EDHEC-Risk European Index Survey 2011

Transcription

1 An EDHEC-Risk Institute Publication EDHEC-Risk European Index Survey 2011 October 2011 Institute

2 2 Printed in France, October Copyright EDHEC The opinions expressed in this study are those of the authors and do not necessarily reflect those of EDHEC Business School. The authors can be contacted at

3 Table of Contents Executive Summary Introduction Background The indexing industry Evaluating the quality of indices Indices in specific asset classes Methodology and Sample Results Evaluating qualities of indices and overview across asset classes Equity indices Fixed Income indices Equity volatility indices How do Responses Differ between Respondent Types? Asset owners vs. third-party asset managers More equity-oriented countries vs. less equity-oriented countries Small and medium investors vs. large investors Highly satisfied by current equity indices vs. less satisfied by current equity indices Conclusions References About EDHEC-Risk Institute EDHEC-Risk Institute Publications and Position Papers ( ) An EDHEC-Risk Institute Publication 3

4 About the Authors Noël Amenc, PhD, is professor of finance at EDHEC Business School, where he heads EDHEC-Risk Institute. He has a masters degree in economics and a PhD in finance and has conducted active research in the fields of quantitative equity management, portfolio performance analysis, and active asset allocation, resulting in numerous academic and practitioner articles and books. He is a member of the editorial board of the Journal of Portfolio Management, associate editor of the Journal of Alternative Investments, member of the advisory board of the Journal of Index Investing and a member of the scientific advisory council of the AMF (French financial regulatory authority). Felix Goltz is head of applied research at EDHEC-Risk Institute. He does research in empirical finance and asset allocation, with a focus on alternative investments and indexing strategies. His work has appeared in various international academic and practitioner journals and handbooks. He obtained a PhD in finance from the University of Nice Sophia-Antipolis after studying economics and business administration at the University of Bayreuth and EDHEC Business School. Lin Tang is a senior research engineer at EDHEC Risk Institute Asia in Singapore. She has contributed to industry surveys on ETFs, green investing and private wealth management and to a publication on dynamic asset allocation with ETFs. She has a master s in risk and asset management from EDHEC Business School. Prior to joining EDHEC, Lin worked as a product engineer for one year after receiving her bachelor s in engineering, with first-class honours, from Nanyang Technological University in Singapore. 4 An EDHEC-Risk Institute Publication

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6 Executive Summary 1 - The number is an approximation based on ranges of assets under management provided by the survey respondents. 2 - According to the statistics from European Fund and Asset Management Association (EFAMA) in 2010, the total assets under management by European asset management industry is 12.8 trillion Euros by the end of This figure is much higher than the one reported by Olsen (2011) as the previous one only count assets that internally tracks an index. Indexation continues to play an important role in global asset allocation. Total worldwide assets under internal indexed management rose to $5.994 trillion as of June 30, 2011, a 25% increase over $4.781 trillion as of one year earlier (Olsen 2011). In view of the growing volumes in assets under management in passive indexing strategies, a great many index providers have emerged worldwide; not only the organisations specialising in the index service but also stock exchanges, as well as investment banks. Each provider has created or is creating a host of indices representing a full complement of asset classes, as well as asset class subsegments. In the entire history of indices, countrybased capitalisation-weighted indices have proven to be the most popular indices for both equity and bond markets. Such indices are often used as a bellwether for the economy, as they are supposed to represent market trends. Nowadays, a growing demand for indices as investment vehicles has led to innovations including new weighting schemes and alternative definitions of sub-segments. As the choice of an index is a crucial step in both asset allocation and performance measurements, it is useful to investigate index use and perceptions about indices. EDHEC-Risk European Index Survey 2011 aims to analyse the current uses of and opinions on stock, bond and equity volatility indices. It is our hope that this survey will provide unique insight into the users perspective in the index industry. Furthermore, there is a growing body of research on index construction and index use. Recent studies assess current indices and also propose alternative approaches to construct indices. This survey also serves as a tool to explore views of institutional index users on the conclusions of the literature. This survey allows us to gather opinions from 104 institutional investment managers, which represent approximately seven trillion Euros 1 of assets under management. This represents more than half of all assets under management by the European asset management industry. 2 These respondents are from asset management companies, pension funds and insurance firms located all over Europe. The opinions collected reflect investors overall judgement on index quality, on the key issues they see with current indices, and the likely future trends for the index landscape. Since more than half of respondents are from large institutions (i.e., more than 10 billion Euro AUM), and since we receive a higher response rate from professionals with a significant interest in indices (self-selection), our survey, overall, represents views of the average sophisticated index user within a large European institutional investor scope. 1. Investor's Overall Judgement on Index Quality The indexing industry has grown in importance. From the supply side, both global index providers and investment banks offer indices. This growing competition naturally tends to lead to a variety of competing indices coming to the markets. So from the demand side, index 6 An EDHEC-Risk Institute Publication

7 Executive Summary 3 - This difference between the investability and the liquidity requirement perhaps needs to be explained in more detail and this is best done using a simple example. For instance, in China, there are two classes of shares for a company: A share and B share. Domestic investors can trade A shares but foreign investors are only able to access to B shares. In principle, these two classes of shares are identical with their payoffs and voting rights, but research has shown that A shares are traded much more heavily than B shares (Mei et al. 2009). Hence, an index comprising China A shares would be very liquid but not investible for investors outside China, as investors could not access those shares, and as a result they are not able to replicate the index. users would face more and more choices. Hence, how to select a better index which is suitable to an investor s objective becomes crucial. A first important question is therefore by which criteria investors actually judge index quality in the first place. Another important point is how widely current indices are used and whether users are satisfied by the current indices. 1.1 Index quality criteria The usual basic qualities that are typically cited for indices include representativity, transparency, liquidity and investability (see e.g. Arnott et al. (2008, pp64) and Kamp (2008)). Representativity usually remains undefined, but the basic notion is that the index should be related to developments in a given market segment or region. Transparency usually refers to the fact that indices should be designed by publicly available and non-discretionary rules. At the same time, indices are usually required to be liquid large position trading will not impact the market price and investable the constituents included should be accessible to all investors. 3 In our findings, we conclude that liquidity and transparency are the most important criteria for indices to respondents in our sample. In addition, objectivity, which refers to avoiding discretionary choices, is also critical to our respondents. On the other hand, our respondents state that economic representativity is often not a requirement for an index. To investors, indices could serve other purposes provide specific style exposures, or efficient risk/reward ratio, etc. other than representing the economy. But essentially, investors have to be able to replicate the indices easily. Since their buy-and-hold character is often justified as a reason to stick with standard cap-weighted indices, it is perhaps somewhat surprising that the buy-and-hold property of an index is not of prime importance to our respondents. Interestingly, our findings on the required qualities of indices open many possibilities to construct indices that would be acceptable to investors. In fact, any transparent and liquid portfolio construction rules could be appreciated by investors. Furthermore, our survey provides interesting insights on the debate of how far an index can move away from a traditional passive strategy. Some papers (Ranaldo and Häberle 2007; Fuller et al. 2010) argue that current indices are not completely passive as they involve lots of active choices. On the other hand, in our survey, the majority of respondents think that indices should not only reflect passive strategies (58%). But they also indicate that indices should not be based on alpha (75.2%). This finding implies that for most respondents an index is not required to be passive in a very strict way holding a portfolio without any trading but rather is required to be passive in a broader sense holding a portfolio without trying to generate alpha. Together with the low importance of a buy-and-hold property (which corresponds to a very narrow definition of a passive strategy) of an index, our survey suggests that passive investing to our respondents does not mean buy-and-hold or not being dynamic. These results show that the notion of passive investing is quite different from the traditional idea of a pure buy and hold strategy. From the fact that An EDHEC-Risk Institute Publication 7

8 Executive Summary respondents think that indices should not be based on alpha, we conclude that passive investing mainly means, being exposed to risk premia or normal returns as opposed to abnormal returns. This notion that an index can be acceptable even if it is not purely passive in the sense of a buy and hold strategy probably reflects an acceptance of new index offers which maintain systematic rules and thus allow investors to reconcile their concern over reliability and transparency with an improvement of risk/reward properties. In this sense, new offers of smart or advanced beta position themselves in the range of investment options as low cost means of managing a relative risk budget with respect to traditional cap-weighted reference indices. 1.2 Use of indices and satisfaction with indices As there is a clear requirement on the qualities of indices, it is interesting to find out whether the current indices have fulfilled the criteria listed by investors. To get a broad view of current index use, we first try to understand the adoption rate of the indices for equity, bonds and equity volatility. Our results have shown that more than 90% of respondents who invest in equity use indices, which is not surprising as equity indices have been the first indices historically and there is a vast variety of products based on equity. On the other hand, bond index adoption rates are not as high as that for equity indices, only 71.6% for government bond indices and 61.1% for corporate bond indices. Besides the shorter time for development for bond indices, difficulties with the properties of bond indices could contribute to the lower adoption rate. For example, the characteristics of bond indices, such as duration, change over time due to the replacement of the matured bonds or simply due to the passed time. So Benning (2006) has concluded that a bond index is a moving target, when it is selected today, it may become inappropriate tomorrow. Furthermore, the data problems which cause pricing difficulties in bond indices might make investors hesitant to use bond indices as the index value may not truly reflect the price of the underlyings. For instance, most bonds are traded over-the-counter (OTC) not on exchange (Jankowitsch et al. 2002), which implies that prices are not directly observable as these prices are provided by dealers. Hence, prices are either an estimation of the dealers or a reflection of their last transaction price, which may however not be as timely as desirable. Among the asset classes we included in our survey, indices for equity volatility have the lowest adoption rate by investors (60.9%). This is expected as equity volatility indices are newly introduced products only available since In general, the trading volumes are low and not so many investable products are available. Though equity volatility indices may be more popular used as indicators or information sources for investors to invest in other investment vehicles, our survey targets at the actual usage of equity volatility indices. Hence, we are more care about the actual trading volume and the investable products linked to equity volatility indices. If the adoption rates clearly show the prevalence of indices, the satisfaction rates for indices in various asset classes reveal a number of serious concerns. Overall, satisfaction rate of indices are relatively low. Two thirds of users in our survey are 8 An EDHEC-Risk Institute Publication

9 Executive Summary satisfied with indices in equity and equity volatility investments and only half are satisfied with indices in bond investments. The satisfaction with indices is the lowest in corporate bonds (46.5%). Dissatisfaction with indices is not necessarily explained by the same issues across asset classes. Indeed, rather, there are specific issues associated with indices in each asset class. For example, cap-weighted equity indices have been criticised as being inefficient (Haugen and Baker 1991; Grinold 1992; Goltz and Le Sourd 2010); bond indices are often criticised by having unstable credit exposure and unstable duration caused by change in constitution (Levine, Drucker and Rosenthal 2010; Siegel 2003); equity volatility indices lack of liquidity and available products (Dash and Moran 2005) and our survey results reveal that such criticism voiced in the literature is widely shared by institutional index users as well. 2. Key Issues with Current Indices for Equity, Bonds and Volatility As mentioned above, our survey results show that the current indices are not very satisfactory for investors. Beyond a general assessment of satisfaction rates, our survey went into more detail in order to investigate which specific issues existed with indices across different asset classes. 2.1 Broad market indices versus sub-segment indices One can divide indices broadly into two kinds: broad market indices, such as regional or global equity indices, which aim to represent the overall market movements; as well as sub-segment indices such as style or sector indices (e.g. a growth index for equity, or a 1-3 year maturity index for bonds). Our survey tries to get a better understanding about the importance of sub-segment indices relative to broad market indices across different asset classes (excluding equity volatility). Our results (see the summary in table 1) show that sub-segment indices are only really important for bond indices. The lack of importance of sub-segment indices for equity indices may stem from equity investors preference for exposure to the general risk premium of broad equity exposure (rather than a risk hedge for precise risk factors). Fixed-income investors, by contrast, seek to hedge precisely defined risk factors (credit and duration targets). As fixed-income investors are, in general, exposed to such factors as interest-rate risk, inflation risk, and others, they need fixed-income instruments with specific characteristics to match their risk exposures. Another point is that it is quite clear what the relevant risk factors are in the bond universe (e.g., interest rate risk and credit rate risk) whereas in the equity universe it is controversial what the relevant risk factors are. For example, Amenc and Le Sourd (2005) summarise the many possible choices of relevant risk factors for Table 1 Comparison of importance of sub-segment indices across different asset classes Importance of sub-segment indices as opposed to broad indices Equity indices Government bond indices Corporate bond indices Dominance of broad indices High importance of maturitysegment High importance of credit- and credit rating rating segment and maturity- segment indices segment indices An EDHEC-Risk Institute Publication 9

