Futures & Forwards: Contracts, Pricing & Mechanics

TAKEAWAYS:

• Forward contracts are custom OTC agreements with no exchange trading, while futures are standardized, exchange-traded contracts with daily margin adjustments.
• The futures price equals the spot price adjusted for interest, storage costs, and convenience yield (if applicable), calculated as $F=S(1+r{)}^T+(C-Y)T$.
• Margin requirements (initial and maintenance) ensure liquidity but can lead to forced liquidation if the contract’s value drops below the maintenance margin.
• Hedging with forwards/futures locks in prices (e.g., a farmer selling wheat futures to avoid price risk), while speculation bets on price movements.
• Delivery vs. settlement: Futures often settle in cash, while forwards require physical delivery (unless offset).
• Negative futures prices occur when storage costs exceed the risk-free rate (e.g., perishable commodities like milk powder).

1. Definitions: Forwards vs. Futures

Forwards and futures are derivative contracts obligating two parties to buy/sell an asset at a predetermined price on a future date. The key differences:

2. How Forward Contracts Work

A forward contract is a private agreement between two parties (e.g., a silver dealer and a jeweler) to buy/sell silver at Rs 1,500 per tola in 12 months. Key features:

• No upfront margin: The dealer pays storage costs (Rs 50/tola/year) and interest on the loan if financing the purchase.
• Custom terms: Delivery date, quantity, and quality are negotiated.
• Credit risk: If the dealer defaults, the jeweler bears the loss.

Example: Silver Forward Contract

• Spot price (today): Rs 1,500/tola
• Storage cost: Rs 50/tola/year (paid semi-annually)
• Risk-free rate (r): 8% per annum (continuous compounding)
• Time to maturity (T): 1 year

The forward price (F) is calculated as: $$F=S\cdot e^{rT}+(C-Y)T$$ Where:

• $S$ = spot price (Rs 1,500)
• $C$ = storage cost (Rs 50)
• $Y$ = convenience yield (assume 0 for silver)
• $r$ = risk-free rate (0.08)
• $T$ = 1 year

Plugging in: $$F=1500\cdot e^{0.08\cdot 1}+50\cdot 1=1500\cdot 1.0833+50=\text{Rs 1,635/tola}$$

Why Rs 1,635?

• The dealer expects to pay Rs 1,500 today, lend it at 8% for a year (Rs 120), and cover storage (Rs 50), totaling Rs 1,670. However, the convenience yield (opportunity cost of holding silver) offsets some costs, bringing the forward price to Rs 1,635.

3. How Futures Contracts Work

Futures are standardized, traded on exchanges (e.g., NEPSE for gold, ICE for wheat), and settled daily (mark-to-market). Key mechanics:

• Margin system: Buyers/sellers deposit initial margin (e.g., Rs 20k for gold futures) and maintenance margin (e.g., Rs 15k). If the contract’s value drops below maintenance margin, a margin call is issued.
• Daily settlement: Gains/losses are settled daily, reducing counterparty risk.
• Liquidity: Traded like stocks; can be bought/sold anytime before expiry.

Example: Gold Futures Margin Call

• Contract: 1 kg gold at Rs 8,400,000/kg
• Initial margin: Rs 200,000
• Maintenance margin: Rs 150,000
• Your position: Long 1 contract (bought at Rs 8,400,000)

Scenario: Gold price drops to Rs 8,200,000/kg.

• Loss per contract: Rs 200,000
• Total margin: Rs 200,000 (initial) – Rs 200,000 (loss) = Rs 0
• Action: You receive a margin call to deposit Rs 50,000 (maintenance margin – Rs 0) to avoid liquidation.

flowchart TD
    A["Gold price drops"] --> B["Calculate loss: Rs 200k"]
    B --> C["Check margin: Rs 200k (initial) - Rs 200k (loss) = Rs 0"]
    C --> D["Margin < Maintenance (Rs 150k)? Yes"]
    D --> E["Margin call: Deposit Rs 50k"]

4. Pricing Futures and Forwards

Forward Price Formula

For non-dividend-paying assets (e.g., silver, gold): $$F=S\cdot e^{rT}+(C-Y)T$$ Where:

• $S$ = spot price
• $r$ = risk-free rate
• $T$ = time to maturity
• $C$ = storage cost
• $Y$ = convenience yield (if applicable)

Futures Price Formula

For dividend-paying assets (e.g., stocks), adjust for dividends: $$F=S\cdot e^{(r-q)T}+\sum _{i=1}^n{D}_i{e}^{(r-q)(T-t_i)}$$ Where:

• $q$ = dividend yield
• $D_i$ = dividend at time $t_i$

Worked Example: Wheat Futures Pricing

• Spot price (S): Rs 2,500/quintal
• Risk-free rate (r): 6% per annum
• Storage cost (C): Rs 100/quintal/year
• Convenience yield (Y): Rs 50/quintal/year (opportunity cost of storing wheat)
• Time (T): 6 months (0.5 years)

Plugging in: $$F=2500\cdot e^{0.06\cdot 0.5}+(100-50)\cdot 0.5=2500\cdot 1.0305+25=\text{Rs 2,583/quintal}$$

Why Rs 2,583?

