Beta-arbitrage strategies: when do they work, and why?

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Notes

1 Erb and Harvey (2006) show the potential of portfolio excess growth rate in the domain of commodity indices. Regularly rebalancing a portfolio in which asset variances are high and correlations are low, as equation (1(1) ) clearly shows, is one of the few high-confidence ways investors can boost portfolio return. More recently, Choueifaty and Coignard (2008) introduce ‘Most-Diversified Portfolios’ whose weights maximize a ‘diversification ratio’ defined as the ratio of the weighted average of asset volatilities divided by the portfolio volatility. They show that these portfolios have the strongest out performance potential relative to a market-cap benchmark. It should be mentioned that maximizing the diversification ratio is related to maximizing portfolio excess growth rate.

2 Our results are robust to alternative choices of the size of the rolling window.

3 Asset covariance are estimated using a one factor market model.

4 Results in the table are in monthly values.

5 A possible explanation for the over performance of the beta strategy described above is related to credit margin, as explained in Frazzini and Pedersen (2014). We address this issue in section 4.2 by considering an investment strategy which is based on indices and therefore not subject to the credit margin restrictions.

6 In the following section all the covariance estimates are obtained by computing the sample covariance over a 60-month rolling window. The focus of the following sections is to illustrate that our results apply to various data-sets. A formal implementation of these strategies might benefit from an improved covariance estimation. We leave this analysis for future research.

7 The use of monthly returns is justified by our assumption that asset logarithmic returns obey Brownian motion processes and by the fact that at short time scales (e.g. daily), the distribution of logarithmic asset returns is known to deviate from normality.

8 Our results are robust to alternative choices of the size of the rolling window.