10 Executive Summary - equity portfolios including explicit factors and implicit factors. And within explicit factors there are macroeconomic factors and fundamental factors. As so many different definitions of factors exist, there are debates over which factor is more important for equity portfolios (also see Grinold 1991 or Engerman 1993). Such controversy over the most relevant set of risk factors in research probably explains the relatively low importance of factor based sub-segment indices for equity in practice. 2.2 Alternative weighting schemes As the standard practice of weighting constituents by market capitalisation has come in for harsh criticism (Haugen and Baker 1991; Grinold 1992; Goltz and Le Sourd 2010), indices with different weighting schemes have emerged. There are mainly three kinds for equity indices: those based on de-concentration, such as equal weight indices or equal risk contribution indices; approaches aiming at creating more representativity such as fundamentally weighted indices or GDPweighted indices; and approaches that explicitly focus on improving efficiency in the sense of the efficient frontier, such as minimum variance indices or efficient indices (maximum Sharperatio indices). Similarly for bond indices, approaches using de-concentration, or aiming at improving representativity have been proposed, as well as indices that use weighting by inverse duration for example. Since there are lots of alternative weighting schemes available and respondents are generally dissatisfied with the capweighted indices, one could perhaps expect that there might be considerable adoption rate in the alternatives. However, though there are only about one-third of respondents who do not see current indices as problematic, our survey results show that the adoption of alternative weighting schemes is relatively low, especially for bond indices (see table 2). For bond indices, one explanation could be the unfamiliarity of these approaches, as about one-fifth of respondents indicate that they are in fact not aware of the alternative weighting schemes. This relatively low adoption rate can likely be explained in part by the marketing of alternative weighting schemes as replacement options for standard capweighted indices while due to relative risk which these alternatives represent with respect to the cap-weighted indices, they would be natural candidates as a cost efficient and attractive alternative for using the tracking error budgets that are conventionally entrusted to active managers. 2.3 Equity volatility indices Equity volatility indices, as a new product compared to stock and bond indices, Table 2 Comparison of adoption of alternative weighting schemes Adoption of alternative weighting schemes % respondents who see current indices as not problematic % respondents who are not familiar with alternative weighting schemes Equity indices Government bond indices Corporate bond indices 45.2% 17.6% 12.5% 24.7% 35.1% 23.6% 1.1% 20.3% 18.1% 10 An EDHEC-Risk Institute Publication

11 Executive Summary have attracted increasing attention from investors (Whaley 2008). This is also reflected in our survey results. Among the respondents to our survey, about one-fifth of respondents have invested in equity volatility, and for those who do invest in volatility instruments, such investments take up about an average of 4.5% of the total assets under management (AUM) of the entire portfolio. Among these equity volatility investors, 60.9% choose to use published indices as a tool, and the satisfaction rate is 64.3%. This is relatively higher than for bond indices for example, where the satisfaction rate is in the order of 50%. Szado (2009) has shown that there is a naturally negative correlation between the equity volatility indices and the standard equity market indices. We find that most of our respondents invest in equity volatility indices seeking diversification with equity indices. This confirms that practitioners are aware of findings on low correlation and diversification potential from volatility instruments. However, both the literature (Whaley 2008; Figlewski 2008; Goltz et al. 2011) and our survey results reveal that lack of available products as well as lack of liquidity becomes the most difficult barrier for investors to gain access to this market. 3. The Future of Indexing: Towards More Purpose-Built Indices? Currently, the market capitalisation weighting scheme, which is the default scheme in the indexing industry, has proven to be the most popular scheme with both equity and bond indices. It often serves as a bellwether for the economy and is used for many kinds of investment objectives, users, and markets without any question of suitability. Only recently, there have been criticisms from both academics and practitioners questioning the issues with cap-weighted indices (Haugen and Baker 1991; Grinold 1992; Amenc et al. 2006). In response to these criticisms, various alternative weighting schemes have been developed recently. Nevertheless, alternative schemes are also often applied to different asset classes (e.g. GDP weighting and characteristicsbased weighting are applied to both equity indices and bond indices). But our survey shows that investors have often very different objectives across asset classes. The results also show that even in a given asset class, different investors may not have the same objectives. Hence, the suitability of these schemes to various investors becomes an issue. This section provides some details of our findings on these issues. 3.1 Generic market indices for different investment purposes? Other than representing the market, indices based on systematic and transparent weighting schemes could be used as a tool to achieve different investors objectives. Within an asset class, investors may have different investment objectives, such as hedging various risk exposures or achieving diversification benefits based on low correlation across different instruments. Obviously, the best way to construct an index may differ depending on the objectives. Below we consider a simple example on government bond investing to illustrate this point. If investors use bonds to seek diversification both within the bond market and with An EDHEC-Risk Institute Publication 11

12 Executive Summary other assets, what are important are the returns, volatilities and correlations within securities and with other assets. Within bond markets, an index could comprise a large number of bonds and try to exploit the correlation properties within the bond universe to create a diversified index. On the other hand, government bonds, as an asset class, have low correlation with the stock market, though the relationship is not stable over time. Hence, the inclusion of some bonds in the portfolio could help achieve diversification with equity holding (see e.g. MSCIBarra 2009). An index aiming at the diversification of equity holdings may in principle aim at lowering correlation with equity or achieving a stable correlation over time. On the other hand, if investors would like to use bonds to hedge risk exposures, they need bond indices that match their risk exposures. For instance, an investor s concerns about interest rate exposure could be hedged by going long on government bonds, as the present value of a bond is the sum of the discounted future cash flow. Similar to inflation hedging, inflation-linked government bonds pay coupons based on both coupon rate and the inflation index. In this way the risk of inflation on the investments is cut-off. As for hedging liability risk, which is usually a concern for pension funds, the objective is to stabilise the interest rate and inflation fluctuations of the liabilities. Therefore, a portfolio of bonds which matches the exposure to interest rate and inflation of an investor s liabilities could be desirable to investors. This simple example shows that even within a single asset class, investment objectives can be different. Hence, we explored in our survey the main objectives investors have to invest in an asset class and how these objectives are different across asset classes. Table 3 shows us the differences in investment objectives among government bond, corporate bond, and volatility indices. It is obvious that seeking diversification is the main purposes for investors to invest in indices of any asset class (government bonds, corporate bonds and equity volatility). However, corporate bond indices are rarely used for hedging. Only 11.1% of investors use corporate bond indices for hedging in contrast to 62.2% for government bond indices and 39.1% for equity volatility indices. This is surprising given that corporate bonds are perhaps a more natural hedge than government bonds for corporate liabilities as pension payments have a credit risk component (Scherer 2006). This may be due to the difficulties with the existing corporate bond indices (such as the lack of stability of risk exposures and the lack of availability of specific rating or maturity sub-segments) which limit their value as useful hedging tools. An important implication from the fact that investors use indices in the same asset class for quite different purposes, such as diversification or hedging, is that a one-size-fits-all approach to creating indices for a given asset class might Table 3 Comparison of objectives to use bond indices and equity volatility indices Objectives Government bond indices Corporate bond indices Equity volatility indices Diversification benefits 66.2% 70.8% 82.6% Hedging risk exposure 62.2% 11.1% 39.1% 12 An EDHEC-Risk Institute Publication

13 Executive Summary not be sufficient to offer solutions to the current investment needs of survey respondents. 3.2 Generic market indices for different users? We have seen that investors may pursue different purposes with their investments and the purpose at hand may be important for defining what a good index would be. It is natural to think that there may also be systematic differences between different types of investors. This variation in objectives may stem from the fact that investors are influenced by different investment cultures, or are constrained by various factors, such as size and liabilities. Hence, investors could be classified into various groups according to different criteria. These classifications could in fact lead to significantly different views on choices of instruments and investment strategies. In our analysis, we classify our respondents into three types of groups: asset owners versus asset managers; more equity oriented countries versus less equity oriented countries; and small/medium investors versus large investors. Now we turn to summarise the differences in the following texts. And here we only focus on statistically significant differences. Firstly, we investigate the differences between asset owners and third-party asset managers. Asset owners, such as pension funds, are often seen as rather long term investors and have a strong focus on liability driven investing. On the other hand, third-party asset managers are seen to be more oriented towards an asset-only perspective (as opposed to a liability-oriented perspective) and often assess the performance of their investments at shorter time horizons. Such differences in the type of investment management organisation may naturally lead to differences in views on which indices are the most appropriate. Our results on this comparison show that in general, the majority of asset owners are concerned about stable risk exposures when assessing/using indices. For example, nearly 90% of asset owners consider overinvestment in more risky corporate bond indices as important or very important, while on the contrary, only half of third-party asset managers do so. This finding makes sense since asset owners have liabilities and thirdparty asset managers do not. Thus, they will assess the quality of indices with respect to their objectives. Third party asset mangers investment objective is to outperform the index, so they are less concerned about the index s risk exposures. Secondly, we distinguish our respondents between strong equity culture countries and weak equity culture countries. Regions that have strong equity investment cultures include the UK, Netherlands, Switzerland and Northern Europe (Okamoto 2009 and Beke 2011) and countries with weak equity investment cultures usually include France, Germany and etc. (Okamoto 2009 and Beke 2011). It is common to distinguish between these two regions, since investors in strong equity culture countries tend to invest more in equity and employ more advanced and complex investment strategies. Our findings show that 87.8% of respondents from more equity-oriented An EDHEC-Risk Institute Publication 13

14 Executive Summary countries are concerned about the risk/ reward efficiency of an index, and 53.5% are concerned about the representativity. On the other hand, roughly the same attention is paid to both efficiency and representativity by respondents in less equity-oriented countries (76.2% concern about the representativity and 69.8% concern about the efficiency). This difference could stem from the fact that investors in more equity-oriented countries have a strong focus on achieving the highest possible risk/reward ratio which implies the importance of the risk/return efficiency of an index. Market representativity in the context of a focus on efficiency will not be an important consideration. Respondents in the rest of Europe, given that their investment processes for equity may be somewhat less developed, may be more driven by peer group considerations and representing the average returns in the market or in the economy. Lastly, we group respondents according to their total assets under management. Investors with large sizes of assets under management (AUM) are more likely to be sophisticated (Amenc et al. 2011a) and would tend to be more concerned about potential price impact on index constituents when investing in an index, whereas a small investor would not usually have to consider this issue. The result is also interesting. Large investors see a reasonably low turnover as critical (84% regard it as important to very important) to assess an index s quality, whereas small and medium investors are less concerned about this issue (only 58.7% see it important to very important). This difference may come from the fact that as large investors usually hold large positions on an index, potential liquidity issues may rise if the constituents are thinly traded or small in market capitalisation. However, this concern is less serious for small and medium investors. Furthermore, we find that in general, large investors have a higher adoption rate (53.5%) of alternative equity weighting schemes compared to small and medium investors (for whom the adoption rate is 35.7% ). A possible interpretation is that large investors are more likely to be sophisticated (Amenc et al. 2011a) so that they would have more resources and broader access to alternative weighting schemes. In summary, index users would have different focuses when investing in the indices depending on their investment purposes, investment cultures and sizes. Given the varying requirements for indices, the historic one-size-fits-all approach of creating generic market indices using similar methodologies may not be able to address the variety of needs of different index users. 3.3 Generic market indices for different types of markets? We have seen above that various kinds of investors invest differently in indices within a particular asset class. It is not surprising that when it comes to comparing across asset classes, differences in requirements and issues are even more pronounced. The literature has criticised equity indices mainly in terms of its overinvestment in the overpriced stocks (Hsu 2006), and the concentration in few large stocks (Tabner 2007) and 14 An EDHEC-Risk Institute Publication

15 Executive Summary 4 - The rating is based on a scale of -1 (not important), 0 (I don t know) and 1 (slightly important) to 3 (very important) excluding non-response. For equity volatility indices, since all issues have received very high scores, these two issues which receive the highest scores of 2.44 are listed. Malevergne et al. 2009), which leads to poor diversification. The issues that were raised by the literature with bond indices are different. Commonly cited issues are the pricing difficulties (Elton and Green 1998) and instable duration or credit risk exposures (Siegel 2003, Benning 2006 and Campani and Goltz 2011) for example. Equity volatility indices are often criticised as having a lack of available products, due to the reliance on liquid option markets to extract information on volatility (Whaley 2008; Figlewski 2008; Goltz et al. 2011). A quick look at the literature thus suggests that challenges to construct good indices differ across asset classes. Our survey allows us to assess the importance of these issues to index users. Table 4 shows the important issues that respondents have seen across different asset classes. These issues listed in the table have received an importance level of at least The findings of our survey make it clear that the issues investors see with existing indices differ across asset classes. Equity investors fear overinvestment in overpriced stocks and insufficient diversification due to concentration of the indices in a small number of highly correlated stocks. Fixed-income investors, by contrast, are more likely to be concerned by duration stability and liquidity of the indices. As for equity volatility investors, liquidity and available index tracking products need the most careful consideration during asset allocation. This divergence of opinion across asset classes suggests that investors in a given asset class need indices that provide solutions to problems different from those faced by investments in other asset classes. Even in the fixedincome industry, different investors with the same aim of hedging liabilities, Ryan (2010) suggested that there is no generic index that could offer hedging solutions to all the liability requirements. Our results imply that there may be a possibility to design more objective oriented as opposed to generic indices. 4. Conclusion In conclusion, the status quo, in which index-weighting schemes (for both capitalisation weighting and alternatives) are usually the same for different asset classes, may not be the best solution for all investors. In light of the fact that the only strict requirements of respondents on index construction are that the index is transparent, systematic and ensures liquidity, and considering the wide range of different purposes that investors have with their investments, it seems indeed counterintuitive to assume that a single index construction method would be sufficient. Since investors have different objectives and problems Table 4 Comparison of important issues associated with indices across different asset classes Equity indices Government bond indices Corporate bond indices Important issues associated with indices Overinvestment in overpriced stocks Poor diversification Sector and size biases Difficult to invest/ replicate Instability of duration Inconsistent security selection rules and nonsystematic pricing Lack of liquidity Overinvestment in more risky companies Unreliable credit and duration exposure Equity volatility indices Poor liquidity of option market when options are used to extract volatility Lack of available products An EDHEC-Risk Institute Publication 15

