Frequently Asked Questions on the EDHEC-Risk Efficient Index Methodology
- What is wrong with cap-weighted indices?
- What is the focus of the efficient index methodology?
- How are risk parameters obtained?
- How are return parameters obtained?
- What are the main insights from the academic literature regarding the risk-return relationship?
- Are there any studies that argue against a positive relation between risk and return?
- Is the performance of efficient indices explained by the presence of tilts to risk factors such as value, size, momentum or credit?
- Do efficient indices have sector tilts?
- What is the turnover in the index?
- Would capacity become a problem if the efficient index were to be tracked by a large amount of assets?
- How does your method compare to Fundamental Indexation?
- How does your method compare to equal-weighted indices?
- How does your method compare to the minimum variance approach?
- How transparent is your methodology?
- What is the difference between an efficient index and an active fund that also seeks to outperform a cap-weighted reference in terms of risk-adjusted performance?
- What are the expected uses of the efficient indices?
- Which indices are available?
- What is wrong with cap-weighted indices?
- What is the focus of the efficient index methodology?
- How are risk parameters obtained?
- How are return parameters obtained?
- What are the main insights from the academic literature regarding the risk-return relationship?
- Are there any studies that argue against a positive relation between risk and return?
- Ang, Hodrick, Xing and Zhang (2006, AHXZ henceforth) find that high idiosyncratic volatility stocks actually yield low expected returns. It should however be noted that AHXZ analyse a very specific short term effect linked to a particular and model-dependent type of risk measure, a stock’s past month’s idiosyncratic volatility after regressing its returns on equity risk factors. Even when using this risk measure, many authors question the robustness of these results. Among other concerns, the findings are not robust to changing the data frequency, portfolio formation, screening out illiquid stocks (Bali and Cakici 2008), or adjusting for short-term return reversals (Huang et al 2010). Other authors have changed the short term measure of volatility in AHXZ with measures obtained over longer horizons and then find a positive relation (Fu 2009, Spiegel and Wang 2006, Brockmann and Schutte 2007, and Eiling 2006).
- It has been shown that low idiosyncratic volatility stocks are actually more risky in terms of their skewness (Boyer, Mitton and Vorking 2010, Chen, Hong and Stein 2001) or their exposure to shocks in aggregate market volatility (Barinov 2010).
- Is the performance of efficient indices explained by the presence of tilts to risk factors such as value, size, momentum or credit?
- Do efficient indices have sector tilts?
- What is the turnover in the index?
- Would capacity become a problem if the efficient index were to be tracked by a large amount of assets?
- How does your method compare to Fundamental Indexation?
- How does your method compare to equal-weighted indices?
- How does your method compare to the minimum variance approach?
- How transparent is your methodology?
- What is the difference between an efficient index and an active fund that also seeks to outperform a cap-weighted reference in terms of risk-adjusted performance?
- What are the expected uses of the efficient indices?
- Which indices are available?
Market cap-weighted indices are not good choices as investment benchmarks because they are poorly diversified portfolios. In fact, cap-weighting tends to lead to exceedingly high concentration in relatively few stocks. As a consequence of their lack of diversification, cap-weighted indices have empirically been found to be severely inefficient portfolios, which do not provide investors with the fair reward given the risk taken.
For further details, please refer to the following publications:
• "Does Finance Theory Make the Case for Cap-weighted Equity Indices"
The focus of the efficient index methodology is to maximize the index reward-to-risk ratio based on careful estimates for risk expected return parameters. In other words, the focus is on weighting stocks as a function of their contribution to a high Sharpe ratio, as opposed to their market cap.
For further details, please refer to the following publication:
• "Efficient Indexation: An Alternative to Cap-Weighted Indices"
The key problem in covariance matrix estimation is the curse of dimensionality; when a large number of stocks is considered, the number of parameters to estimate grows exponentially. Sophisticated statistical techniques have been developed in academic research, which can be used to address the curse of dimensionality and generate robust risk estimates. In particular, we use an implicit factor model, which has been shown to allow for a substantial reduction of sample risk (because co-movements between stock returns are indirectly estimated as a function of the co-movement between stock returns and a parsimonious set of common risk factors) without the introduction of a large amount of model risk (because the factors are not imposed a priori but extracted from the stock return time-series from a Principal Component Analysis).
