Contango vs Backwardation - Futures Curve and Cost of Carry

Hook: Why Can Oil Cost $82 and $85 at Same Time?

May 15 2025 you look at NYMEX: Crude June $82, December $85. Same commodity, two sellers, $3 difference. Not a system error. It’s contango. And that contango eats your money if you hold DBC or USO ETF.

On other hand, March 2022 when war broke: March $115, December $95 – $20 backwardation! Market screamed: “I need oil NOW, not December”. Those who understood made fortune on spreads.

Futures curve is EKG of commodity market.

Table of Contents

1. What futures term structure is
2. Cost of carry - storage costs
3. Convenience yield - why owning physical has value
4. Formula F=S*e^(r+u-y)T – breakdown
5. Contango vs Backwardation – definitions and causes
6. Roll yield – silent ETF killer
7. Why it matters for trader
8. Numerical example: Gold price calc
9. Case study: USO and -$37 in 2020
10. How to apply
11. Common mistakes
12. Practical exercises
13. Checklist
14. Summary

Futures Term Structure - What Is It?

Term structure is chart of futures prices on same commodity with different expiries. X axis: time to expiry (M1, M3, M6, M12). Y axis: price.

Two states:

• Contango: Further contracts cost more (upward sloping). F > S. Normal state for most storable commodities.
• Backwardation: Further contracts cost less (downward sloping). F < S. Signal of shortage, panic for immediate delivery.

Cost of Carry - How Much to Store Oil in Tank?

Cost of carry = all costs to hold physical:

• r – interest rate: cost of capital (borrow to buy oil)
• u – storage cost: tank rental, insurance, transport
• y – convenience yield: benefit of holding physical NOW (refinery can produce)

When warehouses full, u up → deeper contango. When empty, y up → backwardation.

Formula: F = S * e^((r+u-y)T)

Fundamental futures pricing model for commodities with convenience yield:

F = S e^((r+u-y)T)

Where F futures price, S spot price, r risk-free rate (continuous, e.g., SOFR 5%), u storage cost as % of spot per year (e.g., oil 8% annually), y convenience yield % per year (e.g., 15% in shortage crisis), T time to expiry in years (0.5 =6 months), e natural log base.

Sign interpretation:

• (r+u-y) >0 → F>S → contango
• (r+u-y) <0 → F<S → backwardation

Numerical Example: Gold GC

S = $2000/oz r=5%=0.05 u=0.5% (gold cheap to store in vaults)=0.005 y=0% (gold has no industrial convenience yield normally) T=1 year

F = 2000 e^((0.05+0.005-0)*1 = 2000 e^(0.055 = 2000 * 1.0565 = 2113 USD

So 1-year gold should cost ~$2113. In practice gold market is in mild contango 2-6% yearly.

Example: Oil in Backwardation 2022

S=$110 r=3%=0.03 u=8%=0.08 (tanks expensive, no space) y=25%=0.25 (refineries pay fortune for immediate delivery due war) T=0.5 year

Exponent = (0.03+0.08-0.25)*0.5 = (-0.14)*0.5=-0.07

F = 110 * e^{-0.07} = 110 *0.9324 = 102.56 USD

Backwardation $7.44 despite high storage – convenience dominates.

Roll Yield - Why ETFs Lose?

Commodity ETFs (USO oil, UNG gas) don’t hold physical oil. They hold front month futures and must roll monthly: sell expiring contract and buy next.

• In contango: sell cheap (82), buy expensive (85) → loss -3 USD each roll = negative roll yield 15-20% annually!
• In backwardation: sell expensive (85), buy cheap (82) → gain +3 = positive roll yield

Thus USO lost 80% vs spot oil price over 10 years though spot flat.

Why It Matters For Trader?

1. Don’t hold commodity ETFs long-term in contango. Better buy producer stocks or futures with far date.
2. Backwardation = strength signal. If CL in backwardation >5%, don’t hunt short hard. Market says shortage.
3. Calendar spreads: When contango extreme (>10% annualized), short spread (sell front, buy back) betting on normalization.
4. Physical purchase timing: Airlines buy annual forwards when curve in contango is flat and cheap.