16 Executive Summary in each asset class, the best way may be to differentiate construction methods to solve these problems. In fact, even within each asset class, it may be hard for a single weighting scheme to address all problems. The results of our survey thus suggest that there may be room to design more objective-oriented as opposed to generic indices. Building such indices would be challenging, to be sure, but they may provide useful tools for investors to manage their portfolios in coherence with their objectives. improved weighting schemes while keeping a reference with cap-weighted indices allows investors to distinguish between questions of complete transparency and representativity (which are required from a reference index) and questions of performance and diversification properties of their equity portfolios (which are objectives of advanced beta approaches). However, it seems clear that alternative forms of indices are not likely to replace generic cap-weighted indices. Seeing alternative indices as a replacement options for standard cap-weighted indices probably does not sufficiently take into account the practical investment context. In fact, any alternative to standard capweighted indices will be perceived as creating a relative risk with respect to the peer group, which is following such cap-weighted indices either through passive investment or through closely constrained active managers with relatively low tracking error budgets. In fact, cap-weighted indices despite the fact that their shortcomings are widely acknowledged are likely to remain the most practically relevant reference for equity portfolios for some time to come, due to their popularity, the extensive availability of track records, and due to the fact that they represent the average decision of investors. Alternative indices are therefore more likely to be used as a cost efficient alternative for using up the tracking error budgets that are conventionally entrusted to active managers. Such an approach of using 16 An EDHEC-Risk Institute Publication

17 2. xxxxxxxxxxxxxxxxxx 1. Introduction An EDHEC-Risk Institute Publication 17

18 1. Introduction 5 - Salomon Brothers introduced its Long-Term High-Grade Corporate Bond Index in 1973, at the same time that Kuhn, Loeb (ultimately acquired by Lehman Brothers) set up three U.S. bond indexes (Flagel and Wardley 2009). Indexation continues to play an important and growing role in global asset allocation. SPDR (2011) reports that index tracking products take up an increasing share of inflows into open-ended funds in the US. Exchange traded funds (ETFs) accounted for 11% of inflows in the US in 2010, while they only accounted for about 1.5% in Traditional index funds (which are not exchange traded) accounted for 12% inflows in 2010, up from 9.8% in This shows that while index products still account for a minority of inflows into open ended funds, their share has grown considerably over the past few years. The growing importance of index investing can also be observed from the use of indices for assets under internal management. Total worldwide assets under internal indexed management rose to $5.994 trillion as of June 30, 2011, a 25% increase over $4.781 trillion as of one year ago (Olsen 2011). In terms of the number of products, Russell Investments (2010) has reported that there is a substantial growth of the number of U.S. institutional equity products that are benchmarked to indices (shown in table 1.1). Against the backdrop of this recent market success, it is useful to point out the long history of indices. The history of indices can be dated back to the 19th century, when the first stock market index the Dow Jones Industrial Average (DJIA) was introduced in DJIA is a price-weighted index, which represents an average of 30 stocks from leading American industries. Later in 1923, Standard & Poor s introduced its first cap-weighted stock index, which was meant to provide information on the market s mood and direction. Such cap-weighted country indices later have come to dominate the market for equity index products. In 1926, the first indices were developed in the bond market. These bond indices measure the average yield of bonds, but not the interest (coupons) paid on them. Total rate-of-return bond indices were not developed until in the 1970s (Reilly et al. 1992). 5 A more recent addition to the index world is equity volatility indices. Whaley (1993) proposed an idea to provide a benchmark of expected short-term market volatility VIX which later becomes the most popular volatility index. More recently, indices have made forays into alternative asset classes beyond stocks and bonds. The present document however limits it scope to the traditional asset classes, as well as volatility indices associated with them. In the over one-hundred-year history of indices, capitalisation-weighted indices have proved to be the most popular indices for both equity and bond markets. Such indices are supposed to represent the market average returns and due to their representativity often serve as sources of information and as a bellwether for the economy. Beyond this informational role, the standard cap-weighted indices are also used as tools in the investment process. For long-term investors such as pension funds, endowments, and insurance companies, cap-weighted indices have become an integral part of the investment process. Table 1. 1 Number of U.S. institutional equity products that benchmarked to indices Number of equity products Sources: Russell investments, An EDHEC-Risk Institute Publication

19 1. Introduction 6-1) Examples of equally weighted indices: S&P introduced an equalweighted version of its flagship US and Canadian indices in 2003 (S&P 500) and 2009 (S&P TSX 60); Similarly, Russell, following S&P s step, launched equal weighted equity index family in 2010; In Europe, STOXX introduced equal weighted version of European benchmark index in October ) Examples of characteristics based indices: FTSE launched Research Affiliates Fundamental Index (RAFI) US 1000 index and Global Wealth Allocation (GWA) index series in 2005; VTL Associates launched Revenue-Weighted Indices in 2006; most recently in December 2010, MSCI introduced a series of valueweighted indices, which reweight the constituents in the standard parent MSCI index by sales, earnings, cash earnings and book value. In 2011, Russell in partner with RAFI launched a set of fundamental indices as well. 3) Examples of optimisation based indices: MSCI launched the World Minimum Variance index in recently in 2010, FTSE launched EDHEC- Risk Efficient index series. With the increasing use of indices, recent innovations have proposed new methods for creating indices that often deviate from the standard cap-weighting. Index providers have recently launched indices based on equal-weighting, characteristics-based weighting, and portfolio optimisation. 6 As the choice of an index is a crucial step in both asset allocation and performance measurements, it is useful to investigate index use and perceptions about indices among investment professionals. The EDHEC-Risk European Index Survey 2011 aims to contribute to this awareness by analysing the current uses of and opinions on stock and bond indices. It is our hope that this survey will provide unique insight into the users perspective in the index industry. Overall, this survey collected 104 responses, which represent investors from asset management companies, pension funds and insurance firms located all over Europe. Our survey finds that liquidity, objectivity and transparency are the most important criteria investors have for indices. On the contrary, buy-and-hold characteristics are not requirements for an index. This finding has strong implications as it suggests that any liquid and systematic methodology could be adopted for index construction. In terms of specific requirements for indices in different asset classes, we find that while sub-segment indices (e.g. for styles, sectors etc.) play a subordinate role in equity investing compared to broad market indices, sub-segment indices are far more popular for bonds. This finding can be explained by the fact that bond investors have a clear target on hedging clearly identified risk factors such as interest rate and credit risk, while equity investors typically seek exposure to the broad equity risk premium. The relevant risk factors within equity markets are subject to much more debate when compared to bonds. By investigating different issues associated with indices in specific asset classes, we discover that investors encounter problems with indices that are often quite specific to the asset class at hand. For example, equity investors are mainly concerned that standard cap-weighted indices overinvest in overpriced stocks and provide poor diversification within the constituent universe. In contrast, fixed-income index users pay more attention to reliable duration exposure and are concerned with liquidity issues. Even within each asset class, it should be noted that investors see a variety of issues with index investments and the most appropriate index construction approach for a given investor may depend on which problem is the most relevant for him. Overall, our results imply that there may be a requirement for more objective oriented as opposed to generic indices. Regarding the recently introduced alternative weighting schemes, index providers have paid much attention on developing alternative weighting schemes for equity markets. However, the adoption rate of alternative weighting schemes for bond indices is quite low. One possible explanation is the unfamiliarity of investors with such alternatives. Another is the relative scarcity of alternative index products for bonds. This suggests that both researchers and practitioners may have work to do to on designing and explaining alternative weighting schemes in general, not just in equity. An EDHEC-Risk Institute Publication 19

20 1. Introduction This report has been divided into four sections. It begins with the background which discusses the relevant criteria when evaluating the quality of indices in general and discusses the main issues associated with indices in specific asset classes. The background provides an overview of the development of the indexing industry and of research that has been published on index design and index use. Then we turn to introduce the methodology we used for this survey and describe the sample we have collected. Detailed results will be presented in the following section followed by a conclusion. 20 An EDHEC-Risk Institute Publication

21 2. Background An EDHEC-Risk Institute Publication 21

22 2. Background Since the beginning of the industry for indexing in the 19th century, indices have been playing an important role in portfolio management. The concept of indexation has been extended from equity to fixed-income and even alternative asset classes. In this broad universe, there is a large amount of academic literature and industry analysis dedicated to further improvements and possible innovations in the construction of better indices. Therefore, to make our report more comprehensive, a background on topics we have covered in our survey is necessary for readers to have a better understanding of our work. In addition, a survey is always guided by the prior knowledge of the researchers, as the design of the questionnaire is not neutral to the outcome of the study. While we have taken care to design a complete questionnaire, leaving possibilities for open answers in addition to pre-specified ones, it is nevertheless important to document the choices that have been made in terms of the material that we decided to cover in the questionnaire for our survey. This background helps us explain the reason that certain areas have been covered in our questionnaire and the background in academic and industry research that guided our choice of topics. It is useful to begin with the overview of the indexing industry. The importance of the indexing industry has grown tremendously. From the supply side, while historically there tended to be one dominating index provider for each market, both global index providers and investment banks now offer indices and compete on a global scale. This growing competition has also lead to more innovative indices coming to the markets. So from the demand side, index users face more and more choices. Hence, it is natural to ask how to select an appropriate index for an investor s objective. This crucial question also leads to one of our survey topics Index evaluation. In the background, we focus on the common definition of index qualities. These qualities are defined by academic and practitioner research and index providers typically highlight the criteria they deem to be important. In our survey, we aim to discover the ways to select or assess an index from an investor s perspective. Consequently, the results will allow us to draw conclusions on whether the industry s emphases match investors needs and whether there may be room for future improvement. We will look into indexing in specific asset classes for more details. As the most important two basic building blocks of portfolio construction are stocks and bonds, we only include equity indices, bond indices (both government bond and corporate bond) and equity volatility indices in our scope. Cross asset class indices (e.g. target date indices, target risk indices and other multi-asset class indices) and alternative asset class indices (hedge fund indices, commodity indices, and etc.) are excluded from our discussion. We include equity volatility because while it is an extraction from equity index options, it is related to equity indices which we cover in detail. We are interested in understanding investors perceptions on this product. In this background, we will briefly introduce the index history for each asset class, followed by the review of issues raised from literature associated with specific asset classes. 22 An EDHEC-Risk Institute Publication

23 2. Background With a brief introduction of our motivations to this background and topics involved, we shall turn to a detailed discussion on each topic. The background is organised as follows: first, we will provide an overview of the current indexing industry; second, we will turn to the evaluation of the index qualities; last, we shall discuss indices for specific asset classes including equity indices, bond indices and equity volatility indices. 2.1 The Indexing Industry In this section, we will provide a brief overview of the indexing industry. In order to structure this overview, we first look at the landscape of index providers and then discuss index users The index providers (supply side) In view of the growing volumes in assets under management in passive indexing strategies, which has been shown in the introduction, a great many index providers have emerged worldwide; not only the organisations specialising in the index service such as Dow Jones, Standard&Poors s (S&P), Morgan Stanley Capital International Inc. (MSCI), FTSE Group (FTSE), Markit, Russell or Wilshire, but also stock exchanges, such as NYSE, Deutsche Boerse, Euronext and CBOE as well as investment banks including Barclays Capital, JP Morgan and so forth. Each provider has created or is creating a host of indices representing a full complement of industries and sectors. Indexing was first developed for stocks, and then it was quickly adopted in the fixedincome market. Now indices are expanding to all asset classes, such as hedge funds, real estate, currencies, and volatility. Moreover, the index family structures have become increasingly diverse. For example, equity indices, apart from the broad-based market index, are specifically designed to reflect size or style characteristics, while others focus on sector orientation and geographic orientations and so on. Similar cases for fixed-income indices, maturity-segment and credit risk-segment indices are well developed on top of broad indices. Beyond single-asset indices, strategic (or portfolio) indices such as target date indices, relative risk indices have been introduced recently (Alldredge and Prestbo 2007). They are constructed by building a multi-asset-class portfolio. A favourable factor for the expansion of index providers is the growth of exchangetraded funds (ETFs). ETFs have recorded a continuously exponential increase by number since And the total assets under management have reached $1.3 trillion (Fuhr and Kelly 2010). This assetgathering potential of ETFs could benefit index providers, as they are typically paid according to the assets under management of ETFs based on their indices (Skypala 2009) The index users (demand side) The demand in indexing industry has been continuously growing. This can be best seen through the dramatic growth of ETF markets. Especially in the 2008 financial crisis, many actively managed funds did not perform well. In response, more investors would like to switch to passive investing (Skypala 2009). This trend is reflected in market statistics on fund inflows. For example, the inflow of US open-ended actively managed funds drops from 89% in 2001 to 77% in 2010, while on the other hand, the inflow of ETFs jumps from 1.5% to 11% within the same period (SPDR 2011). An EDHEC-Risk Institute Publication 23

