## Saturday, October 3, 2015

### Momentum signals in the term structure of commodity futures - Boons, Prado 2015

Basis-momentum (the difference between the momentum of nearby and next nearby contracts) strongly predicts spot returns. It also predicts the spread return. These returns are beyond the classical momentum and carry returns for commodity futures. This does not depend on the presence of institutional investors in commodity markets.

#### Introduction

Literature states that cross-sectional variation in commodity futures returns in largely driven by the characteristics basis (carry) and momentum. Portfolio sorted on basis-momentum predicts both outright and spread with an IR of around 1. This is 12-1 kind of momentum on the cross-section. Basis momentum effectively captures the interaction effect between basis and momentum. The motivation for looking at basis-momentum is that there should be additional information in the decision of producers, consumers, and speculators as to where in the futures curve they take their positions, due to seasonality in production and demand.

#### Methodology

Continuous contracts are rolled on the last day of the month before expiry. The basis is defined as $B(t)=\frac{F_{T_1}(t)}{F_{T_2}(t)}-1$. The momentum is defined as $M(t)=\prod_{s=t-11}^{t-1}(1+r_{T_1}(s))-1$. Finally, the basis momentum is $BM(t)=\prod_{s=t-11}^{t-1}(1+r_{T_1}(s))-\prod_{s=t-11}^{t-1}(1+r_{T_2}(s))$ and spread return momentum is $SM(t)=\prod_{s=t-11}^{t-1}(1+r_{T_1-T_2}(s))-1$. Spread returns are defined as $r_{T_1-T_2}(t)=\frac{(F_{T_1}(t)-F_{T_2}(t))-(F_{T_1}(t-1)-F_{T_2}(t-1))}{F_{T_1}(t-1)}$

We see that $$r_{T_1-T_2}(t) = r_{T_1}(t)-r_{T_2}(t) + r_{T_2}(t)\frac{B(t-1)}{1+B(t-1)}.$$ which translates to $$SM(t) = BM(t) + \sum\left(r_{T_2}(t)\frac{B(t-1)}{1+B(t-1)}\right).$$ The second term is the interaction effect, which consists of next nearby momentum and carry momentum.

A large literature shows that sorting commodities on the basis (carry) leads to large spot returns. Szymanowska (2014) show that basis also predicts spreading returns. Similarly, a large literature shows that sorting commodities on momentum leads to large spot returns as well. Szymanowska (2014) show that momentum do not predict spreading returns. This paper shows that sorting commodities based on basis momentum outperforms the previous two. Persistence in the tilting of the term structure is what basis-momentum tries to capture.

#### Tests and results

1. Does Basis-momentum predict returns in the cross-section?: We regress the spot and spread returns over the three factors Basis, momentum and basis-momentum in two regressions. - We see that all three signals have predictability but it is basis-momentum which beats them all. Basis momentum is the only factor predicting cross-sectional spreading returns.
2. Is Basis-momentum a priced risk factor?: We do time series regressions to determine whether the basis-momentum factors are spanned by basis and momentum factors. Then we conduct Fama-MacBeth cross-sectional regressions for commodity factor pricing models containing basis, momentum and basis-momentum. - basis momentum provides the best Sharpe of 0.93 for spot and 0.99 for spreading returns.