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Carry

Authors: Ralph S.J. Koijen, Tobias J. Moskowitz, Lasse Heje Pedersen, Evert B. Vrugt | Year: 2018 | Journal: Journal of Financial Economics, 127(2), 197-225

Thesis

Carry -- the expected return from holding an asset assuming the spot price stays constant -- is a ubiquitous return predictor across asset classes. For commodities (including gold and silver), carry is the negative of the futures basis (the slope of the futures term structure). A commodity in backwardation (spot > futures) has positive carry; one in contango (futures > spot) has negative carry. A diversified long-short carry portfolio earns significant risk-adjusted returns. Carry predicts returns even after controlling for momentum, value, and other known factors. The paper unifies carry across equities, bonds, currencies, commodities, and credit into a single framework.

Key Math

Carry for a commodity futures contract:

\[C_t = \frac{S_t - F_t^{(T)}}{F_t^{(T)}} \approx y_t^{(c)} - r_t^{(f)}\]

Where \(S_t\) is the spot price, \(F_t^{(T)}\) is the futures price for maturity \(T\), \(y_t^{(c)}\) is the convenience yield, and \(r_t^{(f)}\) is the funding rate. In practice, using front and second contracts:

\[\hat{C}_t = \frac{F_t^{(1)} - F_t^{(2)}}{F_t^{(2)}}\]

The carry portfolio return is:

\[r_t^{\text{carry}} = \sum_i w_{i,t} \cdot \frac{1}{\hat{\sigma}_{i,t}} \cdot r_{i,t+1}\]

where \(w_{i,t} = \text{rank}(\hat{C}_{i,t})\) (cross-sectional rank) and positions are volatility-normalized.

Data & Method

  • 24 commodity futures (gold and silver included), plus equity indices, bonds, currencies, credit.
  • Sample: 1972-2012 for commodities (varies by asset class).
  • Cross-sectional rank-based portfolios: long top-quintile carry, short bottom-quintile.
  • Time-series variant: long if carry > 0, short if carry < 0.
  • Controls: Fama-French factors, momentum (both cross-sectional and time-series), value.
  • Transaction costs estimated using bid-ask spreads from futures markets.

Our Replication Verdict

PARTIALLY CONFIRMED -- The carry factor works well in a diversified commodity portfolio, but gold and silver specifically are weak carry assets: (1) Gold is almost always in contango (negative carry) due to storage costs and low convenience yield, so the time-series carry signal for gold is persistently short -- which has been a losing position during secular gold bull markets. (2) The cross-sectional carry signal (gold vs. other commodities) is more useful, but requires a commodity universe beyond just precious metals. (3) Silver's carry signal is slightly more variable than gold's due to industrial demand creating periodic backwardation, making it marginally more useful. (4) The key insight for our system: do not use carry as a standalone signal for gold/silver -- use it as a cost-of-carry adjustment to trend and value signals.

Signal Mapping

  • Carry cost adjustment (SS5.2) rather than a standalone signal for gold/silver.
  • The term structure slope (contango depth) modulates position sizing: deeper contango reduces the trend-following position by a carry penalty factor.
  • Cross-sectional carry signal used when trading gold vs. silver vs. platinum (relative carry rank determines relative allocation).
  • Roll yield tracking: The system monitors the futures curve daily and optimizes contract selection to minimize negative roll yield (e.g., rolling at optimal points in the calendar spread).

References

  • Koijen, R.S.J., Moskowitz, T.J., Pedersen, L.H. & Vrugt, E.B. (2018). "Carry." Journal of Financial Economics, 127(2), 197-225. DOI: 10.1016/j.jfineco.2017.12.002
  • Szymanowska, M. et al. (2014). "An Anatomy of Commodity Futures Risk Premia." Journal of Finance, 69(1), 453-482.
  • Erb, C.B. & Harvey, C.R. (2006). "The Strategic and Tactical Value of Commodity Futures." Financial Analysts Journal, 62(2), 69-97.
  • Fuertes, A.M., Miffre, J. & Fernandez-Perez, A. (2015). "Commodity Strategies Based on Momentum, Term Structure, and Idiosyncratic Volatility." Journal of Futures Markets, 35(3), 274-297.