What is contango?
– Contango is a market state in which the futures price of an asset is higher than its current spot price. On a futures curve (plotting price versus contract maturity), contango shows up as an upward slope: later-delivery contracts trade at higher prices than near-term or spot contracts.
Key definitions
– Futures contract: a standardized agreement to buy or sell an asset at a specified price on a specified future date.
– Spot price: the price to buy and take delivery of the asset immediately.
– Carrying costs: expenses related to holding a physical commodity (storage, insurance, and financing).
– Convenience yield: the non-monetary benefit of holding the physical commodity now (for example, ensuring supply for production).
– Backwardation: the opposite of contango—futures prices are below the spot price (downward-sloping curve).
Why contango happens (main drivers)
– Financing/interest costs: money tied up to buy the asset now has an opportunity cost equal to interest rates.
– Storage and insurance costs: physical commodities incur outlays while held; future buyers avoid those costs.
– Low convenience yield: if holding the physical asset offers little operational advantage, futures will include carrying costs more fully.
– Expectations about supply/demand or future shocks: optimistic expectations about future scarcity can push future prices above spot.
– Market structure and liquidity: how market participants hedge, speculate, and roll positions affects curve shape.
Simple pricing relation (no-arbitrage intuition)
– In a basic, no-arbitrage model, a futures price equals the spot price plus net carrying cost over the contract life:
F ≈ S × (1 + r × T) + storage − convenience yield
where S is spot, r is the risk-free rate (annual), T is time to expiry in years. This is an approximation; continuous compounding or other adjustments may be used in precise models.
Worked numeric example (3-month oil contract)
– Assumptions: spot oil S = $50 per barrel; annual risk-free rate r = 2%; storage cost for 3 months = $0.40 per barrel; convenience yield = $0 (assumed negligible).
– Interest for 3 months: r × T = 0.02 × 0.25 = 0.005 → S × (1 + 0.005) = 50.25
– Add storage: 50.25 + 0.40 = $50.65
– Interpretation: the 3-month futures price would be about $50.65, i.e., higher than spot — an instance of contango. If observed market futures are at or above that level, the curve is in contango given these assumptions.
What contango tells you about the market
– Normal condition: contango is common, especially for commodities with meaningful carrying costs, because those costs raise future prices relative to spot.
– Sentiment signal: contango can reflect expectations of higher future prices (bullish), or simply reflect carrying costs and low convenience yields; interpretation requires context.
– Convergence: as the contract approaches expiry, futures prices and the spot price tend to converge. That convergence is a structural property of futures markets.
Impacts on investors and funds
– Rolling cost for long commodity funds: funds that maintain constant exposure by selling near-term futures and buying longer-dated ones pay the difference if the curve is in contango. These “roll losses” can erode returns over time.
– Beneficiaries: holders of physical inventory (producers, consumers with storage) can profit by selling forward at higher prices; arbitrageurs can exploit predictable differences when logistics allow.
– Hedging and supply management: producers can lock in future sale prices; consumers can delay buying to avoid storage costs.
Small numeric example of ETF roll loss
– Suppose a commodity ETF holds front-month futures at $50 and next-month futures trade at $51 (contango of $1). Each month the ETF must sell the $50 contract and buy the $51 contract, realizing a $1 per-unit roll cost. Over 12 months that would sum to $12 per unit (ignoring price moves), which materially reduces returns for buy-and-hold investors.
Advantages and disadvantages of contango
– Advantages:
– Allows producers/consumers to hedge future prices.
– Reflects real carrying costs — prices internalize storage and financing.
– Can signal market expectations about future scarcity or demand.
– Disadvantages:
– Persistent contango creates headwinds for investors using rolling futures-based strategies (ETFs/ETNs).
– It can be costly to maintain exposure without taking physical delivery.
– Large contango can indicate surplus supply today but uncertainty about future availability—ambiguous for macro outlook.
Backwardation—brief contrast
Backwardation — brief contrast
Definition and intuition
– Backwardation (pronounced “back‑war‑day‑shun”) is the opposite of contango. It occurs when futures prices for later delivery are lower than near‑term futures (F2 < F1). Traders typically call this a “backwardated” term structure.
