Fundamentals of Smart Beta Investing Swings & roundabouts ...

By Lise Renelleau, Director of Managed Volatility Strategies, and Ram Rasaratnam, Senior Research Associate March 2015

ROSENBERG EQUITIES

Fundamentals of Smart Beta Investing Swings & roundabouts of diversification: A look at equal weighting schemes

This communication is intended for non U.S. institutional use only and must not be relied upon by retail clients. Circulation must be restricted accordingly.

There are many reasons why an equity investor may decide not to follow market capitalization-weighted indices. The search for lower volatility solutions, fears of concentration risk, and concerns about buying securities that appear overpriced can drive investors to look for alternatives. Some of the more mechanical implementations of this type of alternative investing within equities are referred to as “smart beta”, and investors are now benefiting from a wide range of commercial smart beta approaches. In parallel, these strategies have received good coverage in the academic literature, some claiming that even monkeys can beat the cap-weighted market.1 But the devil, as always, is in the details. In a series of papers about smart beta investing, we will attempt to provide insights into smart beta terminology and concepts. Our aim is to demonstrate how these concepts lead to tangible investment outcomes, and to identify the key beliefs that underline several popular smart beta strategies. Quick read

§ Broad market cap-weighted indices can be highly concentrated in a handful of large capitalization names. This partly reflects known behavioral inefficiencies such as over-optimism for high-flying stocks and over-pessimism for underperforming stocks.

§ “Diversification by number”, as found in equal weighting or risk parity approaches, is a mathematical way of ad-

dressing the afore-mentioned concentration risk directly. While these approaches have their merits, they also lead to non-trivial side effects when applied to equity indices. As this paper attempts to illustrate, portfolios built in this manner will be exposed to one primary performance driver: their increased exposure to the smallest index names.

§ The equal-weighted portfolio achieves diversification in number by definition. However this approach creates a

significant bias away from larger cap stocks. It therefore overlooks the fundamental size of the businesses in which it invests, and in particular, the economic importance of company earnings.

§ The equal-weighted portfolio exhibits higher average turnover and lower liquidity than the market cap index and

systematically allocates significant turnover to the least liquid segments of the index.

§ While a risk parity approach can be seen as an enhancement to equal weighting, it is prone to similar shortcom-ings such as high exposure to smaller cap names, high turnover, and low liquidity as its construction is “anchored” on equal weighting.

§ From a performance perspective, both equal-weighted and risk parity portfolios have historically outperformed

capitalization-weighted indices, but the return pattern was similar to that of the mid/small capitalization segment of the market, adding fuel to the argument that a persistent capitalization bias is behind the positive excess return.

§ Equal weighting and risk parity could be seen as a way of systematically allocating to smaller capitalization stocks

rather than simply addressing concentration issues. For investors looking to capture the small cap risk premium, a purposeful, direct allocation to the small cap segment of the market could be more transparent and allow better control of liquidity and turnover.

1 Cass Consulting. An evaluation of alternative equity indices. Part 1 and 2. Andrew Clare, Nick Motson and Steve Thomas. March 2013.

AXA INVESTMENT MANAGERS - INVESTMENT RESEARCH n 2

Foreword Many smart beta strategies, including equal weighting, risk parity (also known as equal risk contributions2), minimum vari-ance, and maximum diversification3, claim to offer “a more diversified portfolio” than the standard market capitalization-weighted index. We will illustrate how this assertion can be interpreted in different ways and how these approaches work in practice. In doing so, we hope to provide insights relevant to asset owners’ investment decisions. In this article, our focus is on equal weighting and its sibling, risk parity. This is a timely topic given the recent performance of equal-weighted indices relative to their cap-weighted counterparts. Over calendar year 2014, the MSCI World Index posted a return of 5.5% (USD, gross). The MSCI World Equal-Weighted Index returned 3.4% over the same period. The recent mild underperformance of equal-weighted indices may cause in-vestors to more carefully examine investment strategies oriented around the idea of “diversification by number” and gauge their own comfort level with the capitalization bias that these strategies can introduce. We argue that, if it is a simple cap bias that is desired, there are cheaper, more direct and more controllable ways of achieving this. How diversified is the market index?4 As seen in Figure 1, the MSCI World Index exhibits a high level of concentration, with half of the index’s weight made up of just 10% of the number of stocks. Moreover, three quarters of the index’s weight is represented by just under one third the stocks. This certainly looks like too many ‘eggs’ in one basket. This pattern of concentration persists across all regions, as presented in Figure 2.