24 2. Background Furthermore, indices are always important to investors, not only for passively managed investments. In fact, index choices are critical to the investment process for active managers, as indices are frequently used as benchmarks for active managers. As active managers aim to beat a reference index but are subject to certain tracking error constraints, or relative risk, these constraints limit managers capability to deviate much from the benchmark. Hence, active managers in general hold portfolios that are similar to the benchmark (Rappaport and Mauboussin 2001), while the choice of the benchmark will influence/ dictate the overall performance of the active funds. In addition, the evaluation of active manager performance relies on how well the portfolio does relative to the return earned on a reference index; hence, index choice also has an impact on manager performance evaluation. Therefore, with a large number of options available to index users, how to choose an adequate index becomes the most critical question to answer. The next section is going to discuss qualities an index should have based on the literature. 2.2 Evaluating the Quality of Indices Given the variety of available indices and the crucial importance on the investment outcome that choosing an index has (see insert Indices and benchmarks have a central role in the investment process which explains in detail the reasons for the crucial importance of indices on the investment outcome), a natural question is what makes a good index? In literature, there are some commonly held rules for selecting and assessing an index. Arnott et al. (2008, pp64) argue that an index should be representative, replicable, transparent and rule-based, as well as having low turnover. Kamp (2008) also points out that an index should be transparent, broad and investable. Although different terms are used by different authors for index quality criteria, overall, we can summarise them into four main qualities: representativity, transparency, liquidity and investability. First of all, representativity is an oft-cited quality for an index. It refers to the belief that an index must represent market activity in e.g. a market segment or region. However, it should be noted that representativity is rarely clearly defined, and it is an outstanding question how to measure whether an index is representative. Second, transparency focuses on the availability of the documents on the concepts and methodology used to compute the index, as well as availability to current and historical data on index values and composition. This is critical for investors as transparency helps investors to fully understand what indices are doing. In Arnott et al. (2008, pp64) s definition, this transparency also includes consistent and systematic rules in index construction methodology. Third, liquidity ensures that an index could be traded by many investors without any price impact. Finally, investability guarantees that the underlying securities of an index are accessible and tradable so that the index can be reconstructed. This difference between the investability and the liquidity requirement perhaps needs to be explained in more detail and this is best done using a simple example. For instance, in China, there are two classes of 24 An EDHEC-Risk Institute Publication

25 2. Background shares for a company: A share and B share. Domestic investors can trade A shares but foreign investors are only able to access to B shares. In principle, these two classes of shares are identical with their payoffs and voting rights, but research has shown that A shares are traded much more heavily than B shares (Mei et al. 2009). Hence, an index comprising China A shares would be very liquid but not investible for investors outside China, as investors could not access those shares, and as a result they are not able to replicate the index. How systematic and transparent are standard equity indices? For an index to be entirely systematic and transparent, it is usually required that the index ground rules contain all construction details which are followed by the index so that the process is completely replicable. This is of particular importance if the index is used as an external reference, as for example in the case of a pension fund which approves an index by its board of trustees. If the reference has been created with some layer of transparency, accepting it as a reference may be difficult. However, it cannot be said of all indices that the process used is fully transparent; for example, many standard cap-weighted indices could not possibly be reconstructed from a systematic process and available data. Constitution is in some cases determined by discretionary committee decisions and not simply by applying systematic rules concerning market cap. Evidence of discretionary committee decisions concerning index constituent selection To give an illustration of committee decisions, we consider a specific example. On 1st June 2009, Dow Jones Industrial Average (DJIA) replaces General Motors Corp. (GM) and Citigroup Inc. with Cisco Systems Inc. and Travelers Cos. due to the global economic recession. This decision has been criticised subsequently, see e.g. Fuller et al. (2010). Arguments against the change in constituents are that while GM had just filed for bankruptcy protection there was no similar case for Citigroup which had simply issued a declaration that it is in the midst of a substantial restructuring which will see the government with a large and ongoing stake (Dow Jones 2009). The need for replacing the existing constituents as well as the choice of replacement has been criticised. While Citigroup has been replaced with a company from the financial sector, the replacement of an industrial manufacturer with an information technology company has been questioned (Fuller et al. 2010). However, the question is not so much whether these replacement decisions were reasonable or not but rather this example shows that such an index is not fully based on systematic and non-discretionary rules. Sometimes the choice of constituents is dependent on the market situation. Take an example from S&P 500. Arnott et al. (2008) point out that during the period of the tech bubble in 2000, S&P 500 substantially increased the number of companies from Nasdaq, which comprises of technology and emerging growth stocks, in its new An EDHEC-Risk Institute Publication 25

26 2. Background 7 - For examples, some index providers use free float bands rather than an exact free float percentage, and the definition of these bands may vary among providers. For example, FTSE uses the rule that free float less than or equal to 15% will not be eligible for free float greater than 30% but less than or equal to 40% will be using a factor of 40%. MSCI s inclusion factor is equal to its estimated free float rounded-up to the closest 5% for constituents with free float equal to or exceeding 15%. In addition to the different definition of bands, some authors have argued that free float rules are not transparent. Arnott et al. (2008, pp 64) comment on the free-float rules defined by Russell indexes and point out that the company maintain the enough secret source in the definition of available float. 8 - In Russell, the country assignment has systematic rules for companies with sufficient information available. Otherwise, the stock will be by default assigned to its headquarter country. In FTSE, nationality of stocks is classified based on the categories the stock belongs to. An example of a category would be that if a company is incorporated in a developed country, and solely listed in another developed country, FTSE will normally allocate the company to the country of listing. However, in some cases, the committee could override the rule after taking into account factors including tax residency, market perception and currency of trading and etc. In principle, the committee has the right to choose whatever it believes to be appropriate from investors perspective, additions (24 out of 58 additions come from the Nasdaq). In contrast, during 1995, the Nasdaq only contributed 4 out of 33 additions to the S&P 500. Again, this is an arbitrary decision, no matter if it is right or wrong in the eye of the beholder. After all, this is not something systematic and based on objective criteria that could be defined through an index rulebook. These are two examples of discretionary committee decisions based on index constituent selection. In practice, the reasons for these decisions may vary from case to case. What is typical of these two cases is that committees often make discretionary decisions on stock inclusion based on considerations of economy or sector representation. Typically, index providers and exchanges point out the existence of index rules for constituent selection as a proof of transparency. However, sometimes these rules give rather substantial room for discretionary decisions. As an example, the CAC 40 index methodology by Euronext (2006) points out that The Conseil Scientifique of the CAC40 index may decide to change the composition of the index due to events, which affect one or more of its constituents. Such a rule obviously implies that the historical constitution could not be reconstructed by simply following systematic rules. Other discretionary choices Other than the constituent selection, committees often make discretionary choices with other aspects, including the constituent weights. Recently, many major indices have shifted from total market capitalisation to free-float market capitalisation. The idea behind this is that instead of weighting the companies by their total market capitalisation which investors could not access, it would be more reasonable to weight companies by the shares available to investors. In this way, it could reflect more accurately the market accessible to investors. However, the conversion between the two methodologies involves some discretionary decisions made by the index construction committees. In fact, index providers have different definitions on the free-float conversions. 7 From an investors perspective, how exactly to compute the float is not always entirely verifiable. Another interesting example about the sometimes discretionary decisions made by committees is about the nationality of the stocks. Nowadays, it is common to see companies that are incorporated in one country, headquartered in another country, and listed in a third country. This could create discrepancies when index providers assign stocks to countries. 8 While index providers have systematic rules on nationality classification, some index providers also use committees and leave a certain amount of discretionary decision making possibilities for defining the nationality of a company. In summary, when going into the details, one can ascertain that standard indices which are sometimes understood to be completely transparent and systematic often involve different levels of discretionary choices. 26 An EDHEC-Risk Institute Publication

27 2. Background The aforementioned qualities representativity, liquidity, transparency and investability - have been commonly cited as guidelines to select and assess an index. Besides the above characteristics, investment managers explicitly or implicitly seek efficiency from an index. When indices are used as investment benchmarks, the focus on representativity may be of little relevance, while achieving the highest possible risk/reward ratio is crucial if one does not want to have an inefficient starting point for the investment process (Amenc et al. 2006). So a benchmark should represent the best investment choice the investor can make in the absence of privileged information or bets on specific securities. In addition to risk/reward efficiency, investors typically perceive the benchmark to be a neutral choice of long-term risk factor exposures. However, some studies have suggested that the currently available market indices (both equity and bonds) display a lack of stable risk exposure (Amenc et al. 2006, Campani and Goltz 2011). It has been argued that the risk factor stability of a benchmark is an important consideration to assess an index with. In fact, an index with unstable implicit exposures over time could potentially compromise the explicit risk factor allocation decisions that investors have taken when defining their global asset allocation. In summary, faced with a great number of options for index choices, the literature has proposed several important qualities that an index should equip. Our survey will assess in more detail which of these criteria are indeed the most relevant for investors. Indices and benchmarks have a central role in the investment process The choice of indices is a determining element in the investment process. It is also the first step. Prior to portfolio construction, investors conduct asset allocation studies to decide on the asset mix. Such studies are based on information about risk and returns for various asset classes or asset class segments, which in general is obtained by looking at indices. Thus, the choice of indices used for analysis will have an impact on asset allocation decisions. Subsequently, the monitoring of managers and performance analysis will depend on the selection of the index as it is commonly used as a reference, even if the investments are implemented using active managers. In fact, it is commonly the case that active managers are subject to relatively tight tracking error control and hence will not be able to deviate too far from the reference index, which means that performance and risk properties of the portfolio will largely depend on the reference rather than on the specific choices of the active manager. Hence, index selection is an essential source of both the risk and the returns of a portfolio. The choice of an index or benchmark as a reference point is thus determining the outcome of many other choices that are made subsequently. Thus, for investors it seems reasonable to pay close attention to this first step rather than just using standard indices without questioning them. This reasoning is similar to the use of reference portfolios in the academic literature. Academics use reference portfolios when testing An EDHEC-Risk Institute Publication 27

28 2. Background asset pricing models, just like institutional index users use indices when implementing asset allocation decisions and when evaluating performance. Academics use a standard set of cap-weighted reference portfolios, the Fama-French portfolios sorted by size and value characteristics, and the associated market, small cap and value factors. Just as the choice of an index matters in practical asset allocation, the choice of these reference portfolios and factors have been shown to matter for the conclusions of academic researchers. Indeed, recently, the case has been increasingly made that the choice of these reference portfolios matter in the results of asset pricing tests. Daniel and Titman (2005) argue that a new set of portfolios is required to identify important factors because the Fama and French s factors (1993) serve as a capture all and thus the asset-pricing tests could be blinded by these major factors from others. Lewellen et al. (2010) review the commonly used asset-pricing tests and conclude that reference portfolio choice could directly affect the asset pricing tests. In addition, Cremers et al. (2010) also show that the amount of alpha generated by a portfolio strongly depends on the choice of reference indices. Ahn et al. (2009) propose a new way to construct basis assets to be used in asset pricing tests by minimising the inter-group correlations and maximising the intra-group correlations. In summary, whether it is institutional index users defining allocations or academics testing their theories, it is good common sense to closely scrutinise the building blocks that form the basis of an analysis. Index and benchmark selection is thus of central importance. 2.3 Indices in specific asset classes We have given an overview of the common criteria to evaluate the qualities of an index in the previous section. However, the requirements for indices vary across different asset classes. For instance, investors seek performance through equity but look for hedging capacities from bonds. On top of the general criteria, these specific objectives will lead to requirements that are especially important to indices in that particular asset class. In another words, indices in different asset classes are exposed to different challenges. In this section, we are going to discuss the issues associated to indices in equity, bonds and volatility Equity Indices As the equity index represents the largest indexing industry, we shall start with the discussion of equity indices Common criticisms to cap-weighted indices As mentioned in the introduction, after the first price weighted indices, weighting by market cap has become the default way of constructing an index. Therefore, we focus on the issues highlighted with these standard indices in the literature. As mentioned in the first section, indices have played an important role in performance measurement as well as in investment decision making, i.e., in the investment 28 An EDHEC-Risk Institute Publication

