## Choose Your Betas

Systematic equity strategies that try to improve performance compared to cap-weighted reference indices have received considerable attention recently (see this Financial Times article). However, commercially available advanced beta strategies are pre packaged offerings that often provide little justification of how their methodological components are chosen. In particular, the existing strategies combine stock selection decisions with weighting scheme choices and hence make it difficult to understand how different parts of the methodology influence portfolio’s return and risk. While this is true across a large variety of commercial index offerings it may be useful to indicate some specific examples. For example, the Russell Defensive Index selects stock by characteristics (such as low volatility, low leverage etc) and uses market cap weighting to build a low volatility portfolio. On the other hand, the MSCI Risk Weighted Index avoids any stock selection (and rather uses the standard MSCI index constituents) but then weights the stocks by inverse of historical variance to achieve the same low risk objective. Why the respective provider chooses stock selection or weighting as a means to obtaining the low risk objective is little justified. Another example is that of fundamentals-based equity indexation. Certain strategies like the MSCI Value Weighted Index do not change the stock selection relative to the standard index and simply weight stocks by a fundamental measure of firm size while others like the FTSE RAFI index series select stocks by the fundamental measure of firm’s size in addition to weighting stocks by the same measure of firm size. In all these cases there is little analysis available on what each construction step contributes to the final outcome in terms of risk and performance.

In order to provide more transparent insights into the performance and risks of advanced beta equity strategies, Amenc et al (2012) propose to benchmark advanced beta by adopting a two-step portfolio construction method to disentangle the two decisions: ** constituent selection** that reflects which stock associated characteristics an investor wants to hold, and

**that is determined by the portfolio investment objective (minimum volatility, maximum Sharpe ratio, maximum decorrelation to name a few) and that takes into account the dependence structure of stock returns to attain it.**

*diversification-based weighting scheme*This two step analysis provides for a range of interesting insights: Firstly, they show that, for a given portfolio concentration, a diversification-based weighting scheme performs better at attaining diversification objective than a pure stock selection strategy. Portfolio concentration can be measured as *effective number* (EN) which is the inverse of the sum of squared of individual stock weights (Malevergne et al, 2009). For an equally weighted portfolio, EN is equal to the total number of stocks and, for a totally concentrated portfolio, it is equal to one. As an example using minimum volatility objective in S&P 500 stock universe, figure 1 shows that one must choose an extremely highly concentrated portfolio (EN = 95 stocks) to attain the volatility level of an optimized portfolio with EN equal to 167.

*Figure 1:** Concentration Problem when focusing on Stock Selection to attain Objective: The case of low volatility – The plot shows, in blue curve, the portfolio volatility as a function of stock concentration for low volatility portfolio and the red line represents the benchmark volatility i.e. the volatility of optimized minimum volatility portfolio.*

Furthermore, one could use stock selection as a tool to correct undesirable risk factor exposures brought implicitly by the diversification-based weighting scheme. Amenc et al (2012) found that diversification-based weighting schemes lead to considerable improvements in their objective even after the correction for relevant factor exposure contradicting that the claim that these schemes merely thrive on factor premiums. As an example, they perform portfolio optimization on a selection of stocks to obtain zero value tilt and show that the resulting portfolios still over-perform cap-weighted index (table 1).

*Table 1: Excluding value stocks when using alternative weighting schemes –** The table summarizes the performance of diversified strategies based on low dividend yield stock selection. The fraction of stocks included, as shown in the first row, is determined separately for each strategy so as to bring the ex-post value exposure close to zero. *

Given the wide variety of product offerings, it has become important to understand clearly how different methodology components contribute to strategy’s performance. The research shows that making a clear distinction between *stock selection* and *weighting scheme* in portfolio construction process is an important element of transparency of advanced beta offerings. However, this is only one step towards a better understanding of the myriad of advanced beta strategies and further research in this area is needed if investors want to fully understand the risks and benefits of such strategies.

**References:**

Amenc, N., F, Goltz., and A. Lodh, 2012. ” Choose your Betas: Benchmarking Alternative Equity Index Strategies .” The Journal of Portfolio Management, Vol. 39, No. 1 (Fall 2012), pp. 88-111. (Forthcoming)

Malevergne, Y., P. Santa-Clara, and D. Sornette, 2009, “Professor Zipf goes to Wall Street.”

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