Figure 1 MSCI World Index Capitalization weights structure

Source: MSCI World Index, AXA Investment Managers as of 31 December 2014.

2 See Maillard, Sébastien, Roncalli, Thierry and Teiletche, Jerome, On the Properties of Equally-Weighted Risk Contributions Portfolios (September 22, 2008). 3 Choueifaty, Y. and Y. Coignard (2008), Toward maximum diversification, Journal of Portfolio Management, vol. 35, 40-51. 4 Analysis using MSCI World Index (or MSCI regional indices) uses MSCI published holdings as of a stated date. All position sizes are calculated by Rosenberg Equities based on constituent stocks’ capitalizations on the observation date. All returns are calculated by Rosenberg Equities. All index characteristics are calculated and/or observed by Rosenberg Equities.

Diversification by number

There is a long tradition of diversification in asset management, especially as an asset allocation tool to spread risk across asset classes. It is based on the principle that combining two assets exhibiting low or negative cor-relations and similar return potential may result in superior risk-adjusted total returns relative to holding either of the two assets individually. Another facet of diversification relies on controlling the negative impact that any single asset can have on the whole portfolio by reducing concen-tration risk. This is well understood and used, for example, when control-ling stock-specific risk in equity investing. We will call this second, simpler objective “diversification by number” – the underlying idea being that there is undiversifiable, asset-specific risk that a portfolio is exposed to when investing too much into too few assets.


Figure 2

MSCI Regional Indices Capitalization weights structure

This supports the view that “the market” is not sufficiently efficient. We observe that:

§ Many market cap-weighted indices are concentrated, with most of the portfolio invested in a handful of names.

§ Market prices are inefficient as a result of over-optimism for high-flying stocks and over- pessimism for un-derperforming stocks. Market capitalization-weighted indices reflect these inefficiencies through their defini-tion of weight as shares multiplied by price.

Investors concerned about portfolio concentration and avoiding market inefficiencies have looked for alternatives to cap-weighted investing including the diversification techniques described here, but we warn that with improved tech-nical diversification can come some potentially unexpected side effects. An alternative to market cap weighting: equal weighting5 More than ten years ago, equal weighting was put forward as a new form of equity indexation when applied as a stock weighting mechanism. Equal weighting is an intuitive remedy for the concentration risk present in cap-weighted indices. Such approaches have existed for many years, used, for example to reduce asset weights in sec-tor indices. Equal weighting has often found favor among the academic community, partly for its simplicity, and partly because its implementation does not require accessing any other data. A key question that one may ask: in which sense is an equal-weighted portfolio well diversified? To measure diversi-fication we first measure concentration using the Adjusted Herfindahl Index (see box on the following page). Using this approach, the equal-weighted portfolio is the most diversified portfolio with an Adjusted Herfindahl index value of zero.

5 Important note on methodology: the equal weighted index (or equal weighted portfolio) referred to throughout this document is constructed by Rosenberg Equities, based on the constituents of the MSCI World Index (or MSCI regional indices, where appropriate). All returns are calculated by Rosenberg Equities. All index characteristics are calculat-ed and/or observed by Rosenberg Equities.


What does equal weighting mean for an equity portfolio? Given the fact that equal weighting achieves the goal of perfect diversification when viewed through the Herfindahl lens, we contrast the capitalization-weighted MSCI World Index to its equal-weighted analog on December 31th 2014 to examine the side effects associated with adopting an equal weighting scheme. The most obvious change is with respect to the portfolio’s capitalization profile. To measure size (capitalization) exposure, we rank stocks by market cap and define the mega cap segment as the top 15% of names, large cap is the next biggest 25% of names and mid/small cap are the smallest 60% of names by region.6

Figure 3 Market index weights by capitalization segment

As seen in Figure 3, equally weighting the MSCI World Index constituents leads to a significant and systematic rela-tive size bet. 6 Four regions are defined using AXA Investment Managers’ home region definitions: North America, Europe, Asia ex Japan and Japan.