For further details, please refer to the following publication:
• "Efficient Indexation: An Alternative to Cap-Weighted Indices"
While statistical techniques are useful for estimating risk, statistics do not allow us to estimate expected returns reliably. In fact, direct estimation of expected returns from past returns is close to useless (Merton 1980). One answer to this challenge is to refrain from using expected return estimation by using a minimum variance approach. The minimum variance portfolio is however only optimal in terms of risk-reward ratio if the expected returns of all stocks are identical, which is a highly unrealistic assumption.
Efficient Indexation relaxes the unrealistic assumption of identical expected returns and recognises that expected returns can differ across stocks. Differences in expected returns are derived from differences in risk. This is based on the common sense notion of a risk-return trade-off. Recognising that expected returns are hard to estimate, we nevertheless use this relation between risk and return parsimoniously. We use a model-free measure of total downside risk (a stock’s semideviation) to rank stocks into groups with higher or lower expected returns. The grouping avoids attributing expected returns to each individual stock, which may be subject to estimation error.
The indirect estimation of expected returns through the riskiness of stocks also has the effect of penalizing low risk stocks through low expected return inputs and avoids concentration in low risk stocks. Independent of the existence of a risk-return trade-off, avoiding such concentration allows improved diversification compared to a Minimum Variance approach and puts the focus of Efficient Indices on exploiting correlation effects.
For further details, please refer to the following publication:
• "Efficient Indexation: An Alternative to Cap-Weighted Indices"
While it is possible to rely on statistics to extract meaningful factor models for covariance estimation, statistics are close to useless in estimating expected returns, as explained in Merton (1980). On the other hand, a vast academic literature has confirmed the intuition that there exists a positive relationship between risk and return (i.e., investors expect an additional return for taking on more risk), which therefore suggests that one may use a risk indicator as a proxy for the expected return in excess of the risk-free rate. The first risk indicator that has been argued to be a reasonable proxy for excess expected return is the beta, as indicated by William Sharpe's celebrated Capital Asset Pricing Model (CAPM). The existence of a linear expected return/beta pricing relationship was eventually extended to the multi-factor setting by Steve Ross' Arbitrage Pricing Theory (APT). Subsequently, it has been recognized that not only systematic risk is rewarded, but specific risk should also earn a premium in real-world market conditions where investors are holding with imperfectly diversified portfolios. Finally, more recent academic research has confirmed investors’ concern over downside risk, as opposed to average risk as measured by volatility. Building on these academic insights, and recognising the difficulty of using sample-based expected return estimates in portfolio optimisation, we use a robust downside risk estimate as a proxy for excess expected return in our Sharpe ratio maximization procedure.
For further details, please refer to the following publication:
• "Efficient Indexation: An Alternative to Cap-Weighted Indices"
It is sometimes argued that low volatility stocks actually yield higher expected returns. From a common sense perspective, this is counterintuitive as it violates one of the principles in modern financial theory, that there is a trade-off between being rewarded in terms of high expected return and taking on risk. From an empiricist’s perspective, there exists evidence of a negative relation between volatility and expected returns, but this finding does not hold up to close scrutiny1. From a risk measurement perspective, it is important to underline that low volatility does not mean low risk, as other risk dimensions would need to be taken into account as well2.
For further details, please refer to the following publication:
• "Is There a Risk/Return Tradeoff across Stocks? An Answer from a Long-Horizon Perspective"
By construction, our methodology, solely based on maximizing the risk-return trade-off, is not expected to lead to specific style exposures. In particular, the approach does not consider any information on valuation ratios, and thus cannot explicitly favour either value or growth stocks. This stands in contrast with the well-documented value bias that accounting-based indices have by construction, because their weights depend on accounting characteristics such as a measure of firm size. The efficient index construction methodology also excludes any exposure to small caps, as the universe we have used to apply the weighting scheme does not contain any small cap stocks.
Regression results for value and small cap exposures will however also be influenced by the definition of the factors. A cap-weighted market factor will have most of its weights in growth stocks, so the regression results will show a value exposure even for an equal-weighted index. This is in spite of the fact that any reasonable definition of style or factor neutrality would lead to the conclusion that equal weighting should be free of a value or growth bias. In fact, since no information whatsoever on valuation enters the determination of weights in an equal-weighted index, it is difficult to imagine that such an index would imply any choices in terms of value or growth exposure. That an equal-weighted index shows a value bias with respect to the cap-weighted index indicates only the relativity of the reference point, and one could actually argue that the cap-weighted index has a growth bias relative to the equal-weighted reference.
