Financial Markets
Christophe Spaenjers
spaenjers@hec.fr
Topic 9: Forwards and Futures
• A. Basics of Forwards and Futures
• B. Spot-Futures Parity
• C. Index and Currency Futures
HEC – MBA Financial Markets
9-1
Topic 9: Roadmap
• What is the difference between forwards and
futures?
• Does using futures contracts eliminate
counterparty risk?
• Who uses forward and futures contracts? Why?
• How big is leverage in a futures contract?
• How are the futures prices related to the spot
prices?
HEC – MBA Financial Markets
9-2
A. Basics of Forwards and Futures
• A Forward contract is a commitment to purchase
at a future date a given amount of a commodity or
financial instrument at a price agreed today
 The price agreed now is the Forward Price
 The buyer has a “long” position
 The seller has a “short” position
• Forward contracts
 They are customized, traded Over-the-Counter (OTC)
 Money is exchanged, along with commodity, only at
delivery date
 There is counterparty risk
HEC – MBA Financial Markets
9-3
A. Basics of Forwards and Futures
• A Futures contract is similar to a forward contract,
except:
 It is exchange-traded
 It has guaranteed settlement by the clearing house
 It has standardized terms
•
•
•
•
Type and quality of commodity or asset to be delivered
Quantity
Maturity
Specified delivery
 It is marked-to-market daily, using a margin account
HEC – MBA Financial Markets
9-4
A. Basics of Forwards and Futures
• Payoff of long position at T is: ST – K
• K is either the forward price or the initial futures price F0
• Payoff of short position at T is: K – ST
HEC – MBA Financial Markets
9-5
A. Basics of Forwards and Futures
• Typically a futures contract is closed out before
settlement unless you want to take delivery of the
commodity
 E.g., suppose you are long 1,000 oz. of gold
 You can close the position (and get your margin back) by
selling a contract for 1,000 oz. of gold
 The two positions cancel each other out
 Less than 5% of contracts are held until delivery
• Some contracts settle in cash only
 Stock index, eurodollars
• Who uses forwards and futures?
 Hedgers: to remove price risk
 Speculators: to bet on price changes (with lots of leverage)
HEC – MBA Financial Markets
9-6
A. Basics of Forwards and Futures
Futures Mechanisms
• Example: On the morning of December 12 you
buy (go long) a gold futures contract on 1,000 oz.
of gold that has delivery date on December 15
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

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The initial futures price is F0 = $500/oz.
At the market close on Dec. 12, F1 = $495/oz.
At the market close on Dec. 13, F2 = $491/oz.
At the market close on Dec. 14, F3 = $497/oz.
At the market close on Dec. 15, F4 = $498/oz.
How much do you have in the margin account
each day (per oz. of gold)?
HEC – MBA Financial Markets
9-7
A. Basics of Forwards and Futures
Futures Mechanisms
Solution:
• Time convention:
 t = 0 is when you buy futures contract
 t = 1 is end of Dec. 12, …, t = 4 is end of Dec. 15
• At t = 0 you post initial margin, which is usually
5% of the total amount, i.e., $25/oz.
 As we will see, this gives you a leverage of 1/5% = 20
 The margin account will reflect (unrealized) gains and
losses: “variation margin” or “mark-to-market margin”
HEC – MBA Financial Markets
9-8
A. Basics of Forwards and Futures
Futures Mechanisms
• On day 1 the futures price change is F1 – F0 = –$5
 This is –1% of the initial futures price, F0 = $500/oz.
 But it is –20% of the initial margin of $25/oz.
 So you have a leverage of 20!
• Both positive and negative returns are amplified by 20
• Each day t:
 Your margin account changes by Ft – Ft-1
 So if you cancel the contract that day (by selling a gold
futures), you are left with Ft – F0 profit
HEC – MBA Financial Markets
9-9
A. Basics of Forwards and Futures
Futures Mechanisms
• At delivery t =T = 4
 The futures price (FT) equals the spot price (ST)
 You now have to pay ST to get 1 oz. of gold, which
means that you are left with –ST + (ST – F0) = –F0
 So by waiting until delivery you get 1 oz. of gold, and
you essentially pay F0 = $500/oz. for it
 This leads to the same outcome as in the case of a
forward contract with forward price F0
• The payoff at delivery is ST – F0 = 498 – 500 = –2
HEC – MBA Financial Markets
9-10
B. Spot-Futures Parity
• There are two ways of getting gold in the future
1. Go long a gold future, with futures price F0
2. Borrow money and invest it directly in gold
• Borrow S0 and buy gold now at the spot price S0
• By arbitrage, it must be that:
ST – F0 = ST – S0 (1+r)T + Benefits – Costs )
F0 = S0 (1+r)T – Benefits + Costs
HEC – MBA Financial Markets
9-11
B. Spot-Futures Parity
• By definition, the costs minus the benefits of holding
the underlying asset are called Costs of Carry
• Costs of carry can include (apart from financing):
 Transportation costs
 Storage costs
 Insurance costs
• Benefits (convenience yield) can include:
 Dividends, coupons, etc.
 Lending fees
 Ability to keep production process running
HEC – MBA Financial Markets
9-12
C. Index and Currency Futures
• Stock Index Futures
 We apply the spot-futures parity
 Benefits: S0 multiplied by the dividend yield d
 Costs: brokerage costs are small
 Index arbitrage keeps the futures and spot price in line
with each other
• E.g., suppose that F0 < S0 (1 + r – d)T
• Then buy the futures and short the stocks in the index

Shorting stocks in the index may be difficult (e.g., in Oct. 1987)
HEC – MBA Financial Markets
9-13
C. Index and Currency Futures
• Currency Futures
 E.g., a futures contract on Euro
 The futures price is called the forward exchange rate
F0$/Euro
 Costs (of financing): local interest rate, r$
 Benefits: the foreign interest rate, rEuro
 The formula is called Covered Interest Parity
HEC – MBA Financial Markets
9-14
Topic 9: Roadmap
• What is the difference between forwards and
futures?
• Does using futures contracts eliminate
counterparty risk?
• Who uses forward and futures contracts? Why?
• How big is leverage in a futures contract?
• How are the futures prices related to the spot
prices?
HEC – MBA Financial Markets
9-15