Measuring Portfolio Concentration

To measure the concentration of any basket of stocks we use the Herfindahl Index. It is defined as the sumof the squares of the weight of each stock in the index or portfolio. It was first used in the measurement of market share as it related to monopoly or oligopoly situations. Higher values of the Index indicate higher levels of concentration; lower values indicate better diversification. When comparing a market index containing a large number of stocks to one containing a fewer number, the standard Herfindahl Index can be misleading. The Adjusted Herfindahl Index is there-fore the desirable measure as it normalizes by the number of stocks (N) in the given market, mak-ing it possible to compare market indices or portfolios with different numbers of constituents. The Adjusted Index has zero as a lower bound indicating perfect diversification given a number of actual assets, which is only achieved by the equal weight portfolio. Hence any methodology that mechanically seeks to minimize, reduce or control the Herfindahl Index implicitly pushes a portfo-lio towards equal weighting. Herfindahl Index: H = ∑ w2 Adjusted Herfindahl Index: H* = (H - 1/N)

1-1/N As we can see from the formula, the inverse of the Herfindahl Index is equivalent to a specific number of stocks. This number is called the “effective number” of stocks. If the effective number is equal to the actual number of stocks, the assets in the market index are equally weighted. If the effective number is much lower than the actual number, the basket of stocks is very concentrated. One key difference between portfolio weighting and market concentration measurement is that the ultimate goal of the former is to build an investable portfolio. Non-trivial investment risk is a side effect of solely focusing on the Herfindahl Index without any consideration for investment outcome such as portfolio liquidity.

N

i = 1 i


As expected, the weight of the 955 smallest names increases, with a corresponding decrease in the weight of the 236 mega cap stocks. But what may be surprising is that equal weighting does not have much effect on the weight allocation to the 379 large cap names in the middle of the index. The weight in mega cap is effectively transferred straight to the mid/small cap segment, creating an index heavily biased toward smaller companies. These results lead to the following questions:

1. Was this transfer of weight and change to the index profile necessary to reduce the concentration risk that plagues cap-weighted index portfolios?

2. Is it reasonable to invest 60% of a broad cap index portfolio in small companies that represent only 20% of the market?

To answer the first question, we calculate the Adjusted Herfindahl Index within each market cap segment for each region in the MSCI World Index and then take the average across segments (noting that the mega cap concentration pattern persists in each region).

Figure 4 Adjusted Herfindahl Index, regional average by capitalization segment, MSCI World Index constituents

The results in Figure 4 show that the concentration of the MSCI World Index is driven almost exclusively by the very concentrated mega cap segment, and that both the large cap and the mid/ small cap segments are already well diversified. Rather than focusing on the problem – the mega cap segment – a diversification strategy that aims for a ‘perfect zero’ Herfindahl score affects all segments. Hence it is fair to say that equal weighting may be diversifying well beyond what is needed to address the concentration of market capitalization weighting schemes and this may exacerbate the undesirable effects of such diversification mechanisms. With regard to the second question, we take a brief look at the fundamental characteristics of the equal-weighted index using the US market as an example. This question, in essence, is concerned with an index portfolio’s partici-pation in the real economy. How does equal weighting fare in terms of its exposure to company earnings?


To illustrate the fundamental risk associated with equal weighting, we took the MSCI USA Index as of December 31th 2014 and calculated the total earnings of stocks within each size segment. What can be seen in Figure 5 is a strong correlation between total earnings and market capitalization.

Figure 5 MSCI USA Index aggregate earnings by capitalization sector

Simply put, bigger companies generate more earnings. This natural connection between earnings and position size is lost when one implements an equal weighting scheme as only 19% of the index, for example, is allocated to stocks representing 60% of the index’s total earnings. One could logically argue that market capitalization-based weighting provides a more reasonable representation of economic importance than equal weight, and choosing a weighting scheme that wholly ignores company size could have knock-on effects with respect to portfolio return and risk. Turnover and liquidity of the equal weight portfolio What are the investment consequences of this purely mathematical, “perfect Herfindahl” approach in terms of portfo-lio management and implementation risks? In this section, we back test the equal weight index portfolio over the trailing 24 years and note that the strategy outperformed the cap-weighted index over the full period. As importantly, though, are observations about the nature of the equal-weighted index along the dimensions of turnover, liquidity, and country biases. § Higher turnover – As illustrated in Figure 6, annualized average turnover of the equal-weighted index is 26%, higher

than the market cap index (8%), but perhaps lower than one would expect given the equal-weighted index portfolio is rebalancing back to equal weight every quarter.7 One important characteristic to note is that the majority of the turnover takes place in the smaller end of the cap spectrum, where liquidity would be much lower than in mega and large cap, and where market impact and transaction costs would be much higher. These higher implementation costs would direct-ly eat into the return of any index portfolio. Again, this additional turnover is happening within the most diversified seg-ment of the market-cap index.

