**NoÃ«l Amenc, Felix Goltz**and

**Nicolas Gonzalez**of the Edhec-Risk Institute assess how easy it is to invest in smart beta equity indices. The arrival of smart beta equity indices has raised a major question on their investability: at what cost will investors be able to trade the index constituents in the same proportions as the underlying strategy? In fact, departing from the traditional cap-weighting investment scheme leads to risks that are sizable and that vary significantly. These include common exposures to systematic risk factors such as size and liquidity. Smart beta indices exhibit higher levels of turnover than their cap-weighted counterparts. Importantly, for any level of liquidity, the level of turnover in the index will impact the performance of the tracking fund through the frequency of occurrence of transaction costs. A key implication is that the smart beta index turnover and capacity constraints need to be methodologically and carefully handled through the construction of the index. The turnover of an equity index is an early indication of the aggregated trading activity of funds that will track that index. Although knowledge of a portfolio’s turnover does not provide a precise measure for estimating the actual costs of trading, it provides an intuitive and parsimonious idea of the fund’s trading activity and, as such, is a sensible indicator. Turnover varies greatly from one index to another, and the methods for managing it are a complex problem in constructing indices. ERI Scientific Beta, an Edhec venture, has opted for a “trigger” rebalancing approach that activates rebalancing whenever the gap between the current index weights and new target weights reaches a specific threshold, such as +5%. The trigger approach is that it avoids unnecessary rebalancing unless a significant amount of new information has been received. The threshold level of an index is determined through a calibration procedure over its back-test history. First, different versions of the index are constructed over the calibration period, each with a conditional rebalancing dictated by a threshold. Then, the smallest threshold that results in an average one-way annual turnover below or equal to 30% over the calibration period is used as the specific turnover threshold for that index in its live period. Finally, irrespective of whether or not the threshold is reached, suggested optimised weights will be used if the index has not been rebalanced optimally for seven consecutive quarters. Scientific Beta USA Indices exhibit levels of turnover that can exceed reasonable investability levels. This is notably the case for the Maximum Decorrelation, Efficient Minimum Volatility and Efficient Maximum Sharpe Ratio Indices, which respectively exhibit 59.51%, 54.81% and 65.02% average annualised one-way turnover over the period from June 29, 1970, to December 21, 2012. After controlling for turnover, the same indices exhibit a much more reasonable level of turnover (respectively 29.22%, 29.83% and 27.84%). Most interestingly, the reduction in turnover is accompanied by no, or at most a marginal, loss in returns and volatility reduction. The changes in volatilities are very small. Reducing the turnover does not alter the benefits of Scientific Beta strategies over the long run to a significant extent, and brings implementation costs down substantially. Capacity is key in the constitution and construction of an equity index. To achieve it, adjustments in stock weights can be implemented post-optimisation with the use of cap-weight multipliers. The principle used is to impose a threshold for the weight of a stock and for the weight change at rebalancing, relative to the market-cap-weight of the stock in its universe. “Holding capacity constraints” are where each stock weight is capped at a multiple of ten of its free-float-adjusted market-cap-weight to avoid big investment in the smallest stocks. “Trading capacity constraints” are where change in weight of each stock is capped to its free-float-adjusted market-cap-weight to avoid large rebalancing in small stocks. The capacity constraints do not have a substantial impact on overall performance and turnover metrics over the selection of indices. The Scientific Beta US Maximum Decorrelation Index exhibits an estimated number of days to trade at 95% of 0.12 days and an average market capitalisation of $10.12 billion (€8.24 billion) before the capacity constraints are applied. These figures are marginally improved to 0.10 days to trade and $10.17 billion average float after the capacity constraints are applied. This marginal shift in performance and liquidity is a side effect of capacity constraints, which are designed to address deviations in weights of smaller cap stocks between the index and its cap-weighted reference. Smart beta indices can exhibit a bias toward smaller cap stocks relative to their cap-weight reference. Capacity constraint has a big impact on the ratio decile weight of index and decile weight of cap-weights, especially in the low market cap decile. For example, in the case of the Scientific Beta US Maximum Deconcentration Index, weights before adjustments are equally distributed to each market capitalisation bucket. The ratio between sum of weights of the Maximum Deconcentration Strategy to cap deciles and sum of cap-weights in the “low market cap” decile, where the Maximum Deconcentration strategy tends to concentrate 14.42 times more than the cap-weighted index on average historically, is above the 10-multiple threshold set in the capacity rule. Hence the adjustment on the “low” decile. After applying the capacity constraint, we observe the ratio dropped to 9.66, respecting the capacity holding constraint.

**REDUCED TURNOVER**

Even over long-term horizons, a very reasonable ex-post turnover level that is in line with the ex-ante targets can be maintained with the use of a threshold-based method. The average annual one-way turnover of the indices we studied was reduced from 46% to 26% through the turnover rules, a level which is shown to have little impact on performance. Capacity constraints allow us to manage deviations from the cap-weighted reference index in terms of individual component market capitalisation both at the trading and holding levels. Notably, we showed how the capacity constraint has an impact on controlling the imbalance between the weight allocated to smaller market cap stocks and their corresponding cap-weight. On average this ranges from a 12.77 ratio to an 8.11 ratio.

*Noël Amenc is a director and Felix Goltz is head of applied research at the Edhec-Risk Institute, and Nicolas Gonzalez is a senior quantitative analyst at ERI Scientific Beta*

**©2014 funds europe**