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Evaluating Alternative Beta Strategies |

February 24, 2012 |

Comparing approaches to factor indexing Since the first market capitalisation-weighted ("cap-weighted") equity index was introduced by Standard & Poor's in 1923, cap-weighted indexing has become the dominant form of index investing. Today, cap-weighted indices account for the vast majority of assets in index-linked investment products such as ETFs and index funds, as well as trading volumes in exchange-traded and over-the-counter ("OTC") index futures, options and other derivatives. In recent years, there has been a proliferation of alternatively weighted indices, such as fundamentally weighted indices, equal-weighted indices, and low-volatility indices. Correspondingly, there have been increased debates about the role of alternatively weighted indices (or "alternative beta") in investment portfolios. While some proponents of alternative beta criticise market capitalisation-weighted indices as "inefficient", most market participants believe that market-cap weighting will always be the dominant form of indexing. It is not only the most representative of the market, but also has the lowest implementation cost due to its investment capacity and automatic self-rebalancing. In addition, as the cap-weighted portfolio is the only portfolio that all investors can collectively hold, it represents the ultimate benchmark, where outperformance and underperformance become a zero-sum game relative to the market. The key to understanding alternative equity beta strategies is the extensive empirical evidence that stock returns are driven not just by the overall market factor, but also by other common risk factors that are related to the characteristics of the stocks. Notably, small-cap stocks and value stocks have historically acted differently from large-cap stocks and growth stocks, respectively, and have generated higher long-term returns. Fama and French (1992, 1993) found that a three-factor model of market, small-cap and value factors would explain more than 90% of diversified portfolio returns, which significantly improved the explanatory power of a single-factor model, such as the Capital Asset Pricing Model (CAPM). Many studies (e.g. Jegadeesh and Titman (1993) and Carhart (1997)) identify momentum as another common equity risk factor, due to the persistency in the relative performance of past winners and past losers. Last but not least, empirical research (e.g. Haugen and Baker (1991) and Clarke, Silva, and Thorley (2006, 2010)) has shown that an equity portfolio's exposure to the volatility factor can also have significant impact on its risk and return; and, contrary to finance theory, holding high volatility stocks has not been compensated by higher long-term returns than holding low-volatility stocks. To a certain degree, this range of empirical evidence has motivated attempts to achieve better risk adjusted returns than the market capitalisation-weighted portfolio, by tilting a portfolio's exposure to certain common equity factors, such as small-cap, value, and volatility. Figure 1 shows the historical return and volatility over the last 30 years of these most recognised equity factors for the US equity market. The market factor represents the excess return from investing in the cap-weighted US equity market. The small-cap, value, momentum and volatility factors represent the returns from portfolios that are long small stocks and short large stocks, long high book-to-market stocks and short low book-to-market stocks, long past winners and short past losers, and long high-volatility stocks and short low-volatility stocks, respectively. It is notable that the small-cap, value and momentum factors have historically been associated with substantial positive returns. If such trends were to continue, this implies that portfolios that systematically overweight small-cap, value and momentum stocks can outperform the market. On the other hand, as the volatility factor has historically had negative returns, portfolios with a tilt to low-volatility stocks would have been better rewarded than the market. Another important observation from Figure 1 is that, similar to the market factor, the small-cap, value, momentum and volatility factors have been very volatile. In other words, the potential reward from systematically tilting the portfolio towards any of these factors can vary significantly from one period to another. The results shown in Figure 1 suggest that these well-known risk factors can all have significant impacts on both the risk and return of equity portfolios.
The authors of several recent studies have compared the increasingly numerous alternative equity beta strategies. For instance, Chow, Hsu, Kalesnik, and Little (2011) surveyed various "Heuristic-Based" (experience-based) and "Optimisation-Based" weighting strategies. Using a four-factor model of market, small-cap, value and momentum, the authors identified the sources of outperformance as exposure to the value and small-cap factors, and found no statistically significant alpha after adjustment for the factor exposures. Melas, Briand and Urwin (2011) proposed a generalised framework and characterised all "Risk-Based" and "Return-Based" strategies as special cases of mean-variance portfolio construction, subject to various assumptions for expected risk and return. Dash and Loggie (2008) suggested that all index weighting schemes can be generalised as being weighted by a certain factor raised to a power; if it is desired to amplify the influence of certain factor, an exponent can be applied. For a larger view, please click on the image above.Other often-cited indexing strategies that attempt to achieve more desirable risk characteristics than the market capitalisation-weighted portfolio include (but are not limited to) equal-weighted (Dash and Loggie, 2008), equal risk contribution (Maillard, Roncalli and Teiletche, 2010), and diversity-weighted (Fernholz, Garvy, and Hannon, 1998). It is important to note that these strategies differ significantly from minimum-variance or other low-volatility strategies. Low-volatility equity strategies aim to reduce portfolio volatility, primarily by taking fewer systematic risks (e.g. by holding low-beta stocks); they typically represent relatively concentrated portfolios and may therefore have higher stock-specific risks than the market portfolio. By comparison, equal-weighted, equal risk contribution and diversity-weighted strategies typically do not reduce portfolio volatility as they do not reduce systematic risks; they are designed to reduce stock-specific risks and are less concentrated than the market portfolio. We classify these three strategies that reduce stock specific risks and portfolio concentration risks into the same category, simply termed "diversification strategies".