7 Rebalancing every month would yield a turnover of 47%.


Figure 6 Average turnover by capitalization segment

§ Lower liquidity – To assess liquidity, we calculate average daily volume of each stock over the previous month. We then

take a notional portfolio value of $10bn, and estimate how quickly the portfolio could be traded to cash if using 10% of average daily volume. The results are summarized in Figure 7.

Figure 7

Positions requiting more than five days to trade, MSCI World Index Constituents

As expected, the cap-weighted index portfolio is highly liquid: only 0.2% of the portfolio weight would have re-quired more than a week to trade to cash. For the equal weight index, after one week, 12.3% of the portfolio would have still been in equities.

This is an important consideration, not just for large institutions but for all investors. If strategies employing an equal weighting scheme become a material part of the market, there will be added aggregate exposure to liquidity risk, especial-ly during periods of market distress.


§ Persistent country allocation - Another unforeseen impact of giving an equal weight to each stock in the index is that the overall country allocation became a function of the number of names in the country. If the percent of names that repre-sent a country is less than the market cap weight of that country (for example the United States) then the equal-weighted portfolio would have seen underweight relative to the cap-weighted index. Conversely if the percent of names is higher than the market cap (Japan) then we should have expected equal weighting to overweight. An analysis of re-gional weights by market cap and by number of stocks is illustrated in Figure 8.

Figure 8 Number of stocks by region as percent of total, MSCI World Index Constituents

At the end of December 2014 this was the case: 19% of the names in the MSCI World Index were Japanese but they constituted only 8% of market capitalization. Japan, was thus 11% overweight in the equal-weighted scenario relative to market capitalization. On the other hand, North America represented 59% of market capitalization but constituted only 44% of the names, so was underweighted by 15% in the equal weighted index. In the absence of forward-looking return assumptions along country dimensions, the large country biases associated with equal weighting may seem hard to justify. To summarize, the country bias that arises when one equal weights a global index is simply a function of the number of names in each country, as opposed to being based on anything fundamental or economic. This is a good example of what, for some, may be unintended (and potentially, uncompensated) risk. As illustrated in Figure 9, since 2008 the relative country allocation associated with an equal- weighted global portfolio has been relatively stable, though historically this has not always been the case as the relationship between number of names and market capitalization (per country) has been more variable.

Figure 9 Active country weight-equal-weighted global portfolio vs. MSCI World Index


The historical back-tested performance impact of equal weighting We have illustrated that equal weighting creates a large allocation, in both absolute and relative terms, to the smaller cap segment of the equity market. It also introduces country biases, and changes to the liquidity and turnover profile of a port-folio. Next, we measure the investment outcome of the strategy. Table 1 looks at the performance of the global equal-weighted index over the past 24 years, split by decade.

Table 1 Back-tested historical performance of an equal-weighted portfolio

Annualized cumulative total return Annualized active return

MSCI World

Equal weight

Mega cap

Mid/small cap

Equal weight

Mega cap

Mid/small cap

Jan 90 to Dec 14 – Full Period 7.9% 9.4% 7.9% 9.3% 1.4% 0.0% 1.4%

Jan 90 to Dec 99 – 1990’s 12.3% 9.5% 14.3% 8.1% -2.8% 1.9% -4.2%

Jan 00 to Dec 09 – 2000’s 1.6% 7.9% 0.0% 8.3% 6.2% -1.6% 6.7%

Jan 10 to Dec 14 – 2010’s 11.3% 10.9% 10.4% 13.0% -0.4% -0.9% 1.6% Source: MSCI, AXA Investment Managers, January 1990 to December 2014, equal-weighted portfolio is rebalanced quarterly. Mega Cap is defined as the top 15% of the MSCI World Index by capitalization. Mid/Small Cap is defined as the bottom 60% by capitalization. Returns are gross of fees and trading costs.

The equal-weighted index portfolio outperformed the MSCI World Index by 1.4% on an annualized basis. However, the return pattern bears striking similarities to that of the mid/small capitalization segment of the index, as can be seen in Figure 10.

Figure 10 Active returns of equal-weighted portfolio and mid/small cap-weighted segment relative to MSCI World Index

What is also clear here is that outper-formance of the equal-weighted index portfolio over the full period is driven by the positive active return during the 2000’s, when the mid/small cap seg-ment outperformed the MSCI Index by 6.7% on an annualized basis.

