Temporal Arbitrage

Temporal arbitrage exploits price differences between time periods. When forward prices exceed spot prices (contango), storing commodities becomes profitable. Understanding forward curves and storage economics is essential to this strategy.

Forward Curve Structures

Contango

CONTANGO STRUCTURE
──────────────────

Forward price > Spot price

Price
  │
  │                    ╱
  │                 ╱
  │              ╱ Forward
  │           ╱
  │        ╱
  │     ╱
  │──────────── Spot
  │
  └──────────────────────────► Time
       1M   3M   6M   12M

INTERPRETATION:
- Market expects future prices higher
- OR: Cost of carry being priced in
- Storage is rewarded
- Inventory builds

Backwardation

BACKWARDATION STRUCTURE
───────────────────────

Spot price > Forward price

Price
  │
  │──────────── Spot
  │     ╲
  │        ╲
  │           ╲
  │              ╲ Forward
  │                 ╲
  │                    ╲
  │
  └──────────────────────────► Time
       1M   3M   6M   12M

INTERPRETATION:
- Immediate supply is scarce
- Market needs product NOW
- Storage is penalized
- Inventory draws

Why Curves Take These Shapes

Factor	Effect on Curve	Explanation
High inventory	Contango	Surplus must be stored
Low inventory	Backwardation	Scarcity premium today
Interest rates	Contango pressure	Cost of capital
Storage costs	Contango pressure	Holding costs
Convenience yield	Backwardation pressure	Value of having goods now
Supply disruption	Backwardation	Immediate scarcity
Demand surge	Backwardation	Immediate need

The Theory of Storage

Convenience Yield

The benefit of holding physical inventory rather than a forward contract:

CONVENIENCE YIELD FORMULA
─────────────────────────

F = S × e^(r + c - y)t

Where:
F = Forward price
S = Spot price
r = Interest rate
c = Storage cost
y = Convenience yield
t = Time to delivery

Rearranging:
y = r + c - ln(F/S)/t

If F > S(1 + r + c):
  Convenience yield is low → Contango
  STORAGE IS PROFITABLE

If F < S(1 + r + c):
  Convenience yield is high → Backwardation
  STORAGE IS NOT ECONOMIC

Full Carry vs Market Structure

Scenario	Relationship	Storage Decision
Super contango	Forward > Spot + Full Carry	Store aggressively
Contango	Spot < Forward < Spot + Full Carry	Selective storage
Flat	Spot ≈ Forward	No storage incentive
Backwardation	Spot > Forward	Sell immediately

Storage Economics

Cost Components

FULL CARRY COST CALCULATION
───────────────────────────

CRUDE OIL (6-month storage):

STORAGE COSTS:
Tank rental: $0.35/bbl/month × 6 = $2.10/bbl
Tank cleaning: $0.05/bbl
Loss allowance: 0.1% × $75 = $0.08/bbl
───────────────────────────────────────
Subtotal storage: $2.23/bbl

FINANCING COSTS:
Principal: $75/bbl
Rate: 6% APR
Time: 6 months
Cost: $75 × 6% × 0.5 = $2.25/bbl

INSURANCE:
Rate: 0.08%/month
Cost: $75 × 0.08% × 6 = $0.36/bbl

TOTAL FULL CARRY: $4.84/bbl

Breakeven contango: $4.84/bbl over 6 months
= $0.81/bbl/month

Storage Trade Example

CONTANGO STORAGE TRADE
──────────────────────

MARKET OBSERVATION:
Spot WTI: $70.00/bbl
6M WTI: $76.00/bbl
Contango: $6.00/bbl

FULL CARRY:
Storage: $2.10/bbl
Financing: $2.10/bbl (at 6%)
Insurance: $0.36/bbl
Operations: $0.15/bbl
─────────────────────
Total: $4.71/bbl

ECONOMICS:
Contango: $6.00/bbl
Full carry: $4.71/bbl
─────────────────────
Net profit: $1.29/bbl

EXECUTION:
Day 1: Buy spot crude @ $70.00
Day 1: Sell 6M futures @ $76.00
Day 1: Inject into storage

Day 180: Deliver from storage
Day 180: Close futures position
Day 180: Realize $1.29/bbl profit

On 1M bbl: $1,290,000 profit

Storage Assets

Types of Storage

Type	Commodity	Capacity	Cost	Flexibility
On-shore tanks	Oil, products	50K-500K bbl	Low	Low
Underground caverns	Crude, gas	10M+ bbl	Very low	Very low
Floating storage	Oil	2M bbl (VLCC)	Medium-high	High
LME warehouses	Metals	Variable	Medium	High
Grain silos	Grain	50K-500K MT	Low	Low

Floating Storage Economics

FLOATING STORAGE ANALYSIS
─────────────────────────

VLCC AS FLOATING STORAGE:
Capacity: 2,000,000 bbl
Time charter rate: $35,000/day

COSTS (6 months = 180 days):
Charter: $35,000 × 180 = $6,300,000
         = $3.15/bbl
Bunkers (idle): $500,000 = $0.25/bbl
Port costs: $200,000 = $0.10/bbl
Insurance: 0.5% × $150M = $750,000 = $0.38/bbl
Financing: 6% × $150M × 0.5 = $4,500,000 = $2.25/bbl
─────────────────────────────────────────────────────
TOTAL: $6.13/bbl

Compare to: On-shore storage at $4.84/bbl
Floating premium: $1.29/bbl

WHY USE FLOATING?
1. No on-shore capacity available
2. Location flexibility
3. Can discharge anywhere
4. Super contango justifies premium

