Tim Olson
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description, tags
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| Commodity futures strategy that captures the negative skewness premium by buying low-skewness and selling high-skewness commodity futures, exploiting the empirical negative relationship between return skewness and expected returns. |
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Skewness Premium
Section: 9.5 | Asset Class: Commodities | Type: Skewness / Risk Premium
Overview
There is an empirically observed negative correlation between the skewness of historical returns and future expected returns across commodity futures. Commodities with highly negatively skewed returns have, on average, higher future expected returns, while those with positively skewed returns have lower expected returns. This mirrors the skewness premium observed in equity options markets and reflects investor preference for positive skewness ("lottery" demand).
Construction / Mechanics
The skewness of returns for commodity i (i = 1,...,N) over T observations is:
S_i = (1 / (σ_i³ T)) Σ [R_is - R̄_i]³ (456)
where:
R̄_i = (1/T) Σ R_is (457)
σ_i² = (1/(T-1)) Σ [R_is - R̄_i]² (458)
and R_is are the historical return observations.
Portfolio construction:
- Rank all N commodity futures by S_i
- Buy futures in the bottom quintile by skewness (most negatively skewed, highest expected return)
- Sell futures in the top quintile by skewness (most positively skewed, lowest expected return)
- Zero-cost portfolio; rebalanced periodically
Return Profile
Profits when the negative skewness-expected return relationship holds out-of-sample: low-skewness (left-tail-heavy) commodities outperform high-skewness (right-tail-heavy) ones. The premium compensates investors for bearing left-tail (crash) risk.
Key Parameters / Signals
| Parameter | Description |
|---|---|
| S_i | Third standardised moment of historical returns |
| T | Estimation window length (number of return observations) |
| Quintile cut-offs | Bottom quintile (buy) vs. top quintile (sell) |
| Rebalancing | Periodic (monthly or quarterly) |
Variations
- Use option-implied skewness (from commodity options) instead of realised skewness for a forward-looking signal.
- Combine with value (Section 9.4) or roll yield (Section 9.1) in a multi-factor commodity model.
Notes
- Realised skewness is estimated with substantial noise, particularly for commodities with short or infrequently traded histories.
- The skewness premium can be concentrated in a small number of time periods; the strategy may have poor risk-adjusted returns in normal markets and large gains during commodity stress events.
- Tail risk is inherent in this strategy: buying low-skewness commodities means accepting left-tail exposure.
- Sufficient sample size T is needed for reliable skewness estimates; skewness estimation requires more data than mean or variance estimation.