Core-satellite investing with commodity futures momentum

Abstract

Core-satellite strategies are often implemented to combine the benefits of passive and active investing. Our study analyzes a particularly attractive and quasi-frictionless core-satellite approach: Adding active commodity futures momentum satellites to passive cores diversified across traditional asset classes. We show that momentum portfolios, enhanced by long-term reversal and skewness information, are highly valuable satellites. Considering them with low fixed weights, as suggested by popular strategic allocations, leads to significant improvements in investment performance and reduces portfolio sensitivities to shocks in investor fear. In contrast, using time-varying optimized weights based on satellite alphas or tail risk minimization turns out to be less advantageous. Interestingly and regardless of the considered weighting scheme, momentum satellites shine primarily by lowering portfolio risk (instead of increasing portfolio return) which supports modern interpretations of the role of active management.

Appendices

Appendix A: Supplementary results

See Figs. 4, 5, 6 and Tables 12 and 13.

Fig. 4

Satellite performance for different quantile breakpoints. This figure presents the minimum, mean, and standard deviation of the monthly percentage returns generated by our long–short commodity momentum strategies under median-, tercile-, and quintile-based sorting. Sample period and abbreviations are used as in Table 2

Fig. 5

Satellite value. This figure compares the cumulative investment performance of an equal weighted commodity momentum strategy (Mom-Equal) to two alternatives with robust weighting based on long-term reversal (Mom-LtPot) and skewness (Mom-Skew) information (see Sect. 3.1)

Fig. 6

Satellite composition. For each commodity and sample month, this figure shows whether our momentum satellite suggested a long (blue) or a short (orange) position. The empty space represents the different inception dates of the commodity futures

Table 12 Treynor–Black results without short-selling restriction

Table 13 Return sensitivity of alternative strategic allocations

Appendix B: Robust estimation

The parameters of a standard linear regression model explaining a dependent variable y by an independent variable x are typically estimated via OLS, i.e., by minimizing the objective function ${\mathcal {L}}(\alpha ,\beta )$, which captures the sum of squared model residuals:

$$\begin{aligned} \begin{aligned}&(\hat{\alpha },\hat{\beta })=arg \min \limits _{\alpha ,\beta } {\mathcal {L}}(\alpha ,\beta ), \\&{\mathcal {L}}(\alpha ,\beta )=\sum _{t=1}^T (y_t-\alpha -\beta x_t)^2. \end{aligned} \end{aligned}$$

(8)

Because this objective puts large emphasis on extreme residuals, outliers in the data can have crucial effects on intercept and slope estimates. Robust Huber (1973) regression is a popular method to circumvent such influences. It involves using the alternative objective function

$$\begin{aligned} {\mathcal {L}} (\alpha ,\beta )=\sum _{t=1}^T H(y_t-\alpha - \beta x_t;\,c), \end{aligned}$$

(9)

where

$$\begin{aligned} H(x; c)=\left\{ \begin{array}{lll} x^{2}, & \text{ if } & |x| \le c, \\ 2 c|x|-c^{2}, & \text{ if } & |x|>c, \end{array}\right. \end{aligned}$$

(10)

represents the so-called Huber loss function and c is a tuning parameter. Intuitively, if the residuals are small enough in relation to c, we have the classical OLS objective. However, the more the residuals deviate from c, the more they are smoothed.

The default value for c in the statistics literature is 1.345 which yields 95% efficiency under a Gaussian model. To allow for non-normality of returns, we additionally consider $c \in \{1,2,5\}$ (see Gu et al. 2020).