– Intuition: markets may be backwardated when current demand or shortage makes prompt delivery more valuable than future delivery, or when there are convenience yields (the non‑monetary benefit of holding the physical commodity).
How roll yield works in backwardation
– Roll yield is the gain or loss realized when a futures‑based investor sells (or lets expire) the expiring front‑month contract and buys the next‑month contract. In backwardation, rolling tends to produce a positive roll yield because F2 < F1.
– Simple per‑roll formula (no spot moves, no fees):
– Roll cost (dollars per unit) = F2 − F1.
– Roll yield (fraction) = (F1 − F2) / F1. Positive in backwardation; negative in contango.
– Annualizing:
– Simple annualized ≈ roll_yield_per_roll × number_of_rolls_per_year.
– Compound annualized = (1 + roll_yield_per_roll)^(rolls_per_year) − 1.
Worked numerical examples
1) Contango case (recap to contrast)
– F1 = $50 (front-month), F2 = $51 (next-month). Roll yield per roll = (50 − 51)/50 = −0.02 = −2% per roll.
– If you roll monthly: simple annual ≈ −2% × 12 = −24%. Compound annual ≈ (0.98)^12 − 1 ≈ −21.6%.
– Interpretation: rolling costs compound and materially reduce returns if the term structure stays unchanged.
2) Backwardation case
2) Backwardation case
– Example inputs: front-month F1 = $50, next-month F2 = $49.
– Roll yield per roll = (F1 − F2)/F1 = (50 − 49)/50 = 0.02 = 2% per roll.
– If you roll monthly: simple annual ≈ 2% × 12 = 24%.
– Compound annual ≈ (1.02)^12 − 1 ≈ 26.8%.
– Interpretation: if the term structure stays like this and nothing else changes, repeatedly selling the near contract and buying the farther contract (rolling) produces a positive contribution to total return equal to the roll yield.
Practical checklist — how to measure roll impact yourself
1. Choose the two contracts to compare. For most roll-cost estimates use the front-month (nearest expiry) and the next-month contract. For longer-dated roll programs (e.g., a quarterly roll), use the specific contracts an ETF or fund uses.
2. Read the live futures prices (best bid/ask midpoints or last trade) for both contracts. Use the same timestamp for each price.
3. Compute one-roll roll yield as percentage: (front price − next price) / front price. (Positive = benefit; negative = cost.)
4. Convert to dollars-per-unit if you need cash impact: next_price − front_price.
5. Annualize according to your rolling frequency:
– Simple annual ≈ roll_yield_per_roll × rolls_per_year.
– Compound annual ≈ (1 +
1 + roll_yield_per_roll)^(rolls_per_year) − 1.
Notes on annualization
– For small per-roll yields ( Fee_dollars = $5.00.
Fee_pct = 5 / 50 = 0.10 = 10.0% per roll
Fee_annual = 10.0% * 12.167 = 121.67%
Net_annual_roll = 48.67% – 121.67% = -73.00%
Interpretation: with fixed per-roll fees this small front price example becomes dominated by fees; always scale fees to contract size/price.
ETF adjustment example
– Suppose an index futures strategy shows Roll_annual = 8.0% (i.e., roll is a cost).
– Collateral_yield = 1.5% (cash income from collateral).
– Management_fee = 0.75%.
Net_effect = 8.0% – 1.5% – 0.75% = 5.75% annual drag.
Notes on interpretation
– Annualizing short-term roll yields can create large numbers that overstate economic meaning if constructed naively; always compare to realized variance and other return drivers.
– Per-roll fixed-dollar costs matter most when front prices are low; express fees in percentage terms for apples-to-apples comparison.
– If Y_roll is negative, rolling produces a gain (typical in backwardation). If positive, rolling produces a cost (typical in contango).
10) Implementation checklist for researchers and traders
– Data: obtain continuous front and next contract price series with clean roll rules.
– Snapshots: decide timestamp and use same time each day.
– Contract matching: account for contract codes, exchange holidays, and differing expiry calendars.
– Fees: include commissions, exchange/clearing fees, bid-ask spread estimates, and any known slippage.
– Collateral and financing: estimate collateral yield (cash rates) and financing costs if using margin/leverage.
