Week 5 Foward and future contracts

Question 1

What is a forward contract?

Answer 1

Sign today, pay in the future. No payment to enter the contract. Can be very specific on commodity, forex, FRA, quantity, price, time and place for delivery. Both parties have obligation on specified delivery date. No cash flow before delivery.
It is not protected against default. Commodity is not easily traded. Big companies typically use forward contracts.

Question 2

What is a future contract?

Answer 2

Very specific contract to trade in the future. Item specified, length of time specified, guaranteed by exchange, contract in standard form. Either party can close at any time before maturity. Daily re-settlement of P/L, cash flows occur throughout life of contract. Obligation to buy and sell again, like forward. Clearing house matches the contract, zero sum gain of long + short position.

Question 3

Difference between forward and future contracts?

Answer 3

Futures are more liquid, but less flexible as they come standardised. Lower risk for futures. Futures have daily resettlement.

Question 4

What are clearing houses of exchange?

Answer 4

Makes margin calls against brokers. Matches and records all trading records each day. Announces daily resettlement price. Sets daily price limits, then limited once target hit. Arranges conditions for delivery of contracts. End users deal through brokers e.g. individual investors.

Question 5

Nick Leeson example of speculation?

Answer 5

1994-95 bankruptcy of Barings Bank as Nick Leeson long position in Japanese futures expecting stock prices to rise. However they fell due to earthquake, so stocks rapidly fell leading to $1.5 billion loss and bankruptcy. Show long futures graph.

Question 6

What is cost of carry model?

Answer 6

The forward price should reflect the costs and benefits of holding the asset between now (time
t) and the delivery time
𝑇. If you invest an amount 𝐴 for 𝑇 years at rate 𝑟, with continuous compounding, the future value is:
𝐹 = 𝐴𝑒𝑟𝑇

Option 1: Buy now
Pay the spot price 𝑆
Pay storage or interest costs (called costs of carry)
Receive any benefits (e.g., dividends, convenience)

Option 2: Buy a forward contract
Delay buying
Lock in a price for future delivery: the forward price 𝐹
For no-arbitrage, these options must be equivalent.

This is the net cost of holding the asset until delivery. It includes:

Costs:
Storage
Insurance
Financing cost (interest rate 𝑟)

Benefits:
Dividends or interest income
Convenience yield 𝑦
(the value of having the asset on hand, especially for commodities)

So:
𝑐 = 𝑟 + 𝑢 − 𝑦

F=Se ^c(T−t)

Question 7

What are the special cases of cost of carry?

Answer 7

🔹 Commodities (with storage cost 𝑢 and convenience yield 𝑦):
𝐹 = 𝑆𝑒^(𝑟+𝑢−𝑦)(𝑇−𝑡)
🔹 Stock Index (with dividend yield 𝑞):
𝐹 = 𝑆𝑒^(𝑟−𝑞)(𝑇−𝑡)
🔹 Currency (foreign interest rate 𝑟∗, domestic 𝑟): 𝐹 = 𝑆𝑒^(𝑟−𝑟∗)(𝑇−𝑡)
🔹 Coupon Bond (coupon yield treated like dividend):
𝐹 = 𝑆𝑒^(𝑟−𝑞)(𝑇−𝑡)

Question 8

What is a convenience yield?

Answer 8

This is the non-monetary benefit of holding a commodity now (e.g. fuel on hand, production continuity).
Hard to estimate

Varies across users

Not always arbitrageable (you can’t short-sell oil easily)

Question 9

What is the basis?

Answer 9

The basis is the difference between the spot and futures price:

Basis = 𝑆−𝐹

Backwardation: Basis > 0 ⇒ Spot price > futures ⇒ Market expects prices to fall or convenience yield is high.

Contango:
Basis < 0 ⇒ Futures price > spot ⇒ Carry costs outweigh benefits.

At delivery, spot = futures, so basis = 0.