The table below confirms that relative to equal-weighted indices as a neutral reference, the efficient index has quite a neutral exposure to the value factor. Small cap exposure is also not much different from the neutral equal-weighted reference. Also, when adding credit risk to the usual equity risk factors, we do not find any significant exposure of efficient indices to this factor. Note that if one were to use an equal-weighted index that included a broad set of stocks covering all ranges of market capitalisation, one would ascertain a small-cap bias, as most of the stocks traded on exchanges are small- or even micro-cap stocks. However, the equal-weighted index used here is composed of S&P 500 constituents, i.e., large-cap stocks, so in terms of its actual holdings it cannot have a small cap bias.
Using the typical risk factors, we have also found that only about 50 percent of the excess returns of Efficient Indexation over either cap-weighted or equal-weighted indices can be explained by standard factors which shows that these factors do not suffice to fully capture the return properties of the efficient index portfolio. This arises because the methodology used for the efficient index takes into consideration the correlation structure present among its constituents which cannot be captured by mere static exposure to these factors. Secondly, the efficient weighting method is applied to individual securities rather than to preconstructed factor portfolios so that the efficient weights can be chosen with much greater flexibility compared to an allocation across factor portfolios.
For further details, please refer to the following publications:
• "Improved Beta? A Comparison of Index Weighting Methods", Journal of Indexes, January/February 2011
Efficient indices do not lead to sector biases, which distinguishes them for cap-weighted indices that tend to overweight particularly popular sectors at some points in time (e.g., tech bubble in the late 1990s). The efficient index has more stable sector weights than the cap-weighted index as its focus on long term risk/reward efficiency means that the index stays clear off bets on specific sectors. In fact, our research shows that the main driver of efficient index performance is better use of the diversification potential across stocks. More than 90% of long term outperformance over cap-weighting can be attributed to stock weighting while less than 10% can be attributed to sector allocation effects.
For further details, please refer to the following publications:
• "Improved Beta? A Comparison of Index Weighting Methods", Journal of Indexes, January/February 2011
The index series is rebalanced quarterly in accordance with the review of the underlying FTSE All World Index Series. The turnover incurred by updating the weights through quarterly portfolio optimisation is reduced by applying a rebalancing threshold. Rebalancing will only be carried out if the weights deviate significantly from the revised optimal weights. Such an approach leads to a significant reduction in turnover while maintaining the improved risk/reward efficiency of the index series. This is consistent with insights from control techniques (El Bied, Martellini, and Priaulet 2002; Leland 1999) applied to portfolio optimisation to lower transaction costs. In short, only if a significant amount of new information has appeared since the previous rebalancing will the weights be updated. Applying turnover control leads to turnovers below 30% in the efficient indices.
The constituents of the FTSE EDHEC-Risk Efficient Indices are mid and large caps that have already been filtered by FTSE so as to ensure a minimum liquidity level.
We also use liquidity rules in the production of these indices. We cap each stock’s weight at a maximum multiple of its capitalisation weight and we also cap changes in weights at each rebalancing date. While the overall impact on weights and risk-adjusted performance of these rules is small, they help to avoid large initial weightings or large rebalancings in the smallest stocks and thus improve liquidity of the indices.
The objective of fundamental indices is to improve the representativity of the index compared to cap-weighting, by using an accounting-based measure such as the book value of a firm as a weighting factor to represent its economic footprint. The idea behind this approach is that measures such as book value are a better indicator of the size of the company than its market cap.
Our method is different because it focuses on improving the efficiency, arguably the main concern from an investor’s perspective, as opposed to the representativity, of the index. Rather than using accounting-based information, our weights are derived from risk/return information and a stock weight will depend on its expected return, volatility and correlations with all other stocks.
While accounting-based indices do not explicitly aim at providing optimal risk/reward properties, it can be shown that accounting-based indices would be optimal in terms of risk/reward if the following assumption holds: all risk parameters across stocks are identical and expected returns of a stock are proportional to the accounting measure at hand (e.g. book value).
Equal-weighting is a naïve, as opposed to a scientific, approach to portfolio diversification. Equal weighting would be the weighting scheme that leads to the highest possible Sharpe ratio if all expected returns of stocks, all volatilities and all pairwise correlations between stocks were identical. If investors believe that some meaningful information can be obtained about differences in risk and return across securities, then they should prefer efficient indices based on such information. Empirically, efficient indexation achieves similar (but slightly higher) returns than equal weighting but considerably lowers volatility compared to equal-weighting. This is not surprising as equal-weighted indices make a very unrealistic implicit assumption about correlation and volatility (as it assumes these parameters are equal for all stocks). The efficient index approach, by relaxing these assumptions and bringing in information on differences in correlations and volatility across stocks, typically achieves lower volatility.