Market Example: Calculation for $12,500 Account (50k PLN)

Trader wants long oil but worries about backwardation? Checks CL curve:

M1: 80.00, M3: 79.20, M6: 78.00, M12: 76.50 – backwardation 3.5 to M12 (4.3%).

Interpretation: Market pays premium for oil now. Long front month better than M12 because positive roll yield.

Want long 1 CL front: margin $7,000 (~28,000 PLN). Account 50k PLN = $12,500, utilization 70% – risky! Better MCL (micro crude) 100 barrels – 1/10 size – margin $700 (~2,800 PLN) =7% account, safe.

Roll calc: If hold MCL 6 months in backwardation, earn roll: difference M1-M2 ~0.8 *100 = $80 ~320 PLN premium just from roll besides price move.

Case Study: USO and Armageddon -$37 April 2020

April 2020: oil demand -30%, Cushing storage 95% full.

CL curve: May $10, June $22, Dec $35 – super contango 250%!

USO held May contract. Had to roll April 14: sold May at $20 then $15, bought June at $26 – loss 30% in ONE day roll.

Then May fell to -$37 April 20 because nobody wanted physical delivery. USO lost 75% in 2 months though 6-month oil price down only 40%.

Lesson: In super contango never hold front month. Pros moved to 6-12 month contracts or equities.

How to Apply

5-minute daily workflow:

1. Go to cmegroup.com -> crude settlements, see curve (or barchart.com/futures/quotes/CL*1)
2. Calc % diff M1 vs M12: (M12-M1)/M1*100
3. If >+8% – strong contango – look for short spread or avoid long ETF
4. If <-5% – backwardation – look for long front or bull calendar spread
5. Note implied convenience yield: y = r+u - ln(F/S)/T – if >15% panic buying

For gold curve almost always contango – ignore up to 3%, react above 6% (high rates signal).

Common Mistakes

1. Thinking F = forecast of future spot. No! F is spot + cost of carry today. Market not forecasting 85, only saying cost to carry is 85.
2. Buying UNG/USO for winter/summer and holding. Roll eats you. Check 5-year UNG chart – down 90%.
3. Ignoring seasonality: NG contango summer normal (tanks fill). But contango 30% in January anomaly – mild winter signal.
4. Calculating contango on 1 pair. Look at whole curve M1-M12, not only M1-M2.
5. Forgetting rates: r US 5.5% in 2024 deepens contango vs 0% in 2021. Changes math.
6. Trading futures without checking First Notice Date. If hold to delivery you may get call to receive 1000 barrels oil in Oklahoma.

Practical Exercises

Exercise 1: S = 25 PLN/kg wheat spot, r=6%, u=3% storage, y=2%, T=0.25 (3 months). Calc F.

Solution: exponent=(0.06+0.03-0.02)0.25=0.070.25=0.0175. F=25e^(0.0175)=251.01765=25.44 PLN.

Exercise 2: Check current CL curve at barchart. Calc (M6-M1)/M1100% and (M12-M1)/M1100%. Contango or backwardation? Annual roll yield?

Exercise 3: Account $12,500 (50k PLN). Want gas NG exposure. Micro NG margin $1,100 (~4,400 PLN). ETF UNG roll cost -30% annually. Which choose for 3-month winter trade and why? Calc.

Checklist Before Entering Commodity

• Checked curve M1, M3, M6, M12 – structure type?
• Calculated annualized contango/backwardation %
• Know roll yield if holding >1 month?
• If ETF – front month or optimized (e.g., USO 2.0)?
• Checked EIA inventories (oil/gas) – do high stocks explain contango?
• Accounted for interest rates r – high?
• Know First Notice Date of my contract – won’t accidentally enter physical delivery?

Summary and Next Steps

Term structure is more than chart. It’s info about inventories, fear and costs. Formula F=S*e^((r+u-y)T) says futures price = spot + capital + storage - convenience of now.

Contango = you pay for storage, backwardation = market pays you for giving commodity now. ETFs die in contango via negative roll yield.

Next lesson we dissect specific contracts: GC (gold) safe haven, CL (oil) volatility king, NG (gas) widow-maker and ZW (wheat) weather market – details that decide your margin and profit.

Task: Daily for week note CL curve M1 vs M12. See how it lives.