29 2. Background processes and portfolio selection models. As part of the decision making process, they are used either to find an optimal allocation to different indices or even to passively hold a single index that is assumed to be well diversified. However, indices were initially designed by stock exchanges to measure where the market is and not meant as a tool for long-term investors. To achieve the target of representing the markets consideration of risk-reward properties is not needed (such as the diversification of the portfolio, the stable risk exposure or efficient risk reward ratios). The index will simply reflect how the market behaves, rather than how one could invest systematically in the market to achieve desirable risk-return properties. In contrast, such risk/return qualities play a critical role for long-term investments. Hence, the standard practice of using a capitalisationweighting scheme for the construction of indices has been the target of harsh criticism. The criticisms are mainly from four perspectives: the somewhat counterintuitive mechanics of cap-weighting, the resulting sub-optimality of cap-weighted indices, the resulting unstable risk factor exposures and the active nature of supposedly passive indices. An overview of the most common criticisms grouped into these categories and supporting papers are shown in the following table. Counterintuitive mechanics of cap-weighting Issues, such as trend-following, overweight of overpriced stocks and concentration in a few large stocks, are in general due to the naturally embedded features of cap-weighted indices. Amenc, Goltz and Le Sourd (2006) have studied the qualities of major currently available stock market indices and suggested that cap-weighted indices may lead to trend-following strategies. It is very simple to understand the logic. Cap-weighted indices assign weight to stocks by their market capitalisations, which is the product of the price of one share of the stock and the total amount of shares. If there is no new share offered, the weight of any stocks depends on the share price. Whenever share price goes up (down), the market capitalisation of that company goes up (down). As a result, the weight assigned will increase (decrease). Table 2. 1 Summary of common criticisms to cap-weighted indices Critique point Example of papers Counterintuitive mechanics of cap-weighting Cap-weighted indices may lead to trend-following strategies Amenc, Goltz and Le Sourd (2006) Cap-weighted portfolios overweight overpriced stocks and underweight Hsu (2006) underpriced stocks Cap-weighted indices are heavily concentrated in a few large stocks Tabner (2007) and Malevergne et al. (2009) Sub-optimality of cap-weighted indices in terms of risk/return Cap-weighted portfolio is a poor proxy for the market portfolio under CAPM Haugen and Baker (1991) or Goltz and Le Sourd (2010) Market-cap-weighted equity indices provide an inefficient risk-return trade-off Haugen and Baker (1991) or Grinold (1992) Unstable risk factor exposures Standard indices expose investors to sector or style drifts Amenc, Goltz and Le Sourd (2006) Active nature in the passive indices Many capitalisation weighted indices are active investment strategies Ranaldo and Häberle (2007) or Fuller et al. (2010) An EDHEC-Risk Institute Publication 29

30 2. Background From investors perspective, this weighting scheme is equivalent to a trend-following investing strategy buy more when price goes up and sell when price goes down. The trend-following feature of cap-weighted indices has also been argued to lead to an overweight of overpriced stocks and an underweight of underpriced stocks. It creates severe problems if market prices are noisy. This has been shown by Hsu (2006) in a simple binomial example and later proven mathematically. He has shown that the expected return of a firm should be the fair reward of a firm s fundamental risk. However, in a mispriced economy, the expected return will be increased by the mispricing risk on top of the firm s fundamental risk. In the case of cap-weighted portfolios, he finds that the expected return earned under price inefficiency is below the firm fundamental risk. In other words, cap-weighted portfolios could lead to worse performance in a mispriced economy. Nevertheless, this argument is also criticised by other research. Perold (2007) and Kaplan (2008) point out that the logic of this noisy market hypothesis is flawed, because the key assumption of the model is that investors know the fair value of the stocks. In reality, investors do not know whether the stock is overpriced or underpriced. Another characteristic of cap-weighted indices is the concentration in a few large stocks. For instance, the top 10 holdings in S&P 500 index make up of one fifth of the total market capitalisation of the index. Tabner (2007) has compared the concentration of the top ten firms and industries in the FTSE 100 Index in 1984 and He finds that there is a dramatic increase in the concentration of the top ten firm/sector holdings. This concentration issue is however not unique to the index Tabner studied. In fact, Malevergne et al. (2009) argue that cap-weighted indices are in general heavily concentrated in a few large firms. Sub-optimality of cap-weighted indices in terms of risk/return In the end, the harshest criticism to cap-weighted indices is that the mechanics employed to weight it leads to sub optimal portfolios in the end. This sub-optimality is reflected in the inefficiency of the cap-weighted portfolio (both in theory and by empirical evidence). Haugen and Baker (1991) as well as Goltz and Le Sourd (2010) have both reviewed the theoretical literature on the efficiency of the cap-weighted market portfolio and point out that there are few reasons to believe in the efficiency of cap-weighted equity indices (see insert Does financial theory make the case for capitalisation-weighted indexing? for details). There are several arguments. Firstly, the CAPM which makes the theoretical prediction of an efficient market portfolio is based on a number of highly unrealistic assumptions so that even the academics whose work has led to the model recognise that under more realistic assumptions, cap-weighted market portfolios cannot be expected to be efficient (Markowitz 2005 and Sharpe 1991). In particular, under real constraints like short-selling bans, the market will have many partitions due to constraints of short-sells, so the overall market index is no longer efficient. Also, the market portfolio under CAPM refers to a portfolio that holds all existing assets not only stocks. The market portfolio thus is a theoretical construct that includes other assets including alternative assets, illiquid assets and human capitals. Clearly, the standard cap-weighted equity indices therefore would be very poor proxies for the market portfolio. 30 An EDHEC-Risk Institute Publication

31 2. Background Does financial theory make the case for capitalisation-weighted indexing? The theoretical basis of cap-weighting The standard practice of eq uity index providers is to weight stocks by their market capitalisation. This practice has come in for criticism as researchers have found that the commercially available equity indices are far re moved from providing an effi cient risk/reward profile. But advocates of cap-weighting often point out that cap-weighting is the only theoretically optimal weighting scheme. In an extensive literature review, Goltz and Le Sourd (2010) review the evidence in the academic literature and concluded that only under very unrealistic assumptions would such indices be efficient investments. In the presence of realistic constraints and frictions, cap-weighted indices cannot, according to the academic literature, be expected to be efficient investments. According to the central piece of financial theory the capital asset pricing model (CAPM) formulated by Sharpe (1964) who built on the work of Markowitz (1952), the market portfolio, which held all existing risky assets and is weighted by their market capitalisation, offered an efficient risk/return trade-off. In other words, no other combination of risky assets makes it possible to obtain a better expected return for the same degree of risk, or a lower risk for the same expected return. Any risky portfolio other than the market portfolio will introduce some unsystematic and hence unrewarded risk, and thus will not be a valuable investment. Cap-weighted indices are not good proxies for the true market portfolio If we believe this theo ry reflects the real world, any investor should indeed hold the market portfolio. But stock market indices appear to be very poor proxies for the market portfolio. The true market portfolio is assumed to contain a vast collection of assets, including unlisted and illiquid assets, but stock market indices include only a small fraction of listed assets. Thus, even if an investor believes in the efficiency of the market portfolios, he shouldn t reasonably expect the cap-weighted equity indices to be efficient. Theoretical assumptions Perhaps more important than the fact that standard indices are an imperfect proxy for the true market portfolio is that, it is clear that the CAPM theory does not reflect the real world. The theory assumes investors are identical in terms of preferences and all have the same investment ho rizon. It also assumes unlim ited borrowing or short sell ing, tradability of all existing assets, and absence of any taxes or transaction costs. It is unreasonable to assume these assumptions hold in practice. After all, investors are unlikely to have the same preferences and the same investment horizons. In addition, the existence of taxes and transaction costs is quite real. Nor is unlimited borrowing feasible for most investors. In fact, Sharpe (1991) and Markowitz (2005) themselves have emphasised that the market portfolio may not be efficient in a more realistic setting. An EDHEC-Risk Institute Publication 31

32 2. Background After a detailed review of the literature, Goltz and Le Sourd (2010) conclude that, as soon as one of the CAPM assumptions no longer holds, financial theory does not predict that the market portfolio is efficient. Empirical results Regardless of the assumptions made by the CAPM, one may also test whether the theoretical predictions of the CAPM can be rejected empirically. By summarising the previous results, Goltz and Le Sourd (2010) find that in most cases, empirical studies reject the efficiency of the market portfolio and thus the validity of the CAPM, hardly surprising in view of the assumptions. As a summary of numerous empirical studies on the efficiency of proxies for the market portfolio, Cochrane (2001) concludes that Market indices [ ] are if anything inside that mean-variance frontier. To conclude, the theoretical case for the efficiency of cap-weighted indices is rather weak. Stock market indices are far from being the market portfolio as they reflect only a fraction of wealth in the economy. Even if it were possible to build and hold the market portfolio that includes all these assets, the market portfolio would be efficient only if a set of highly unrealistic assumptions held. In view of these arguments, it seems that financial theory alone does not justify the current practice of using capweighting indices. Empirically, various papers have assessed the efficiency of cap-weighted indices. Haugen and Baker (1991) and Grinold (1992) have shown that cap-weighted indices do not generate efficient risk/reward ratios. Such empirical finding supports the previous theoretical arguments that investment opportunities existed to build equity portfolios that exhibit better risk/ reward ratios than cap-weighted indices. Similarly, Grinold (1992) have adopted a Gibbons, Ross and Shanken (GRS, 1989) test to examine if the five equity benchmarks in the US, the UK, Australia, Japan and Germany are efficient. Their findings show that out of these five countries, the first four indices are not efficient which implies that other portfolios could be constructed to outperform the benchmarks. Unstable risk factor exposure Other than the inefficient risk/reward ratios, the lack of stable risk exposures also contributes to the sub-optimality of cap-weighted indices. Amenc, Goltz and Le Sourd (2006) have studied the stability of major stock indices in terms of exposure to both investment styles and industry sectors and concluded that the relative weight of the different sub-indices varies drastically over time. For instance, for a given sample period from October 1995 to September 2005, they show that the Stoxx Europe 600 index has a variation on the technology sector exposure from 5% at the beginning of the sample period to approximately 20% during the tech bubble around 2000; similarly, the exposure to the technology sector for the S&P 500 jumped to 30% around 2000 from 10% in Such variation of the weights of the sectors/styles in the broad market 32 An EDHEC-Risk Institute Publication

33 2. Background 9 - For example, Wilshire Such as MSCI country indices index leads to a problem for the investor. The instability emphasises the fact that the sector/style allocation becomes an implicit decision induced by the choice of an index, as opposed to an explicit choice of the investor. Active nature in the passive indices Some authors argue that standard cap-weighted indices imply active stock selection choices. Ranaldo and Häberle (2007) argue that exclusive indices, which in contrast to all-inclusive indices, 9 embody a set of selection, rebalancing and maintenance rules that are not necessarily passive. Moreover, some selective types of indices have embedded momentum strategies in their rules of construction, for instance, the selection and rebalancing rules of the most widely used selective equity indices imply the short-run momentum strategies add recent winners and remove recent losers. The authors in fact summarised major characteristics including selective rules of some main indices and compared the performance of exclusive indices and their respective inclusive indices. Their results suggest that exclusive indices are more exposed to both the upside and downside momentum of the market. Furthermore, they argue that dynamic indices, 10 which have changed their components over time, outperform the true passive index (holding the initial components until the end of period). These findings imply that the passive indices may actually adopt active management strategy. Fuller et al. (2010) confirm this point by constructing an index to be representative of US large-cap stocks. The process of building a cap-weighted index involves a number of arbitrary, active decisions, such as how to choose the constituents, how many stocks should be in the index, how frequently and when should the portfolio be rebalanced, how to reinvest the dividends paid by constituents, etc. As addressing these questions requires making a choice among several plausible alternatives, several authors conclude that the index is not entirely passive but rather contains somewhat active decisions. In summary, cap-weighted indices have been criticised from many perspectives. The weighting scheme by nature leads it to be a trend-following strategy and to overweight overvalued stocks. The high concentration in a few large firms may cause exposure to idiosyncratic risks. Even the elegant CAPM which is often viewed as a justification for cap-weighting, does not provide a rational motivation to build cap-weighted indices if one scrutinises the assumptions behind it as well as the nature of the market portfolio thoroughly. It comes as no surprise against the backdrop of financial theory, that most empirical results provide evidence that cap-weighted indices are sub-optimal. To address these criticisms, for several years, researchers have been examining alternatives to conventional capitalisation weighting Alternatives to cap-weighted indices There are mainly two trends to build alternative indices in the industry: more representative or more diversified approaches. More representative approaches Representativity naturally leads to indices that allocate greater weights to larger companies than to smaller companies. Cap-weighted indices belong to this kind. An EDHEC-Risk Institute Publication 33

