Far from the Madding Crowd – Volatility Efficient Indices
Authors: Frank Nielsen, Raman Aylursubramanian
Source: MSCI Barra Research Insights
Date: April 2008
Nielsen and Aylursubramanian note a recent rise in the popularity of minimum variance strategies and propose to develop a global minimum volatility index to serve as a benchmark for evaluating these strategies. Initially introduced by Markowitz (1952), the minimum variance (MV) portfolio is not only the efficient frontier portfolio with the lowest risk for a given set of assets, but also the one that can be computed without estimating expected asset returns.
According to the Capital Asset Pricing Model (CAPM, Sharpe, 1964), any combination of the market portfolio and the risk-free asset should dominate the MV portfolio in terms of efficiency. Nielsen and Aylursubramanian recall that the CAPM is based on various assumptions that do not meet realistic market conditions. In addition, the capitalisation-weighted indices serving as proxy for the market portfolio may not be efficient. As a result, it is possible to produce an empirical MV portfolio dominating an empirical market line constructed using a cap-weighted index. Among others, the major explanation proposed to explain the empirically observed superiority of the MV portfolio is that this portfolio is free from errors in expected return estimation (for example, see Chora and Ziemba, 1993). Building MV portfolios is thus a safe way to produce efficient portfolios.
Using the MSCI World Index security universe, the authors propose to derive a minimum variance index. The index was constructed using the global equity covariance matrix from the Barra Global Equity Model, which is supposed to be more robust than a covariance matrix created using historical returns. The major concerns in the construction rules were to ensure a replicable and investable index. For example, minimum and maximum constraints are imposed on assets, sectors and countries, in order to ensure index diversification. Another rule is to limit the turnover to 10% at each semi-annual rebalancing. This MV index, named the MSCI World MV Index, was computed from June 1995 to December 2007.
The authors present the performance characteristics of the MSCI World MV Index and compare them to the MSCI World Index and to a long duration US Fixed Income Index. Compared to the MSCI World Index, the MV index produces higher returns with a volatility about 30% lower, over the whole period of investigation (1995-2007). During an expansionary period (tech boom and internet bubble), the MSCI World index produced higher returns than the MV index. Conversely, the MV index outperformed during the recessionary period (when the bubble burst). Further, the authors observed a loss of 45% for the MSCI World Index between the top (March 2000) and the bottom (March 2003) of the tech boom, while the MV index encountered a loss of only 18% during the same period, which makes them conclude that the MV index offers downside protection compared to the cap-weighted index. In addition, over the 1995-2007 period, the MV index risk appears to be comparable to the risk of the long duration fixed income index. Finally, looking at the worst monthly declines, MV index losses are lower than those of the MSCI World Index and comparable to those encountered by the fixed-income index. In conclusion, the MV index can serve as a natural hedge against increasing market volatility.
Finally, the authors present the potential applications of the MV index. This index constitutes a suitable benchmark for investors using low volatility equity strategies, e.g. corporate pension plans or insurance companies. Considering, for example, a portfolio made up of 60% equity and 40% fixed income, the authors observed a 20% decrease in the risk with a minimum variance allocation, compared to a traditional allocation, during two periods, one ending in December 2007 and the other ending in April 2001.
The authors present the MSCI MV World Index as the first global benchmark for managed volatility equity strategies. This index has been designed to be transparent, easily replicable and fully investable, as drawn from the MSCI World Standard Index universe. Thus, they suggest it can serve as a support for index products and exchange-traded funds. The performance characteristics found here for the MV index are consistent with earlier studies focusing on the US and European markets. The present study is original compared to other studies on minimum variance portfolios, as it is not restricted to domestic or regional markets, but extended to the global market.
Chopra, V. K. and W. T. Ziemba, “The Effects of Errors in Means, Variances, and Covariances on Optimal Portfolio Choice”, Journal of Portfolio Management , vol. 19, n°2, 2003, p. 6-11.
Markowitz, H., “Portfolio Selection”, Journal of Finance , vol. 7, n°1, 1952, p. 77-91.
Sharpe, W., “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk”, Journal of Finance , vol. 19, n°3, 1964, p. 425-442.