The mechanical effect of equal weighting means that the numbers of stocks in each segment of the chosen investment universe will drive allo-cation to size, country and even industries. This mechanical diversification effect may not be related to the diversity of underlying investment risks.


The strong historical relationship between equal weight and the mid/small cap segment also existed over shorter return intervals. Figure 11 shows that there was a highly positive correlation (+0.79) between the equal-weighted portfolio and mid/small capitalization stocks, and a highly negative correlation (-0.74) with mega capitalization stocks.

Figure 11 Active returns of equal-weighted portfolio and mid/small cap-weighted segment relative to MSCI World Index

This evidence suggests that, given the return outcome was essentially the same as that of the mid-small capitaliza-tion index portfolio, equal weighting could be seen as a way of systematically allocating to smaller capitalization stocks. A look at risk parity, a strategy very simi-lar to equal weight8 While an equal weighting scheme does effectively diversify a portfolio suffering from concentration risk, it may over-correct in that it affects stocks outside of the mega cap range. Importantly, it introduces a size bias as well as undesirable ef-fects on an index portfolio’s turnover, liquidity and country exposures. Risk parity is suggested by some as a slightly more sophisticated approach to diversification by number. Here, we are using a very specific definition of risk parity in which an equity-only index portfolio is constructed based on equal contribution to total risk from each stock.

8 Important note on methodology: the risk parity weighted index referred to throughout this document is constructed by Rosenberg Equities, based on the constituents of the MSCI USA Index. The BARRA USE3L risk model is used in risk parity index construction. All returns are calculated by Rosenberg Equities. All index characteristics are calcu-lated and/or observed by Rosenberg Equities.

What is risk parity (a.k.a equal risk contribution)? A risk parity approach seeks to build an index portfolio in which each asset contributes an equal share of risk to the index portfolio’s overall volatility. Risk parity was born as an asset allocation tool, appropriate for use in the absence of views on asset class returns. It has since appeared in the form of indices such as risk-weighted (assuming zero correla-tions) and equal risk contribution equity index portfolios where the concept is applied directly to a stock universe. Risk parity is similar to equal weighting in that no assumption is required or made about a stock’s expected return, since there is an implicit assumption that the return is the same for all stocks. However, where equal weight assumes that expected volatility and correlation are also constant, risk parity assumes they are known and can be forecast, i.e. a covariance matrix (∑) can be estimated.


To gain an intuitive understanding of what risk parity means in practice, we revisit market cap weighting and equal weighting, but view the index portfolios from the perspective of individual asset contributions to risk. Figure 12 charts portfolio weights from largest to smallest, along with each stock’s contribution to the portfolio’s total predicted volatili-ty (CTV%).

Figure 12 Asset weight and contribution to total portfolio volatility (CTV%), MSCI USA Index constituents

Using the MSCI USA Index as an example of a cap-weighted index portfolio, it is evident that the large exposure to mega caps also means a significant proportion of the portfolio’s predicted volatility comes from that segment. This relationship is summarized in Figure 13.

Figure 13 Summary of contribution to total portfolio volatility (CTV%) by capitalization segment, MSCI USA Index constituents


Equal weighting and portfolio risk contribution As equal weighting is not seeking to diversify along sources of volatility, overall predicted risk contributions are not evenly distributed across holdings even though weights are. Using individual stocks as examples, one can see in Figure 14 that Whiting Petroleum Corp contributed the most to portfolio volatility (0.38%), while Safeway only con-tributed 0.05% even though it had the same portfolio weight (0.17%).

Figure 14 Equal-weighted portfolio contribution to total portfolio volatility (CTV%), MSCI USA Index Constituents

Risk parity: focus on equal risk contributions Risk parity addresses this mismatch by seeking perfect diversification along the contribution to risk dimension. We can see in Figure 15 that in the risk parity portfolio all stocks contribute approximately 0.17% to portfolio volatility.9 To obtain equal risk contribution, the portfolio weights were no longer equal. They needed to decrease for the higher risk companies and increase for the risk diversifying companies. For the MSCI USA Index, security weights ranged from 0.30% (Safeway), to 0.06% (Whiting Petroleum Corp) at 31 December 2014. Visually, though, it becomes clear that given the similarities in levels of risks across stocks, the deviation to equal weight remains somewhat small. Put differently, a risk parity-weighted portfolio bore more resemblance to an equal-weighted portfolio than to a cap-weighted portfolio because the riskiness of most stocks (and the contribution to total risk of most stocks) was within a fairly narrow range.