34 2. Background 11 - It is used for instance, for Wisdom Tree Earnings Index For instance, VTL Revenue Weighted Indices It assumes that market capitalisation is the best measure for the size of a company. Cap-weighted indices have been criticised by many people, but if we still believe that representativity of the market should be the basic feature of an index, there should be other more representative ways to measure the size of a company. The characteristic-based weighting scheme proposes to use more fundamental measures of company size. Siegel (2008) reports that weighting stocks by accounting characteristics, (such as earnings) has been used as a strategy for economic investing since the late 1980s. The concept was made popular by Arnott, Hsu, and Moore (2005), who propose an attempt to be more representative than cap-weighted indices by introducing a different measure of firm size. This approach assigns weights based on an accounting-based measure instead of the stock s market capitalisation. Such measures could be a firm s book value or its sales for example. The justification given for such weighting is that this approach could create an index that does mirror with utter neutrality the composition of the economy (Arnott et al. 2008, pp 75). In this way, providers of such approaches argue that such indices could capture the evolution of the overall economy (Arnott et al. 2008, pp 198). However, this idea of representativity of the economy, while it seems intuitively appealing, has never given rise to any theoretical justification nor to any empirical testing. Although such indices do not explicitly aim at optimising the risk/reward tradeoff, they may somehow improve returns compared to cap-weighted indices, by avoiding the problems of capitalisation weighting. Characteristics-based weighting also results in a value tilt. By weighting companies according to accounting fundamentals, the indices tilt a stock s weight in the corresponding cap-weighted index based on its valuation relative to other stocks (Asness 2006 and Kaplan 2008). For example, compared to cap-weighting, weighting stocks by book value mechanically results in overweighting stocks based on their book-to-market ratio relative to other stocks (Kaplan 2008). These indices thus allow investors to implement a value strategy in a different manner. Blitz and Swinkels (2008) argue that weighting stocks by their fundamental characteristics resembles, more closely, active investment strategies than classic passive strategies. Another relevant question in the context of characteristicsbased indices is also which fundamental characteristics should be used and why. For example, initial economic portfolios were mainly based on earnings. Schwartz and Siracusano (2007) argue that earnings is a relevant weighting criterion for indices. 11 Arnott et al. (2005) do not use earnings but rather test sales, cash flow, book value,dividends and number of employees, where the latter is excluded in the actual indices. Also, note that Arnott et al. (2005) exclude revenues from their list because they see sales and revenues are similar concepts and performers, while other index providers prefer revenues to sales to weight stocks within their indices. 12 More diversified approaches The more diversified approaches are designed to achieve a fair risk/reward ratio. In the discussion on the index qualities in section 2.1, it was clear that an index as a source of information is used to represent 34 An EDHEC-Risk Institute Publication

35 2. Background market movements but when investors use an index as a reference portfolio for their portfolio management, such a reference should reflect the risk and reward available in their investment opportunity set. As indices are often used as reference points in portfolio management, the focus naturally is not on representativity but on achieving a fair risk/reward ratio. As mentioned before, one criticism of the cap-weighted indices is the inefficiency resulting from poor diversification. Several indices have attempted to improve this dimension, while exploiting different approaches to build more well-diversified portfolios. Dash and Loggie (2008) find that equalweighted indices that simply attribute the same weight to each of their constituents could provide attractive risk-return properties. DeMiguel et al. (2009a) show that equally weighted portfolios systematically beat value-weighted portfolios in terms of Sharpe ratio, returns and turnovers. Platen and Rendek (2010) also find that there are consistent positive differences in Sharpe ratios between 53 equally-weighted country indices and their cap-weighted counterparts from January 1973 until March Besides the attractive risk/return profile, these indices may also provide a better representation of the stock market than cap-weighted indices, as their return for a given day actually shows the average return of all stocks on this day. The Equal-weighting scheme is based on naive diversification, which recommends giving an equal weight to each of the N index constituents. It s simple but extreme since it also means that we agree to give up deriving any form of useful information for weighting constituents, and that information on market capitalisation or other measures used to derive index weights is entirely useless. Optimisation-based weighting schemes are different from cap-weighted, equalweighted, or fundamental weighted indices in the sense that they aim to achieve an efficient risk/reward ratio through systematic quantitative approaches weighting constituents by quantitative information on expected returns, correlations, and volatilities. Minimum-volatility weighting is an initial approach to build systematically rather than naively diversified portfolios. This approach leaves estimation of expected return aside, and instead focuses on constructing a portfolio with the lowest possible volatility. To find the optimised constituent weights, one need only estimate volatilities and correlations of index constituent stocks. In the case of identical expected returns for all stocks, such a portfolio would be representative of the optimal portfolio in terms of risk-reward ratio. Therefore, it may also represent the opportunity set of mean-variance investors in the absence of any information on differences in expected returns across stocks. In terms of risk/reward efficiency, the index focuses on lowering risk, without addressing its expected return properties. The minimum variance portfolio is motivated by modern portfolio theory, where it is one of the remarkable portfolios on the efficient frontier. The reference to the efficient frontier clearly shows the difference with more ad hoc approaches. The index sets itself a clear objective of approximating the minimum risk portfolio on the efficient frontier, which may correspond to what some investors see as a desirable property of their equity portfolio. An EDHEC-Risk Institute Publication 35

36 2. Background Other approaches also focus on the efficient frontier, but try to go beyond a focus on risk minimisation, as is the case with efficient indexation (Amenc et al. 2010). The literature has underlined that minimising volatility leads to concentration in low volatility stocks (see insert on Global minimum variance portfolio: problems and possible improvements ). This concentration leads to biases towards utility stocks (Chan et al. 1999). In order to avoid such concentration in low risk assets and to benefit from the diversification effects due to correlations, efficient indexation changes the objective function from minimising volatility to maximising the Sharpe ratio where low risk stocks are penalised by assuming a low expected return. The penalty on the expected returns side counterbalances the attractiveness of low risk stocks. Such indices are consistent with obtaining the tangency portfolio of Modern Portfolio Theory (or maximum Sharpe ratio portfolio) if the common sense principle of a risk-return trade-off holds. The aim of such an index construction approach is to represent the equity risk premium accessible in the stock market when taking into account information on the risk and return properties of stocks. Global minimum variance portfolio: problems and possible improvements The global minimum variance portfolio (GMV) gives up the estimation of expected return but focuses on constructing a portfolio with the lowest possible volatility. This approach is of interest because it is on the efficient frontier and thus draws on a concept from Modern Portfolio Theory. However, Modern Portfolio Theory tells us that there is only one optimal portfolio of interest, the tangency portfolio (Maximum Sharpe Ratio portfolio), which has the highest possible reward per unit of volatility. The GMV portfolio corresponds to this optimal portfolio if and only if a highly unrealistic assumption holds; notably that all expected returns are identical. In addition, to this theoretical consideration, the finance literature has shown that the minimum volatility approach compromises the diversification objective as the GMV portfolio leads to high concentration in few stocks. For instance, Clarke et al. (2010) find that their long-only GMV portfolio averages about 120 long securities, i.e., about 12% of the 1000-security investable set. And DeMiguel et al. (2009b) mention the issue that short sale-constrained minimumvariance portfolios [ ] tend to assign a weight different from zero to only a few of the assets. This concentration issue can be derived formally. Note that the weights in GMV portfolio could be expressed analytically as follows: For uncorrelated stocks, the weights are inversely proportional to squared stock volatilities. In other words, the GMV simply favours the low volatility stocks but does not fully exploit the correlation. Amenc et al. (2011b) have illustrated the impact of dispersion of asset volatilities on the minimum variance weights in the following two 36 An EDHEC-Risk Institute Publication

37 2. Background graphs. The results are based on a hypothetical universe of 100 stocks, the annualised volatilities of which are equally spaced between the highest and lowest volatility stocks (They consider the following cases of more or less pronounced differences in volatility: [16%, 18%], [15%, 19%], [13%, 21%], and [10%, 24%]). They also use a constant correlation model for the covariance matrix of stock returns. Figure 1 shows the effective number of stocks for the GMV portfolios formed from the 100 stocks with different parameter values used for average correlation ranging across stocks (ranging from 0 to 0.99) as the results in the graph show pronounced concentration effects. At reasonable levels of average correlation across stocks (say 0.3 and above), the effective number of stocks is less than 20 for the cases with wider spreads of volatility across stocks. Even when stocks have quite similar volatility levels, the effective number of stocks still remains relatively low for reasonable levels of correlation. Figure 1: Effective number of stocks in a long-only GMV constant correlation model It is interesting to assess which stocks GMV portfolios concentrate in most. Amenc et al (2011b) rank the stocks by volatility in three groups: low volatility, medium volatility and high volatility stocks. Figure 2 plots the sum of these weights in the GMV portfolio as a function of correlation. Note that the assumption here is that differences in volatility are very mild, (i.e. they lie in the interval [16%, 18%]). The figure clearly shows that if average correlation takes on reasonable values of 0.3 or higher, the total weight allocated to the low volatility stocks in the GMV portfolio takes on values of 80% and above and the allocation to the high volatility stocks is zero. For an average correlation value of more than 0.6, the GMV portfolio is concentrated entirely in the lower volatility stocks. In summary, the GMV portfolio loses diversification by concentrating on low volatility stocks. Therefore, the GMV portfolio is a strategy of tilting the portfolio towards the lowest volatility stocks, rather than a strategy that helps improve diversification by exploiting the correlation properties across stocks. Whether such a tilt towards low An EDHEC-Risk Institute Publication 37

38 2. Background volatility stocks is desirable in the end depends on whether an investor wants to make a stock selection decision in favour of low volatility stocks. The properties of low volatility stocks have been analysed in detail in the literature. Figure 2: Weights distribution with changes of correlations Regarding the expected returns of low volatility stocks, the empirical literature has shown that while short term tactical tilting towards low volatility stocks can generate returns through capturing short term reversal effects (Ang et al and Huang et al. 2010), low volatility stocks tend to have low returns from a long term perspective (Fu 2009, Brockmann et al. 2009, Cao and Xu 2010). In addition, low volatility stocks may give rise to pronounced extreme risk exposures (Boyer et al. 2010, Chen et al. 2001). A portfolio of the lowest volatility stocks will also display pronounced sector biases, in particular towards utility stocks (Chan et al. 1999). The figure below reproduces results from Chan et al. (1999). It shows the beta relative to the value-weighted market index and the concentration in the utility sector for different weighting schemes. We can see that the GMV has extremely high weights in utilities compared to both cap-weighted and equally-weighted portfolios since utility stocks tend to have low betas and low volatilities. Chan et al. (1999) in fact state about GMV approaches that the optimizer selects every single utility it is presented with. Beta % invested in utilities GMV % Cap-weighetd % Equally-weighted % Source: Chan, Karceski and Lakonishok 1999 To avoid concentration in low volatility stocks when minimising portfolio volatility, different solutions have been proposed by both practitioners and academics. A natural way to avoid concentration is to impose constraints on weights. Such constraints can 38 An EDHEC-Risk Institute Publication

39 2. Background be set on the level of individual stocks (Jagannathan and Ma 2003) or on the level of sectors, countries etc. Setting such constraints is however very inflexible and may thus compromise the quality of the portfolio optimisation. An alternative is to use more flexible weight constraints. DeMiguel et al. (2009b) impose norm constraints that limit the overall amount of concentration in the portfolio (sum of squares of portfolio weights), rather than limit the weight of each stock. They have shown that using such constraints can effectively improve the out of sample Sharpe Ratio compared to using overly rigid constraints. Setting such constraints will however not change the tendency of the optimiser to concentrate in low volatility stocks; it will simply limit the degree of this concentration through the constraint. An alternative to setting such constraints is to introduce an assumption that will effectively cancel the tendency of the variance minimisation to tilt towards low volatility stocks. Christofferson et al. (2010) assume volatilities are identical across stocks when minimising portfolio volatility. This assumption means that the optimiser cannot exploit any differences in volatility and will thus focus on exploiting the information on correlations across stocks. These three approaches remain within the minimum variance framework but introduce constraints or assumptions in order to circumvent the concentration problem. Another way of avoiding concentration in low risk assets and to benefit from the diversification effects due to correlations is the efficient indexation approach of Amenc et al. (2010). They change the objective function not minimising the volatility but maximising the Sharpe ratio, while assuming that a trade-off between a stock s riskiness and its expected return holds. In such a way, low risk stocks are penalised by assuming a lower expected return. The penalty on the expected return side counterbalances the natural attractiveness of low risk stocks from the risk perspective and thus avoids excessive concentration in low volatility stocks. In addition, such an approach is consistent with obtaining the tangency portfolio of Modern Portfolio Theory and puts the focus back on improving portfolio diversification. While cap-weighting remains the de facto default choice for investors, recent research has developed a range of alternatives, and the list above is a non exhaustive list that reflects research methodologies that have currently given rise to published indices by the main index providers. In the light of numerous alternatives, investors are likely to assess and compare different alternatives in order to select the ones that best reflect their objectives or beliefs. Other investors will perhaps see opportunities to diversify their passive exposure by using multiple approaches at the same time. Our survey will allow assessing the current views that exist in practice on such alternative weighting schemes. A conceptual comparison is provided in the insert Conditions of Optimality. An EDHEC-Risk Institute Publication 39

