, IBES, Worldscope, MSCI.

Sources and date of risk decomposition: Factset, Worldscope, Thomson Reuters, MSCI, March 2015.


There appears to be a positive relationship between the

factor efficiency ratios and the correlations of the factor

index with pure factor returns. As discussed above, quality

has the lowest factor efficiency ratio. It also has the smallest

resemblance to that of a pure quality index.

Factor efficiency ratio vs return correlationsA natural extension of the discussion above is to check

how the return series of pure indexes correlate with long-

short pure style portfolio returns (with unit exposure to the

targeted factor and neutrality to other factors) and how this

relates to factor efficiency ratios. Mathematically, pure style

portfolio returns f_kt are calculated from the cross-sectional

regressions, where X_nkt represents the factor exposure of

stock n to factor k at time t.

Note that pure indexes are long-only index strategies so are

not necessarily representative of pure factor returns.

Figure 12: Correlation with pure style returns

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

00 .2 0.40 .6 0.8

Correlation of Smart Beta Index with Pure Factor Returns

Low Volatility

Quality

Value

Momentum

Small Cap

k=1

KReturnn,t = ∑Xn,k,t fk,t + εn,t

Sources of data and date of risk attribution: Factset, Worldscope, Thomson Reuters, MSCI, July 2001 - March 2015,


ConclusionFactor efficiency ratios are a simple way of

determining the efficiency of smart beta indexes.

By measuring the ratio of desirable active risk to

undesirable active risk, we can evaluate the efficiency

of an index. There have been concerns that smart beta

indexes actually capture unintended factor, country,

industry or currency risks. The factor efficiency ratio

is an effective way of quantifying relative intended

to unintended tracking error, allowing investors to

distinguish between indexes with undesirable or

perhaps unforeseen risks from those that are truly

“efficient”. Investors can then devote most of their

active risk budget towards the factor of interest.

This note highlights the importance of focusing

on criteria beyond simple factor exposure when

buying a smart beta index. More sophisticated index

construction techniques, although more complicated

than simple sorting and weighting, can significantly

improve the overall purity and efficiency of smart

beta strategies.

Important InformationFor Professional Clients only and should not be distributed to or relied upon by Retail Clients.

The material contained herein is for information only and does not constitute investment advice or a recommendation to any

reader of this material to buy or sell investments.

This document is not intended for distribution to or use by any person or entity in any jurisdiction or country where such

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or the solicitation of an offer to purchase or subscribe to any investment.

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projection or target where provided is indicative only and not guaranteed in any way. HSBC Global Asset Management (UK)

Limited accepts no liability for any failure to meet such forecast, projection or target.

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factor efficiency - hsbc · volatility times correlation, msci barra research. 4 ... for a...

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