9 The long only, fully invested constraint prevents the solution from being precisely equal.


Figure 15 Risk parity portfolio contribution to total portfolio volatility (CTV%), MSCI USA Index constituents

How active is risk parity versus equal weighting? Comparing the two directly To further illustrate the mechanics of how risk parity uses the information in the risk model upon which it is based, we look at risk parity’s active weight versus equal weighting, plotting one weighting scheme against the other along two dimensions of risk: correlation and volatility. We use the predicted measures of each stock’s average pair-wise correlation (against all other stocks in the index) and total volatility. This analysis is illustrated in Figure 16, where the size of the circle indicates the size of the active position, with filled circles representing an overweight (in risk parity relative to equal weighting) and an empty circle representing an underweight.

Figure 16 Weights, predicted volatilities, and correlations of risk parity portfolio positions

versus equal-weighted portfolio positions, MSCI USA Index constituents


When viewed in this way, risk parity can be described as an equal-weighted portfolio tilted away from high volatility, high correlation stocks and towards low correlation, low volatility stocks. Because the risk parity setup requires that all stocks be held, and because individual stock volatilities are all similar, the differences between the two portfolios remain small: the active weights of risk parity vs. equal weight in our ex-periment, as represented by the size of the circles, ranged from -0.11% to +0.13%. It is therefore intuitive that the resulting index portfolio characteristics of the two weighting scheme were very similar. As summarized in Table 2, the total predicated volatility of risk parity was 90% of the volatility of the equal weight portfolio.

Table 2 Predicted volatility for equal weight and risk parity, MSCI USA Index constituents

The preference for low volatility, low correlation stocks in risk parity does not reduce the less desirable side effects of equal weighting, specifically the size bias. Exposure to size segments is similar for risk parity and equal weighting as seen in Figure 17. In terms of liquidity, risk parity was even less liquid, as seen in Figure 18 (this may be due to apparent lower price volatility of stocks with low liquidity resulting from less frequent trading). Realized performance of both risk parity and equal-weighted index portfolios will also be subject to higher trading costs and capacity is-sues.

Figure 17

Distribution of portfolio weight by capitalization segment, MSCI USA Index constituents


Figure 18 Percent of portfolio remaining in equities after n trading days, MSCI USA Index constituents

In terms of performance, Figure 19 shows the cumulative active return, from back-test, of both the equal-weighted portfolio and the risk parity portfolio relative to the MSCI USA Index. Over the period of simulation the relative return experience of each approach was broadly similar, as it was mostly driven by the significant small size bias the two approaches take. It is therefore not surprising that they have both outperformed the capitalization-weighted index historically.

Figure 19 Equal-weighted portfolio and risk parity cumulative back-tested portfolio performance relative to the MSCI USA

Index

To summarize, the common bias introduced when moving from a capitalization-weighted portfolio to either an equal-weighted portfolio or one that uses a risk parity weighting scheme is that of size. While the methodologies differ in their mechanics, the resulting portfolios exhibited similar characteristics and similar performance, with risk parity offering an enhancement to equal weighting in terms of reducing volatility, but not in terms of liquidity or capacity. It is therefore not surprising that some alternative beta providers use both risk parity and equal weighting schemes as a way to gain exposure to smaller capitalization stocks.


Conclusion We have looked in detail at the issue of market capitalization concentration in the mega cap segment and how it has been addressed by alternative beta indices such as equal weighting and risk parity. We illustrated how both equal weighting and risk parity introduced another type of concentration risk, by taking a very large position in the smaller end of the capitalization spectrum. Clearly, equal weighting and risk parity could be seen as ways to systematically allocate to small cap names. But if the investment objective is indeed investing in small cap, then one could argue that an explicit allocation would be more transparent, more controllable, and also more efficient when it comes to turnover and costs. In summary, market capitalization may be inefficient when it comes to portfolio construction and diversification, but market prices carry useful information about size and liquidity and cap weighting itself provides an important link to company earnings. While equal weighting and risk parity do act as effective mechanisms to achieve technical diver-sification, their shortcomings make them less attractive as implementable solutions. In future papers we will explore other alternatives to strict capitalization-weighted investing within equities.

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Fundamentals of Smart Beta Investing Swings & roundabouts ...

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