– Historical analysis: compute one-roll series; summarize mean, median, sd, and percentiles; examine seasonality and regime breaks.
– Robustness: test several roll rules (e.g., calendar roll vs. volume/liquidity based) and different rolling horizons.
– Stress tests: simulate spikes in contango/backwardation (e.g., 2–3σ moves) and sudden changes in collateral yield.
– Reporting: present annualized and per-roll numbers, and clearly state assumptions used.
11) Common pitfalls and cautions
– Mixing contract vintages: avoid pairing non-consecutive contracts or inconsistent roll rules when computing a historical series.
– Ignoring basis adjustments: cash-futures basis and local index conventions can affect observed term structure.
– Overannualizing: short periodic yields can look extreme
– Overannualizing: short periodic yields can look extreme — avoid mechanically multiplying a single-roll or one-month roll yield by 12 (or 252) without testing whether the rate is representative and whether compounding is appropriate. Example: a one-month contango of 2.5% implies (1 + 0.025)^12 − 1 ≈ 34.5% if compounded monthly, but simply reporting “30% annualized” or “2.5% × 12 = 30%” can mislead. Instead report per-roll and compounded annualized figures, and show the distribution of monthly roll gains to indicate variability and skew.
– Ignoring transaction costs and slippage: bid-ask spreads, exchange and brokerage fees, market impact and slippage reduce realized roll yield. Always deduct realistic round-trip costs per roll before annualizing. Example: a 0.2% liquidity cost per roll on a 2.5% monthly roll reduces net monthly to 2.3% and the compounded annual result materially.
– Survivorship and selection bias: constructing historical roll series only for contracts that survived or for liquid regimes can bias results. Use the full set of available contract data and document any data exclusions.
– Roll-rule mismatch: using a different roll rule for historical backtest than for live implementation (e.g., volume-weighted roll historically but calendar roll in live trading) produces unrealistic backtest results. Keep rules consistent and stress-test alternatives.
– Mixing instruments and indices: swaps, ETFs, and different futures contract specifications (e.g., physical delivery vs. cash-settled) have different mechanics and costs. Make explicit when converting between contract types or using an index as a proxy.
– Conflating contango with guaranteed losses: contango indicates the futures curve is priced above spot, not that investors will necessarily lose money. Realized P&L depends on roll timing, transaction costs, collateral yield, and spot movement. Backwardation can also produce losses if spot falls sharply.
– Tax and accounting effects: mark-to-market taxation (Section 1256 in the U.S.), realized/unrealized gains treatment, and accounting for margin or collateral can materialy affect after-tax returns. Seek tax guidance for applications.
Practical checklist for evaluating roll yield and contango risk
1. Define universe and contracts: list exchanges, contract months, tick/value, and delivery conventions.
2. Specify roll rule: calendar date, volume/liquidity threshold, or staggered roll; apply consistently.
3. Collect clean prices: front and next contract mid-prices or trade prints; document data gaps.
4. Compute per-roll contango: (NextPrice − FrontPrice) / FrontPrice for percentage; also keep absolute dollar per contract.
5. Adjust for costs: subtract estimated bid-ask, commission, and slippage per roll; include financing/collateral yield.
6. Annualize carefully: show per-roll, simple annualized, and compounded annualized numbers; report assumptions.
7. Analyze distribution: mean, median, standard deviation, skew, kurtosis, and percentiles of per-roll values.
8. Run scenario tests: sudden shifts to 2–3σ contango/backwardation, changes in collateral yield, and liquidity shocks.
9. Document: all assumptions, roll dates, costs, and data sources in reproducible form.
Worked numeric example (crude illustration)
– Front-month price = $80.00; next-month price = $82.00.
– Monthly contango = (82 − 80) / 80 = 0.025 = 2.5% per roll.
– Assume transaction cost per roll = 0.2% and financing/collateral cost = 0.5% (net negative to returns).
– Net monthly = 2.5% − 0.2% − 0.5% = 1.8%.
– Compounded annualized net = (1 + 0.018)^12 − 1 ≈ 23.9%.
– Interpretation: headline contango (2.5% monthly) looks large when annualized, but net-of-costs (1.8% monthly) and volatility of monthly outcomes must be considered; a