Taking the right course navigating the ERC universe

Abstract

We study the equal risk contribution (ERC) investment strategies exploring how these portfolios perform relative to traditional risk-only (minimum variance portfolio), risk–return (Markowitz portfolio) and naïve (1/n) investment schemes when expanding the asset class universe. We propose a combinatorial mechanism to expand the investment universe of all feasible ERC portfolios and then combine them, thus realizing an ERC efficient frontier consistent with the mutual fund separation theorem (Merton in J Financ Quant Anal 7:1851–1872, 1972). In doing this, we mitigate the out-of-sample estimation error in portfolio weights and better diversify asset allocation against unpredictable extreme events. Simulation, bootstrapping and empirical experiments indicate that the corresponding tangency portfolio, computed through the regression-based approach introduced in Britten-Jones (J Finance 54:655–671, 1999), offers better risk-adjusted performance relative to risk-only, risk–return-based competitors as well as the 1/n strategy.

Appendix: Asset class benchmarks

In this Appendix, we report summary statistics and correlations computed for the 8 indices we used as benchmarks for the asset class universe used to realize ERC, GMV, MV and 1/n portfolios. Statistics and correlations are computed over different time intervals.

Tables 7 and 8 report, respectively, summary statistics and correlation structures computed for different time intervals over the entire period from January 1996 to August 2013 of the 8 asset classes used in forming portfolios in our empirical analysis. We first note, as expected, high correlations between equity-based indices especially during stress scenarios (2007–2008 and 2009–2011). Despite the increasing integration of equity markets as shown by correlation structures computed for different time periods reported in the table, European and US equity indices have been notwithstanding included in the dataset, since they are representative of the two main equity markets taken into account by portfolio managers.

Table 7 Asset class benchmarks summary statistics

Table 8 Asset class benchmarks correlations

The Euro government bonds market index plays an important role in portfolio construction, as it tends to act as “portfolio stabilizer” for two reasons. First, as given in Table 7, the index exhibits low volatility also across time with a range of 1.1–1.4%. Second, the index contributes substantially to the portfolio diversification, as proven by looking at correlations with equity markets (except for the periods 1996–2000 and 2012–2013). Similarly, the US Corporate Bond Market index contributes to better diversifying portfolios, as it shows stable returns (Table 7) and sometimes negative correlations (Table 8). However, the index differs from government bond dynamics, especially during periods of corporate default clustering as in 2007–2011, when returns dynamics were mostly driven by credit spreads.

High-Yield and Emerging Market bond indices are two important asset classes, especially in the short run. While descriptive statistics and correlations show that the two indices seem to deliver the same risk-adjusted profile with high correlations, in the short run they may differ significantly in terms of risk and returns (see, e.g., Table 7, 1996–2000 and 2012–2013). Another interesting feature of the High-Yield bond index concerns the high correlation with equity markets with spikes during extreme negative returns of equities, as was the case during the period from 2007 to 2008. This pattern is contrasting with correlations between Investment Grade bonds and equity markets that remained low during times of negative equity returns (see correlations with the Euro, the US and Emerging Markets equity indices during the period 2007–2008).

The emerging market bond index shows higher correlations relative to equity than relative to fixed income, and the Emerging Markets equity index has shown increasing correlations with the Euro and US equity markets as capital market integration became substantial across countries.

Finally, data in tables confirm that commodity acts as an important asset class portfolio diversifier due to its low or negative correlation with traditional asset classes over the long term. However, during periods of economic downturn, such as in the late 2000s, commodities’ correlation with other asset classes, especially equity, tended to sharply increase. Note that commodity delivered equity-like performance over the long run, albeit with significant variations in recent decades. Specifically, such an asset class experienced the best performance relative to equity and fixed income during times of high inflation (2001–2007), thus helping in mitigating the negative effects of inflation risk.