Calendar Spreads

Trading the Spread Directly

CALENDAR SPREAD TRADE
─────────────────────

Instead of physical storage, trade the spread:

TRADE:
Buy M1 (front month) futures
Sell M7 (6 months out) futures

OUTCOME:
If contango widens → Profit
If contango narrows → Loss

ADVANTAGE:
No physical storage needed
Lower capital requirement
Easier to exit

DISADVANTAGE:
Pure financial exposure
No basis relationship
Settlement risk

Roll Yield

ROLL YIELD IN CONTANGO
──────────────────────

CONTANGO MARKET:
M1: $70   M2: $71   M3: $72   M4: $73

LONG POSITION ROLL:
Month 1: Buy M1 @ $70
Month 2: Sell M1 @ $71, Buy M2 @ $72
         Loss: $1 (roll cost)

ROLL YIELD = Negative in contango
Long positions LOSE from rolling

SHORT POSITION ROLL:
Month 1: Sell M1 @ $70
Month 2: Buy M1 @ $71, Sell M2 @ $72
         Gain: $1 (roll benefit)

ROLL YIELD = Positive for shorts in contango

Seasonal Patterns

Commodity Seasonality

Commodity	High Season	Low Season	Pattern
Natural Gas	Winter (heating)	Shoulder months	Store summer, sell winter
Gasoline	Summer (driving)	Winter	Store spring, sell summer
Heating Oil	Winter	Summer	Store summer, sell winter
Grains	Harvest	Pre-harvest	Store harvest, sell pre-harvest
Sugar	Off-crush	Crush season	Counter-seasonal

Seasonal Storage Strategy

NATURAL GAS SEASONAL TRADE
──────────────────────────

ANNUAL PATTERN:
April (injection starts): Low prices
October (withdrawal starts): High prices

TRADE:
April: Buy gas, inject into storage
October: Withdraw, sell

ECONOMICS:
April price: $2.50/MMBtu
October price: $3.50/MMBtu
Spread: $1.00/MMBtu

Costs:
Injection fee: $0.10
Withdrawal fee: $0.10
Storage (6 months): $0.30
Financing: $0.08
─────────────────────
Total costs: $0.58/MMBtu

Net profit: $0.42/MMBtu

10 Bcf position: $4.2 million profit

Term Structure Analysis

Reading the Curve

CURVE ANALYSIS FRAMEWORK
────────────────────────

SHAPE: What does the curve look like?
├── Steep contango → High inventory, weak demand
├── Mild contango → Balanced market
├── Flat → Equilibrium
├── Mild backwardation → Tightening
└── Steep backwardation → Supply crisis

SLOPE: How steep?
├── Front-end → Near-term supply/demand
└── Back-end → Long-term fundamentals

KINKS: Unusual shapes?
├── Seasonal humps → Expected tightness/surplus
└── Single contract premium → Specific event pricing

Curve Shifts

Shift Type	Cause	Trading Response
Parallel up	Demand increase	Long flat price
Parallel down	Supply increase	Short flat price
Steepening contango	Inventory build	Storage trade
Flattening contango	Inventory draw	Exit storage
Flip to backwardation	Supply shock	Immediate delivery

Risk Management

Temporal Arbitrage Risks

Risk	Description	Mitigation
Curve flattening	Spread narrows before maturity	Hedge spread directly
Storage unavailability	Can’t secure tanks	Contract early
Quality degradation	Product deteriorates	Proper storage conditions
Financing cost spike	Interest rates rise	Fix financing terms
Regulatory change	Storage rules change	Diversify locations

Spread Hedging

HEDGING THE SPREAD
──────────────────

PHYSICAL STORAGE POSITION:
Long physical (stored)
Short forward contract

RISK:
If curve flattens, physical storage loss
But forward contract is locked

ADDITIONAL HEDGE (for residual risk):
If using floating benchmark:
Trade calendar spread to lock specific differential

EXAMPLE:
Physical: Bought at M1
Forward: Sold at M1+6

If M1+6 moves vs M1, basis risk exists
Hedge: Trade the M1/M1+6 spread

Case Study: Oil Contango Trade

CASE: 2020 COVID CONTANGO
─────────────────────────

BACKGROUND:
April 2020: Demand collapsed
Spot WTI: Near zero (briefly negative)
6M WTI: $30+
Contango: $30+/bbl (extreme)

OPPORTUNITY:
Full carry: ~$5/bbl
Spread: $30/bbl
Profit potential: $25/bbl (!!)

CHALLENGE:
All storage booked
Floating storage premium spiked
VLCC rates: $200,000/day

EXECUTION (for those with storage):
Buy spot @ $10/bbl
Store for 6 months
Sell forward @ $35/bbl
Cost: $8/bbl (inflated costs)
Profit: $17/bbl

LESSON:
Storage is most valuable when scarce
Those with pre-booked storage captured windfall
Infrastructure ownership = optionality

Key Takeaways

1. Contango rewards storage — Store when forward > spot + costs
2. Backwardation penalizes storage — Sell immediately
3. Full carry sets the floor — Contango rarely exceeds full carry
4. Convenience yield explains backwardation — Value of having goods now
5. Storage assets create optionality — Most valuable in crisis
6. Seasonality creates predictable patterns — But everyone knows them

References

• Working, Holbrook. “The Theory of the Price of Storage.”
• CME Group. “Understanding Crude Oil Contango.”
• EIA Weekly Petroleum Status Report
• ICE Futures Forward Curves