40 2. Background Conditions of Optimality In the past few years, the evidence from both empirical and theoretical analysis have shown that market-cap indices are perhaps neither the best tool to obtain representativity nor to obtain efficiency. The increasing criticism on cap-weighted indices has stimulated the emergence of alternative weighted indices. There are various equity index series which claim to be more efficient than market cap weighting. However, in addition to strong track records, investors may want to focus on the conceptual assumptions underpinning these efforts. The idea is simple. The performance of backtested index track records, by default, should be attractive, but the different assumptions that reside within the indices may make a difference. In this insert, we aim to provide some conceptual guidance to reposition the emerging offers within the context of portfolio theory, so as to assess the underlying conditions of the optimal set-up for each alternative approach. According to modern portfolio theory, the only optimal portfolio is the tangency portfolio, i.e. the spot on the efficient frontier which provides the highest Sharpe ratio. One can show that various weighting schemes can be seen as coinciding with the tangency portfolio under a set of assumptions on expected returns, correlations and volatilities in the constituent universe. Then, one way of looking at these weighting schemes is to analyse under which assumptions they would be optimal. More representative approaches A market cap weighted scheme is the obvious default option when it comes to representing a given segment of the market. However, it may not provide a fair representation of the underlying economic fundamentals. Arnott, Hsu, and Moore (2005) introduce fundamentally weighted indices, which weight firms by their characteristics, such as dividends and book values to address this issue. In this way, such indices could provide a better representation of the economy than cap-weighted indices. This different measure of firm size may be more reliable than market captalisation but the risk/reward optimality of such indices is not explicitly sought as an objective in the construction process. In fact, this type of approach which is based on a weighting of stocks by fundamental criteria does not take the relationship between different stocks into account at all. It resembles systematic stock picking approaches which look at stocks in isolation rather than as a portfolio construction method whose fundamental principle since the work of Markowitz (1952) is to recognise the importance of taking not only the stand alone risk properties of stocks into account, but also the joint risk when combining stocks into a portfolio. Such indices would be optimal in the mean variance sense if for example risk parameters are identical across stocks and expected returns are proportional to the particular mix of fundamental variables used for the weighting. 40 An EDHEC-Risk Institute Publication

41 2. Background More diversified approaches The more diversified approaches are designed to achieve a fair risk/reward ratio. As indices are often used as investment benchmarks, from investors perspectives, a benchmark should represent the fair reward expected in exchange for risk exposure that an investor is willing to accept. Hence, the focus should be not on representativity but on achieving the highest possible risk/reward ratio. There are two ways to achieve this objective: ad-hoc approaches and scientific approaches. We now assess the conditions of optimality It should be noted however, that de-concentration approaches, as well as fundamentalsbased approaches can be shown to correspond to optimal portfolios in the sense of Modern Portfolio Theory if we make specific assumption son risk and return parameters. For example, it can be shown that fundamentals-weighted portfolios would be optimal if risk parameters were identical across stocks and expected returns are proportional to the firm attributes used in the weighting scheme. Likewise, equal-weighting can be shown to lead to optimal portfolios in the mean variance sense if all risk and return parameters are identical across stocks. Equal-risk contribution would lead to optimal portfolios when assuming identical correlations and Sharpe ratios, while maximally diversified portfolios require the assumption of identical Sharpe ratios across stocks. See Martellini (2011) for a discussion of these results The diversification ratio is known as the ratio between portfolio volatility and individual components volatility. Ad-hoc approach The ad-hoc approaches to achieve efficient investment benchmarks are through simple de-concentration strategies since cap-weighted indices are particularly inefficient in terms of concentration in a small number of stocks (Tabner 2007 and Malevergne et al. 2009). These strategies are usually not grounded in portfolio theory. In particular, they do not explicitly aim to construct a portfolio which lies on the efficient frontier. 13 For instance, the equal-weighting scheme is the most naïve approach, which recommends giving an equal weight to each index constituents. It s simple but extreme since equally weighting all constituents is optimal if and only if pair-wise correlations, volatilities and expected returns were identical for all stocks. Another approach which aims to build better diversified portfolios, is the equal-risk contribution approach, which ensures each constituent contributes the same amount of risk based on the formula shown below (Qian 2005; Maillard et al. 2010). Such indices are optimal if and only if all Sharpe ratios and all pair-wise correlations are identical for all pairs of stocks. Choueifaty and Coignard (2008) adopt the measure of diversification ratio 14 in a portfolio optimisation context and introduce the Maximum Diversification (also known as anti-benchmark) aiming at generating portfolios with the highest possible diversification index. Compared to the equal-weighting scheme and the equal-risk contribution approach, Maximum Diversification takes into accountpair-wise correlations. This is because the diversification index can be seen as the inverse of a concentration measure where the concentration measure takes into account the correlations between stocks. While achieving an optimal risk-reward ratio is not the explicit focus of this approach, it follows that maximum diversification portfolios would actually coincide with the maximum Sharpe ratio portfolio if all Sharpe ratios were identical for all stocks. An EDHEC-Risk Institute Publication 41

42 2. Background Scientific approach to diversification Beyond these approaches, which can be understood in the framework of modern portfolio theory but are not explicitly based on this framework, there are other approaches which are directly based on portfolio construction techniques referring to Markowitz s Modern Portfolio Theory (1959). In the absence of a risk free asset, the efficient frontier represents all the possible combinations of risky assets which deliver the best possible expected return for a given level of risk. The Global Minimum Variance (GMV) portfolio could provide the lowest possible portfolio volatility. In the presence of riskless asset, the tangency portfolio at the intersection of the capital market line and the efficient frontier would provide the highest reward per unit of portfolio volatility this is the Maximum Sharpe Ratio (MSR) portfolio. The GMV portfolio is an initial approach to build systematically rather than naively diversified portfolios. The optimisation inputs are only volatilities and correlations. The two challenges one may wish to address are the curse of dimensionality (there will be a high number of correlation parameters which grow exponentially with the number of assets included in the portfolio), and the fact that risk parameters are unlikely to be constant over time. A rich literature on statistical models exist that are suitable to address these two challenges, using factor models to reduce dimensionality and using dynamic models such as GARCH models to model time variations in risk parameters. Though the GMV portfolio would provide a low volatility portfolio, it is only optimal when assuming identical expected returns. On the other hand, the efficient-weighted indices explicitly aim to achieve the maximum Sharpe ratio portfolio by estimating both expected returns and volatilities. This approach focuses directly on the optimisation of risk/reward ratio. It uses suitably designed factor models to estimate the variance-covariance matrix just like in the GMV approach. However, while the optimality of the GMV approach relies on the assumption that all stocks have the same expected returns, the efficient index approach assumes that expected returns between stocks are different, and positively related to risk. In fact, expected returns are estimated by a stock s riskiness using the basic assumption that in the long term one can expect a risk-return trade-off in the stock market. In summary, we have explored the underlying conditions to the optimal set-up for each alternative approach. An important question is whether each set of assumptions is sufficiently moderate to allow for robustness and whether it is realistic enough to be reasonable. Different investors will inevitably come to different conclusions but it is always a useful exercise to clearly state the underlying assumptions Styles vs. Sectors vs. Countries Other than broad market indices, which represent overall market movements, country indices, sector indices, or style indices (small cap or large cap and value or growth) are developed for various 42 An EDHEC-Risk Institute Publication

43 2. Background 15 - Dynamic equicorrelation (DECO) model (Engle and Kelly 2008), dynamic conditional correlation (DCC) model (Engle 2002) and scalar BEKK model (Engle and Kroner 1995) purposes of risk exposures. In the literature, Fama and French (1993) argue that firm size (large cap, small cap) and style (growth, value) are the most important determinants for the crosssectional variation in expected stock returns. So style indices could be used to gain exposures in these particular fields. Sector indices are designed to reflect the expected returns in a specific sector. The motivation for relying on sector exposure to construct an equity portfolio is provided in a study by Ibbotson Associates (2002) that highlights the low correlation of different sectors and the low correlation of sectors and the market. The attractive diversification benefits have also been observed across countries (DeSantis and Gerard 1997). Country indices could be useful for the investor seeking international diversification by exploiting the correlation properties across countries. The various factors lead to an interesting question: which factor is more important? The literature survey has shown that there is a growing influence of sector factors (Hamelink et al. 2001, Ferreira 2006, Eiling et al. 2009). Even though the decreasing effects of country factors has been demonstrated, due to the increasing integration of financial markets, there is no clear evidence that sector factors dominate country factors (Hamelink et al and Ferreira 2006). At the same time, style factors are also important. Vardharaj and Fabozzi (2007) also show that sector and style factors are playing a large role in the explanation of US stock portfolios. As for the diminished influence of country factors, there is a vast amount of results in papers published over the last ten years or so. In the early papers, Errunza et al. (1999) use monthly data from 1976 to 1993 for seven developed counties and nine emerging markets and conclude that diversification across countries has been diminished as a result of increased investing across barriers. Similarly, Bakaert and Harvey (2000) find increasing correlations across countries in the period of study. Recently, Christoffersen et al. (2010) adopt more comprehensive and flexible models dynamic correlation models 15 and analyse the evolution of correlations across developed markets (DMs) and across emerging markets (EMs). They conclude based on the consistent results obtained by three models that the correlations have significantly trended upward for both DMs and EMs from 1973 to Nevertheless, the diversification benefits for the EM case are still strong. Against the backdrop of the research and discussions on which equity categorisations are the most useful in order to create the basic building blocks for portfolio construction, an interesting question for our survey is which of these categories are actually important when investors choose equity sub-indices. In particular, we will assess whether such subcategories play an important role compared to broad regional or worldwide market indices and we will also be able to compare which type of categorisations investors prefer when choosing equity indices. An EDHEC-Risk Institute Publication 43

44 2. Background 16 - The examples of factorbased indices are MSCI Barra Factor Index and Russell Axioma Factor Indexes. Factor based equity indices There has been research analysing the common return drivers within broad equity universes for quite some time. Chen, Roll and Ross (1986) and Fama and French (1993) find that asset returns could be attributed to a few underlying explicit factors such as macroeconomic factors or firm attributes / style factors. These factors represent sources of systematic risk and return. The currently available sector indices or style indices are constructed by the selection of stocks following certain criteria, for instance, industry classification of a stock, or defining criteria for growth and value such as price-to-book ratios of a stock. These dimensions are the ones that have been traditionally used by equity analysts and investment managers. More recently, index providers have started designing indices that reflect not the traditional categories, but rather the factors that have been put forward in empirical finance research as being the most relevant common return drivers. In particular, it has been proposed to achieve a high level of exposure to a particular factor, such as size, value, momentum, volatility, etc., while at the same time, very low exposure to all other factors, through factor-based indices. 16 These indices thus aim at providing relatively precisely defined exposure to factors that may explain differences in stock returns. A frequently cited motivation for such factor-based portfolios is that excess returns of actively managed portfolios often can be linked, to a large degree, to exposure to such factors. For instance, by analysing the active management fund performance, Ang et al. (2009) find that even for active returns, a significant part is linked to the systematic factors. Hence, they suggest embedding the concepts of factor models to the benchmark construction. In such way, it is easy to identify the source of return and the exposure to risk. Moreover, recently, Melas et al. (2010) present alternative methods to construct factor index tracking portfolios. Such factor-based indices could provide investors with clearly defined exposures (since the exposure to other factors is very low but not zero). Therefore they may offer the ease to identify the source of risk and prevent the exposure to unexpected risk. Nevertheless, there is also an open question toward the ways to use these indices. In particular, if investors want to make choices of allocation across different equity factor indices, investors require a view on the risk premium for each factor, which is difficult to estimate. Perhaps, more fundamentally, the usual factor indices correspond to standard factors found to matter in the cross section of stock returns. However, most of these factors are purely empirical in nature they do not necessarily have an economic explanation. For example, Liew and Vassalou (2000) have shown that unlike some factors which can be understood as predictors of economic growth, the momentum factor, whose importance is strongly confirmed in many data sets, cannot be linked to such an economic explanation of its importance. This implies that momentum may not be related to such intuitive economic risk factors. In addition, there is often a criticism that such factors may have come up as a result of data 44 An EDHEC-Risk Institute Publication