• The farmer expects to pay Rs 2,500 today, lend it at 6% for 6 months (Rs 75), and cover net storage costs (Rs 50), totaling Rs 2,625. However, the convenience yield reduces the cost to Rs 2,583.

5. Advantages and Disadvantages

In the Real World

1. eSewa/Khalti (Payment Gateways)

   • Idea: Futures-like settlement for digital transactions.
   • How: eSewa/Khalti use instant settlement (like futures’ daily marking-to-market) to ensure funds are transferred immediately, reducing counterparty risk in online payments.

2. Daraz (E-commerce)

   • Idea: Forward contract for inventory hedging.
   • How: Daraz locks in supplier prices for goods (e.g., electronics) via forward contracts to avoid price volatility during peak seasons (e.g., Dashain).

3. NEPSE Gold Futures

   • Idea: Futures for price discovery.
   • How: Investors trade gold futures on NEPSE to speculate on price movements or hedge against inflation. The standardized contract size (1 kg) and daily margin calls ensure liquidity and risk management.

Worked Example: Farmer Hedging Wheat Price A farmer in Rolpa grows 100 quintals of wheat. The current spot price is Rs 2,500/quintal, but he fears prices will drop due to oversupply. He enters a forward contract to sell 100 quintals at Rs 2,600/quintal in 6 months.

• Spot price drops to Rs 2,400/quintal at maturity.
• Forward contract locks in Rs 2,600, so the farmer gains Rs 200/quintal (Rs 20,000 total), offsetting the price decline.

6. Margin and Short Selling

Margin Requirements

• Initial margin: Deposit to cover potential losses (e.g., Rs 20k for gold futures).
• Maintenance margin: Minimum balance to keep the position open (e.g., Rs 15k).
• Margin call: Issued if the account balance falls below maintenance margin.

Example: Short Selling Gold Futures

• Scenario: You expect gold prices to fall. You short 1 gold futures contract at Rs 8,400,000/kg.
• Price drops to Rs 8,200,000/kg.
  • Profit: Rs 200,000 per contract.
  • Margin used: Initial Rs 200,000 (now Rs 400,000 in your account).
• Price rises to Rs 8,600,000/kg.
  • Loss: Rs 200,000 per contract.
  • Margin call: If your account drops below Rs 150,000, you must deposit Rs 50,000 to cover the loss.

sequenceDiagram
    participant Broker
    participant You
    You->>Broker: Short 1 gold futures contract (Rs 8,400,000)
    Broker->>You: Deposit initial margin (Rs 200,000)
    Note right of You: Price drops to Rs 8,200,000
    You->>Broker: Profit Rs 200,000 (margin now Rs 400,000)
    Note right of You: Price rises to Rs 8,600,000
    Broker->>You: Margin < Rs 150,000? Yes
    You->>Broker: Deposit Rs 50,000 to cover loss

Exam Tip

1. Memorize the pricing formulas:

   • Forward: $F=S\cdot e^{rT}+(C-Y)T$
   • Futures (with dividends): $F=S\cdot e^{(r-q)T}+\sum D_i{e}^{(r-q)(T-t_i)}$
   • Always assume continuous compounding unless stated otherwise.

2. Compare forwards and futures in tables (like above) for 2–3 marks.

3. Worked examples are worth 5–8 marks:

   • Show step-by-step calculations (e.g., silver forward price).
   • Explain why the answer makes sense (e.g., "storage costs increase the forward price").

4. Margin calls are a common question:

   • Calculate initial margin, maintenance margin, and margin call amount.
   • Example: If initial margin is Rs 20k and maintenance is Rs 15k, and your account drops to Rs 14k, you must deposit Rs 1k.

5. Real-world applications:

   • Link forwards to hedging (e.g., farmers, exporters).
   • Link futures to speculation (e.g., NEPSE traders).

6. Watch for negative futures prices:

   • If storage costs > risk-free rate (e.g., perishable goods), futures can trade below zero.
   • Example: Milk powder futures might trade at Rs (–)50/kg if storage costs are high.

Final Note: Always label your calculations (e.g., "Step 1: Calculate forward price using $F=S\cdot e^{rT}$") and round to 2 decimal places unless specified. Use NPR for all Nepali examples.