Figure 5 shows that all three value strategies delivered positive returns relative to the S&P 500 index. Not surprisingly, all three strategies have substantial and statistically significant value factor exposure. The Value Weighted strategy has the lowest level of value exposure, as well as the lowest active risk (tracking error) relative to S&P 500. It is a less aggressive value strategy, since its portfolio construction does not involve stock selection. As the Fundamental Index contains far more stocks than the S&P 500 or MSCI USA universe, it essentially has an extra allocation to mid-cap stocks outside S&P 500/MSCI USA. This also partially explains the Fundamental Index's more significant small-cap exposure than that of the Value Weighted strategy. Given that the S&P MidCap 400 outperformed the S&P 500 by 3.9% per annum in the examined period (June 1995 – October 2011), the mid-cap exposure would have improved the return of the Fundamental Index. We also notice that the Pure Value strategy has the most significant value and small-cap exposures and the highest active risk. Its stock selection and weighting mechanism based on relative value characteristics make it the most aggressive value strategy of the three in the study. For a larger view, please click on the image above. For a larger view, please click on the image above.
For a larger view, please click on the image above.Mean-variance optimisation requires both estimations of stocks' expected returns and a covariance matrix. As expected returns are notoriously difficult to estimate, a typical minimum-variance strategy "simplifies" the optimisation by assuming that all stocks have the same expected returns For a larger view, please click on the image above.
For a larger view, please click on the image above.
For a larger view, please click on the image above.
For a larger view, please click on the image above.For a larger view, please click on the image above.
In this section, we aim to build upon the empirical analysis of alternative equity beta strategies undertaken in the previous section by discussing some key considerations and potential risks of alternative beta strategies.
For a larger view, please click on the image above.The active risks in alternative beta strategies are often primarily the direct results of those strategies' factor exposures. As factor returns can be volatile over time and difficult to predict, a strategy's active exposures to common factors such as value, small-cap, momentum and volatility can have significant implications for the strategy's performance relative to the overall market. For instance, we have shown in Figure 1 that, over the last 30 years, the value factor was associated with an annualised return of 3.6%, while the volatility factor was associated with an annualised return of -1.9%. However, Figures 10a and 10b demonstrate that both value and volatility factor returns varied greatly during this period. Notably, the value factor was associated with substantial negative returns in 1998/1999 during the IT bubble, as well as in 2007/2008 during the credit crisis. Not surprisingly, Figure 9 shows that the fundamentally weighted strategy significantly underperformed the market during these two periods, as this strategy has significant value exposure. For a larger view, please click on the image above.
For a larger view, please click on the image above.
For a larger view, please click on the image above.
Although alternative beta strategies aim to achieve better risk-adjusted performance than the cap-weighted portfolio, they are often constructed with more specific objectives in mind. These objectives include achieving a systematic value tilt, lowering portfolio volatility, or reducing stock-specific risks. While the risk and return profiles of the alternative beta strategies examined in this paper are to a large degree driven by the well-known equity risk factors (market, value, small-cap, momentum and volatility), the primary factor drivers of individual strategies are often distinct, and in turn may define the essence of the strategy. When evaluating an alternative beta strategy, a starting point for investors may therefore be to examine its objective and risk drivers, in the context of those investors' own investment objectives and preferences for risk taking.
- Chopra and Ziemba (1993) discussed the effects of estimation errors on mean-variance optimisation.
- The implication is that a volatile stock which has low correlation with the rest of the portfolio may be included in the minimum-variance portfolio, due to its low marginal contribution to portfolio risk. By contrast, the non-optimised approach ignores correlation and will exclude such a stock as a result of its high volatility.
- As the S&P 500 Low Volatility index shows a substantial alpha of 3% per annum during the examined period, we further tested using the available index data going back to 1990, and found an annual factor-adjusted alpha of 1.2%, without statistical significance.
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