45 2. Background mining. For instance, Black (1993a, 1993b) argues that Fama/French results were likely an example of data mining. Since there are many studies published before on the possible explanatory variables for stock returns, Fama and French chose three of them which have the highest explanatory power. Cochrane (2001) has pointed out that most empirical studies fish for factors, but such factors are not necessarily backed by sound economic theory. Thus, while factor-based indices may be an alternative to implement factor tilts through active managers, there are some questions with respect to how they should best be used in practice, as estimation of factor risk premia and economic interpretations of such factors are difficult questions. To summarise, we have seen the criticisms on current equity index construction. We have also reviewed the alternatives that have been introduced to address these criticisms. Now we shall turn to the discussion on fixed-income indices to understand the different issues involved in another asset class Fixed-Income indices Fixed-income indices both government and corporate bond indices are built to reflect market movements in their respective universe. Similar to stock market indices, the bond indices include many sub-segment indices other than the broad market indices. For example, maturitysegment indices and credit-rating-segment indices are the two important components of bond indices. Since they define the bond universe according to bonds maturity and credit rating, they try to represent certain interest rate risk and credit risk segments. In addition, there are indices for inflation linked bonds. The variety of indices available nowadays reflects the fact that bond indices can have similar to stock market indices many different purposes. However historically, the development of fixed-income indices started a bit later than equity indices. Although the pure price indices, which measure the average yield of bonds but not the interest (coupons) paid on them, have been developed for the bond market since 1926, the investable indices total rate-of-return bond indices were not developed until in the 1970s (Reilly et al. 1992). Salomon Brothers introduced its Long-Term High-Grade Corporate Bond Index in 1973, at the same time that Kuhn, Loeb (ultimately acquired by Lehman Brothers) set up three U.S. bond indexes (Flagel and Wardley 2009). These indices were available on a monthly basis. Daily total return indices were only created at the end of the 1980s. Merrill Lynch started the first daily corporate bond index in late 1986 followed by Lehman Brothers in 1989 (Reilly et al. 1992). The late development may have been due to the difficulties of constructing a bond index. Unlike equities, which usually consist of a single issue per company in an exchange, bonds with different characteristics in terms of maturity and credit risk are issued by a single company (or government). Due to these essential differences between equities An EDHEC-Risk Institute Publication 45

46 2. Background 17 - A sinking fund is a pool of money set aside by a corporation to help repay a bond issue. Similar to callable bonds, the repurchase of the bond issues usually happens when the interest rate is low (bond price is high). The sinking fund provision makes bond issues more difficult to price due to the possibility of repurchasing and bonds, questions such as how a bond index should be built, what should be its objectives, for whom a particular bond index would be suitable, are usually discussed in literature. Hence, in the following two sections, we explain the challenges to construct bond indices as well as to invest in bond indices. The first part is from the index provider s perspective which mainly concerns the difficulties of constructing a bond index and accessing reliable data as an input for index construction. The second part refers to challenges for potential investors of bond indices. The issues faced by investors are not so much with problems of running a bond index, but rather with the more fundamental question of whether the commonly available bond indices are appropriate as investment benchmarks for their fixed income portfolios. Challenges to construct bond indices There are two main reasons for difficulties with bond index construction (Benning, 2005). Firstly, the structure of bonds is comparatively more heterogeneous as compared to equities. There are different terms to maturity, credit ratings and provisions in a bond index. Secondly, unlike equities, bonds are usually traded over-thecounter (OTC), and information is limited to transaction parties. This institutional feature of the bond market renders it relatively opaque, leading to difficulties in data collection for their volume and prices. It is useful to list the most salient challenges in bond index construction and to explain them in detail, which we will now turn to. A. Heterogeneous rules to define constituents As Reilly and Wright (1996) point out, the universe of bonds is much more diversified than those of stocks. Bonds differ in maturity, rating, industries, and coupon payment scheme. Consequently, the index classification, i.e., sorting the bonds into clear defined segments is more challenging than setting up stock index criteria. As a result many bond index providers offer a considerable variety of sub indices, which can be aggregated into broader indices. Furthermore, index providers incorporate different rules to select bonds. Firstly, providers may employ different rules on including bonds with certain technical/ contractual features such as callable, sinking funds and etc, For instance, Dow Jones Corporate Bond index excludes sinking funds 17 while Barclay Corporate Bond index includes them. FTSE Global Government Bond Index excludes all callable and convertible bonds from the defined bond universe, whereas, Citigroup World Government Bond Index can encompass callable bonds for some countries. Secondly, providers may choose which issuers should be included. Such discrepancy in defining the investment universe could lead to further heterogeneity of bond indices. Jelic et al. (2011) study the Euro zone sovereign debt index ETFs and find that selection rules can result in significantly different performance of two similarly structured indices. In particular, funds with riskier issuers exhibit different performance in comparison with funds that exclude those issuers, in the situation of divergent yield trends across constituents. Overall, heterogeneous selection of index constituents, whether the differences are 46 An EDHEC-Risk Institute Publication

47 2. Background based on selection rules for issuers or selection rules for types of securities, can be expected to lead to differences in risk and return properties as well. B. Pricing difficulties In most bond markets the largest portion of trading activity takes place over-thecounter (OTC) and not on exchanges (Jankowitsch et al. 2002). Naturally, in contrast to exchanges, in the OTC market prices are not directly observable because they are provided by dealers for all kinds of bonds. They can be either estimates provided by the dealers or they can reflect their last transaction price. For illiquid bonds, such as off-the-run government bonds and corporate bonds, this problem is critical as they are not likely to be reliable. In addition, pricing a non-callable bond is to discount cash flows by current term structure of interest rate to obtain the present value of future cash flows. However, in practice, price discrepancies exist when discounting cash flows by estimated spot rates (Elton and Green 1998). Several scholars have demonstrated that liquidity issues have contributed to such discrepancies (Amihud and Mendelson 1991; Warga 1992; Strebulaev 2001). To address this problem, financial institutions resort to matrix pricing models. A matrix pricing model obtains theoretical prices through bond pricing models. One way to price bonds is by using the discount rate based on the appropriately estimated yield curve. Although such methods encompass the entire bond universe, they fail to recognise idiosyncratic risk components. Moreover, there is no common census on the best practice for matrix pricing models and it is subject to discretion by index providers. C. Debt-weighting & measuring outstanding debts Similar to equity indices, it is also controversial whether bond indices should be weighted by outstanding debts (market value of the bond), or whether alternative weighting schemes should be used. In the literature, people have argued that weighting by outstanding debts is the only way to reflect the overall market movement (Brown 2002) and investors could be sure to hold the same portfolio (Siegel et al. 2003). However, from the perspective of maintaining and calculating a bond index, there are many challenges associated with a debt-weighted index construction. For instance, the amount of outstanding debt changes over time, and such information is not always made public. Therefore, the calculation of outstanding market value of debt can be difficult. Challenges to invest in bond indices After discussion about the challenges faced by index providers, we turn to explain the challenges for potential index users. A. Suitability As mentioned previously, there are lots of sub-segment bond indices built for different purposes. This facilitates investors with different objectives to invest in appropriate bond indices. Instead of seeking performance like equity investors, bond investors often use bonds to hedge risk exposures (interest risk, credit risk or inflation risk) or to hedge future liabilities. Hence, benchmarks must be selected appropriately - a bond index An EDHEC-Risk Institute Publication 47

48 2. Background 18 - Assume the yield curve is flat and the current interest rate is 4%, there is a bond index containing two pure discount bonds, one with face value of 200 and priced at 192 matures in one year, and the other one with face value of 100 and priced at 68 matures in ten years. The index is weighted by the market prices of the bonds. The corresponding weights to these two bonds should be 74% to the one-year bond and 26% to the ten-year bond. The duration of the bond index should be weighted average of the constituents: 0.74x1+0.26x10=3.34. Immediately after the rebalancing, if the interest rate reduces to 3%, the current price of the two bonds would be 194 and 74 and the current weight of the two bonds change to 72% and 28% respectively. Hence, the index duration becomes: 0.72x1+0.28x10=3.52, which increases due to the decrease of the interest rate. This fluctuation of duration due to the movement of the interest rate could be generalised as follows: if interest rates go up, the present value of ten-year bond decreases more comparatively with one-year bond, which leads to an increase weight in the shortterm bond and thus pushing duration down. The opposite effect happens when interest rates go down. should reflect not only the investable universe of the portfolio manager but also their investment purpose. One-size-fits-all is no longer suitable for bond investing. A typical broad index is unlikely to be the optimal benchmark for any investor and even if so, this would be only by chance, as Brown (2002) highlights. B. Duration problems In addition, Siegel (2003) raises another issue the problem of duration which is more severe for corporate bond investors. Since a corporation issues bonds according to its optimal financing plan, the horizon of bonds is usually not equal to the investors investment horizon. In fact, the duration structure of outstanding bonds reflects the preferences of the issuers in order to minimize the cost of capital. This minimization has no reason, a priori, to follow the investors interests, which usually try to match investors risk exposures. In another word, the duration of these indices is a result of choices made by the sell-side of corporate bonds, and it would be a pure coincidence that this average duration sought by issuers would correspond to the required duration of every bond investor. Given an objective for duration, for example, an investor would have little use for a broad bond index. Whenever a bond retires and a new bond is added, the assumption that newly issued bonds replace the retired bonds in a consistent manner is historically challenged. Take for example the case of the US government debt market where the 30-year Treasury bond was suspended in October 31, 2001, only to be reintroduced four and a half years later in February 2006 (Mizrach and Neely 2006). Frequent changes in the investment universe are not only a mere data problem for the index provider, but involve deeper conceptual issues for bond investors. The change of individual bonds directly affects overall index characteristics, for instance, the duration does not stay the same. Benning (2006) illustrates this effect using the simple example of a debt that is rolled-over at maturity by selling new bonds. Once old bonds are substituted by new ones in the index, we have the following relationship: the lesser the amount of other bonds still outstanding bonds in this specific bond segment, the more the index composition and characteristics change radically just overnight. Even if the investment universe is kept unchanged, the average duration of the bonds decreases over time as the bonds age. Likewise, interest rate changes will change the duration of a bond index even if its constitution does not change. 18 Taken together, even if investors are able to find an appropriate benchmark at a specific point in time, this index is not likely to remain appropriate for long, as Benning (2006) states, bond indices are moving targets. C. Credit risk problem Credit risk was initially a problem only associated with corporate bonds, as investors were not often dealing with creditable corporate bond issuers, and treasury bonds were always treated as free of credit risk. However, the recent European Sovereign Debt Crisis raises the challenge to the creditability of sovereign bond issuers. Investors have now become more prudential in terms of choosing securities when investing in bonds. Creditrating segment indices may be a good 48 An EDHEC-Risk Institute Publication

49 2. Background instrument for investors with different risk appetite. Nevertheless, even within a given credit-rating segment index, the credit risk exposure may change over time. As discussed previously, the index duration and credit risks could be affected by a change of index universe or by bonds aging. Evidence of changing duration and credit risk Campani and Goltz (2011) have studied the stability of index characteristics, i.e. duration and credit risk, for corporate bond indices both in the US and in Europe. Figure 3a shows the evolution of durations over time on four corporate bond indices in the US, within the period from 1st January 1997 to 31st December Out of these four indices, Dow Jones Corporate Bond Index is equally weighted with 96 issues and the rest are debt-weighted with no restrictions on the number of bonds (usually more than 3000 bonds in each index). Obviously, the durations of two kinds of indices are following different paths which are both volatile. In particular, Dow Jones has a spike in duration which goes up to 8 from 7 around the year of Similar results are found for European indices (see figure 3b). The durations of four debt-weighted corporate bond indices in Europe are not stable. For example, the variation of the duration for iboxx Liquid, which contains only 40 bonds, could go up as high as 7.5 around 2000 and drop down to 3.5 at the end of the sample period. The other three indices, though including more than a thousand bonds, have unstable durations as well. This is clearly not what one would understand to be a passive choice in terms of risk exposures. Take an example of a pension fund, which may have the objective to immunize its liabilities by matching its duration to that of its assets. In this case, unwanted risk exposure in interest rate will have critical impact on their portfolios. Figure 3a Comparison of durations of four corporate bond indices in the US over time An EDHEC-Risk Institute Publication 49

50 2. Background Figure 3b Comparison of durations of four corporate bond indices in Europe over time 19 - Campani and Goltz (2011) follow the same approach as in Ferreira and Gama (2007), in which they map the rating into numerical measures by a linear transformation to a scale from 0 (the lowest rating, D) to 20 (the highest rating, AAA). Campani and Goltz (2011) compute the average credit risk exposure of AAA, AA, A and BBB rating classes for each index, which is basically the cap-weighted average of the class values. This unstable risk exposure does not only happen in terms of duration. Campani and Goltz (2011) have studied the indices average credit risk for three debt-weighted investment grade corporate bond indices in the US and four in Europe from 18th August 2000 until 31st December They use the approach of Ferreira and Gama (2007) 19 to transform credit rating categories into a quantitative variable. The results are shown in Figure 4. Again, the credit risk exposure is not stable the average credit riskiness of the three bond indices in the US are between 14 to 15 which corresponds to an average rating of A3 and A2 respectively from 2000 to Strikingly, the average credit risk of bond indices in Europe is even more volatile, for instance, iboxx presented an average index rating ranging from 14.5 up to almost 18 which corresponds to A3 and AA2 over the sample period. The fluctuations seem not necessarily very large but it should be noted that these are investment grade indices that only include rating classes from AAA to BBB. In other words, the fluctuation is bounded by the extremes (i.e. there is low probability to default for investment grade bonds). Still, the dynamic behavior reveals that investors who take implicit decisions on the credit risk may experience unexpected shifts of exposure within the investment grade universe by simply investing in default bond indices. Figure 4 Comparison of credit risk of corporate bond indices both in the US (left) and in Europe (right) over time To summarise, Campani and Goltz (2011) have shown that the current corporate bond indices do not offer stable risk exposures. For investors who have hedging objectives, such as matching durations and credit exposures, these variations may lead to unwanted risk exposures. 50 An EDHEC-Risk Institute Publication