For further details, please refer to the following publications:
• "Efficient Indexation: An Alternative to Cap-Weighted Indices"
• "Improved Beta? A Comparison of Index Weighting Methods", Journal of Indexes, January/February 2011
The minimum variance approach is based on the efficient frontier of Modern Portfolio Theory (MPT). Minimum variance portfolio construction also allows using the advances of decades of academic research that has provided methods to improve the estimation of the covariance matrix of stock returns.
Efficient Indexation goes beyond minimum variance to improve portfolio diversification. Improving diversification is important because, when not penalising low volatility stocks, minimum variance portfolios produce low volatility but do not improve the Sharpe ratio compared to naïve diversification (i.e. equal-weighting), as shown by DeMiguel, Garlappi and Uppal (2007). It can be show that, unless one assumes unrealistically low correlation across stocks, minimum variance portfolios simply concentrate in the lowest volatility stocks. The magic of diversification is however to exploit the correlation properties of stock returns. Rather than lowering volatility by investing only in low volatility stocks, Efficient Indexation allows one to focus on the nonlinear effects of diversification, which is that a combination of stocks that takes into account their correlation properties can achieve relatively low risk even by investing in stocks that have high risk on a stand-alone basis.
The minimum variance index methodology aims at minimizing volatility and does not aim at providing an optimal portfolio in terms of risk and reward (i.e. the Sharpe ratio), while the efficient index methodology focuses explicitly on maximizing the Sharpe ratio. It is only if expected returns of all stocks were equal that minimum variance portfolios would coincide to maximum Sharpe ratio portfolios.
Efficient indices relax this unrealistic assumption that all expected returns are equal by a more realistic and explicit assumption that expected returns are different across stocks and that these differences are linked to the stocks’ riskiness.
Empirically, efficient indices are found to have a slightly higher volatility compared to minimum variance portfolios, but a substantially higher performance, with a resulting improved Sharpe ratio.
For further details, please refer to the following publications:
• "Improved Beta? A Comparison of Index Weighting Methods", Journal of Indexes, January/February 2011
• "A Post-crisis Perspective on Diversification for Risk Management"
As an academic research centre, transparency of the method is an important issue for us. We ensure that the indices are as transparent as possible through the following:
• Our methodology is published and freely available. The ground rules contain all construction details which are followed by us so our process is completely replicable.
• Our past performances are available from data vendors. There is a history since 2002 on the FTSE indices and since 1959 for the EDHEC-Risk Efficient Index US Long Term Data. We also provide the historical weights of index constituents.
• Constitution of our indices follows the constitution of the corresponding cap-weighted indices from FTSE.
The efficient indices are meant to deliver the highest possible normal return, without trying to generate alpha. In particular, no active view is incorporated in their construction. Instead, widely available information on risk and return characteristics is used in a disciplined manner so as to create an equity benchmark with high risk reward efficiency over the long term. Active managers possessing security selection skills and using an efficient index as benchmark could potentially outperform the efficient index by under/over-weighting stocks on the basis of their active views.
Efficient indices are meant to be used as investment benchmarks by asset owners for the core component of their performance-seeking portfolios. These benchmarks will be subsequently used in passive or active investment mandates. Asset managers can also use the efficient indices as a basis for exchange-traded funds.
Currently, there are 14 indices for different regions and countries around the world:
• FTSE EDHEC-RISK Efficient Index US
• FTSE EDHEC-RISK Efficient Index UK
• FTSE EDHEC-RISK Efficient Index Eurobloc
• FTSE EDHEC-RISK Efficient Index Developed Asia Pacific ex Japan
• FTSE EDHEC-RISK Efficient Index Japan
• FTSE EDHEC-RISK Efficient Index All-World
• FTSE EDHEC-RISK Efficient Index All-World ex US
• FTSE EDHEC-RISK Efficient Index All-World ex UK
• FTSE EDHEC-RISK Efficient Index Developed
• FTSE EDHEC-RISK Efficient Index Emerging
• FTSE EDHEC-RISK Efficient Index Developed Europe
• FTSE EDHEC-RISK Efficient Index Dev Europe ex UK
• FTSE EDHEC-RISK Efficient Index Asia Pacific
• FTSE EDHEC-RISK Efficient Index Asia Pacific ex Japan
We also compute custom indices such as the following index which applies an exclusion of stocks based on socially responsible investing criteria:
• FTSE EDHEC-Risk Efficient Eurobloc ERAFP Large Cap Custom SRI Index
