**Dimitris Melas**of MSCI.

**Exchange-traded funds**(ETFs) play an important role in the investment process by providing easy access to various asset classes and investment strategies. To achieve this objective, ETFs typically replicate an index that reflects the targeted asset class or investment strategy in an objective and transparent manner. Many equity ETFs in particular use capitalisation-weighted indices. Capitalisation-weighted equity indices capture the relevant equity market beta and provide an objective representation of the opportunity set.

While capitalisation-weighted indices can be efficient tools to gain passive market exposure and capture the market beta, many investors increasingly recognise that there are additional sources of systematic return associated with particular investment styles and strategies that could be captured through alternatively weighted indices. Indices reflecting the systematic elements of specific investment styles or strategies are often called systematic indices and many of them can be further classified into two broad categories, namely risk-based systematic indices and return-based systematic indices.

Risk-based systematic indices incorporate volatility and correlation estimates. Examples of risk-based indices include minimum volatility indices, maximum diversification indices, equal risk contribution indices, risk- weighted indices, and equally weighted indices. Return-based systematic indices proxy expected returns through a common factor and typically weight securities in proportion to their exposure to the targeted factor. Examples of return-based indices include fundamental indices, value indices, high dividend yield indices, momentum indices, leverage indices, and liquidity indices.

In this article we will focus on two particular systematic indices, the risk-weighted index and the value-weighted index, and we will examine their construction methodology, their historical performance, and their potential applications in the asset allocation process.

**Construction methodology**

The objective of a risk-weighted index is to reflect the equity market return, but with lower volatility. This is achieved by reweighting the constituents of a standard market cap-weighted equity index according to the inverse of each stock’s historical variance. Variance is a statistical measure of dispersion that is used widely by investors to assess the risk of different assets. This simple reweighting method ensures that the risk-weighted index remains objective and transparent by including all the constituents from the standard market cap weighted index, but reweighted in a way that tilts the index towards stocks with relatively low historical volatility. Mean variance portfolio theory provides the theoretical underpinning for risk-weighted indices. We can show analytically that a risk-weighted index is the solution to the mean variance portfolio construction problem, subject to constant expected returns and correlations. In other words, for an investor who wishes to maximise risk-adjusted return using only volatilities and without making any assumptions about expected returns and correlations, the risk- weighted approach yields an efficient portfolio.

The objective of a value-weighted index is to tilt an underlying standard equity index towards value stocks. This tilt is achieved by multiplying the market capitalisation weight of each stock in the parent benchmark index with the stock’s relative valuation ratio (for example, earnings to price, sales to price, book value to price, etc). We can show that this approach of tilting an equity index towards value stocks by multiplying market capitalisation weights with relative valuation ratios is equivalent to weighting the constituents of the index according to the respective fundamental accounting variable (for example, earnings, sales, book value, etc). As a result, value-weighted indices are often described as ‘fundamentally weighted’ indices.

**Historical performance**

Exhibit 1 shows the long-term historical simulated performance of risk-weighted and value weighted-indices based on the MSCI World Index. The risk-weighted and value-weighted indices outperformed the MSCI World Index over the observed period of December 1994 to August 2010, both in absolute and risk-adjusted terms. More specifically, the simulated value-weighted index outperformed the MSCI World Index by 1.50% per annum while the simulated risk-weighted index outperformed MSCI World by 2.84% per annum over the observed period. In addition, both the risk-weighted and value-weighted indices experienced lower-realised volatility compared to MSCI World.

What could explain this historical outperformance of risk-weighted and value-weighted indices and how realistic is it to expect that it will continue in the future? Theories explaining the historical performance of portfolios that emphasise a particular attribute, risk factor, or characteristic such as ‘low volatility’ or ‘low valuations’ generally fall into three camps. The first camp, known as the data mining camp, argues that such historical performance patterns are period specific and therefore not likely to persist out of sample. The second camp, often described as the normative finance camp, argues that certain fundamental or trading characteristics such as size, value, momentum, volatility, etc, are proxies for unobservable risk factors. Therefore portfolios tilted towards these characteristics bear higher systematic risk and earn a premium in compensation for this risk. The third camp, known as the behavioural finance camp, argues that behavioural reasons influence the investment decision-making process, leading to imprecision and bias in the pricing of securities that can be exploited systematically through disciplined investment strategies.

It is worth highlighting that many return regularities associated with particular attributes such as value, size, momentum, volatility, etc, were identified and publicised as early as the 1980s. However, many of them persisted in the subsequent 20-30 years. This observation may bring into question the view that all such empirical return regularities should be seen as period specific and the result of data mining. For investors who believe that the historical performance patterns reported in Exhibit 1 were driven by behavioral biases or systematic risk premia that could persist in the future, systematic indices may offer a potentially efficient tool to exploit these patterns in order to enhance long-term portfolio performance, by making allocations to ETFs or other passive vehicles tracking risk-weighted and value-weighted indices.

**Asset allocation applications**

Assuming initial allocations of 60% to equities and 40% to fixed income, Exhibit 2 shows the historical risk reduction and performance enhancement resulting from allocating part of the equity portfolio to a risk-weighted and a value-weighted index. Reducing the allocation to MSCI World by 40% and making a corresponding 20% allocation to risk-weighted and value-weighted indices enhanced the return of the portfolio by 0.83% per annum and reduced its volatility by 0.75% per annum, leading to a 22.5% improvement in the return-to-risk ratio of the portfolio over the observed period.

Equity markets play a central role in many investment portfolios. Individuals saving for retirement and institutions investing to meet future liabilities typically allocate a significant part of their assets to equities hoping to achieve higher returns compared to deposit accounts and fixed-income investments. Historically, equities fulfilled the promise of delivering superior returns over long investment horizons. However, as the recent financial crisis of 2008- 2009 demonstrated, equities can also expose investors to significant levels of volatility and sharp negative returns.

It is interesting to examine how the risk-weighted and value-weighted indices performed during the recent financial crisis. Exhibit 2 shows that in 2008 the risk-weighted index outperformed MSCI World by 3.2% while the value-weighted index underperformed by 1.2%. In the subsequent market recovery of 2009, the risk-weighted index underperformed MSCI World by 1.6% while the value-weighted index outperformed by 1.7%. Therefore the risk-weighted index exhibited defensive characteristics while the value-weighted index experienced pro-cyclical performance during the recent crisis and subsequent market recovery. As a result, the sample policy portfolio that contained 20% allocations to risk-weighted and value-weighted indices outperformed the initial 60/40 portfolio by 0.5% in 2008 while it performed in line with the 60/40 portfolio in 2009.

**Conclusion**

Risk-weighted and value-weighted indices may provide additional tools for investors to implement their strategic asset allocation. During the period we observed, these indices outperformed standard capitalisation weighted benchmarks with similar or lower levels of volatility. Risk-weighted and value-weighted indices also performed relatively well during the increased market volatility of the recent financial crisis of 2008-09. Investors who believe that these historical performance patterns will continue in the future may be interested in financial vehicles tracking risk weighted and value weighted indices with an aim to lower portfolio volatility and enhance portfolio performance. • Dimitris Melas is executive director, head of Emea equity and applied research at MSCI

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