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Forward and Futures Contracts

Site: Saylor Academy
Course: BUS614: International Finance
Book: Forward and Futures Contracts
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Date: Friday, 4 April 2025, 1:15 AM

Description

One derivative contract is a forward contract, where parties agree to trade assets at a future date at a specified price. Both forward and futures contracts are similar in terms of their nature. However, future contracts are standardized agreements, unlike forward contracts. These videos (along with the attached slides) discuss financial futures contacts in detail, including how to calculate payoffs. What are some other differences between forward contracts and futures contracts, and what determines forward and futures prices?

Table of contents

Forward and Futures Contracts I

This video lecture covers the motivation, definition, features, and examples of forward and futures contracts in light of the uncertainty of exchange rates, illiquidity, and counterparty risk.

Source: Andrew Lo, https://ocw.mit.edu/courses/sloan-school-of-management/15-401-finance-theory-i-fall-2008/video-lectures-and-slides/forward-and-futures-contracts/
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License.

Forward and Futures Contracts II

This video lecture includes examples for calculating payoff, and pricing forward and futures contracts. Applications and qualifications for forwards and futures are also given.

Finance Theory

Critical Concepts

  • Motivation
  • Forward Contracts
  • Futures Contract
  • Valuation of Forwards and Futures
  • Applications
  • Extensions and Qualifications

Motivation

  • Your company, based in the U.S., supplies machine tools to customers in Germany and Brazil.  Prices are quoted in each countrya's currency, so fluctuations in the €/ $ and R / $ exchange rates have a big impact on the firm's revenues.  How can the firm reduce (or 'hedge') these risks?
  • Your firm is thinking about issuing 10-year convertible bonds.  In the past, the firm has issued straight debt with a yield-to-maturity of 8.2%. If the new bonds are convertible into 20 shares of stocks, per $1,000 face value, what interest rate will the firm have to pay on the bonds?
  • You have the opportunity to buy a mine with 1 million kgsof copper for $400,000.  Copper has a price of $2.2 / kg, mining costs are $2 / kg, and you can delay extraction one year.  How valuable is the option to delay?  Is the mine a good deal?
Exchange Rates, 1995 –2003
Exchange Rates, 1995 –2003

Caterpillar, 1980 –1989

Caterpillar, 1980 –1989

Hedging or Speculation?

Alternative Tools?
  • Futures, forwards, options, and swaps
  • Insurance
  • Diversification
  • Match duration of assets and liabilities
  • Match sales and expenses across countries (currency risk)
Should Firms Hedge With Financial Derivatives?
  • "Derivatives are extremely efficient tools for risk management"
  • "Derivatives are financial weapons of mass destruction"

View 1: Hedging is irrelevant (M&M)

  • Financial transaction, zero NPV
  • Diversified shareholders don’t care about firm-specific risks

View 2: Hedging creates value

  • Ensures cash is available for positive NPV investments
  • Reduces need for external finance
  • Reduces chance of financial distress
  • Improves performance evaluation and compensation

Examples:

Homestake Mining
  • Does not hedge because "shareholders will achieve maximum benefit from such a policy".
American Barrick
  • Hedges aggressively to provide "extraordinary financial stability...offering investors a predictable, rising earnings profile in the future".
Battle Mountain Gold
  • Hedges up to 25% because "a recent study indicates that there may be a premium for hedging".

Evidence

  • Random sample of 413 large firms
  • Average cashflowfrom operations = $735 million
  • Average PP&E = $454 million
  • Average net income = $318 million

57% of Firms Use Derivatives In 1997

  • Small derivative programs
  • Even with a big move (3σevent), the derivative portfolio pays only $15 million and its value goes up by $31 million

Basic Types of Derivatives

Forwards and Futures
  • A contract to exchange an asset in the future at a specified price and time.
Options (Lecture 10)
  • Gives the holder the right to buy (call option) or sell (put option) an asset at a specified price.
Swaps
  • An agreement to exchange a series of cashflowsat specified prices and times.

Forward Contracts

Definition:  A forward contract is a commitment to purchase at a future  date a given amount of a commodity or an asset at a price agreed on today.


  • The price fixed now for future exchange is the forward price
  • The buyer of the underlying is said to be "long" the forward

Features of Forward Contracts

  • Customized
  • Non-standard and traded over the counter (not on exchanges)
  • No money changes hands until maturity
  • Non-trivial counter party risk

Example:

  • Current price of soybeans is $160/ton
  • Tofu manufacturer needs 1,000 tons in 3 months
  • Wants to make sure that 1,000 tons will be available
  • 3-month forward contract for 1,000 tons of soybeans at $165/ton
  • Long side will buy 1,000 tons from short side at $165/ton in 3 months

Futures Contracts

Forward Contracts Have Two Limitations:

  • Illiquidity
  • Counterparty risk
Definition:  A futures contractis an exchange-traded, standardized,

forward-like contract that is marked to marketdaily. This contract can
be used to establish a long (or short) position in the underlying asset.

Features of Futures Contracts

  • Standardized contracts:
    – Underlying commodity or asset
    – Quantity
    – Maturity
  • Exchange traded
  • Guaranteed by the clearinghouse - no counter-party risk
  • Gains/losses settled daily (marked to market)
  • Margin required as collateral to cover losses

Example:

NYMEX crude oil (light) futures with delivery in Dec. 2007 at a price of
$75.06 / bbl. on July 27, 2007 with 51,475 contracts traded

  • Each contract is for 1,000 barrels
  • Tick size: $0.01 per barrel, $10 per contract
  • Initial margin: $4,050
  • Maintenance margin: $3,000
  • No cash changes hands today (contract price is $0)
  • Buyer has a "long" position (wins if prices go up)
  • Seller has a "short" position (wins if prices go down)

Payoff Diagram

Payoff Diagram

Example. Yesterday, you bought 10 December live-cattle contracts on the
CME, at a price of $0.7455/lb

  • Contract size 40,000 lb
  • Agreed to buy 40,000 pounds of live cattle in December
  • Value of position yesterday: (0.7455)(10)(40,000)  =  $298,200
  • No money changed hands
  • Initial margin required (5%−20% of contract value)
Today, the futures price closes at $0.7435/lb, 0.20 cents lower. The value

of your position is

(0.7435)(10)(40,000)  =  $297,400

which yields a loss of $800.

Why Is This Contract Superior to a Forward Contract?

  • Standardization makes futures liquid
  • Margin and marking to market reduce default risk
  • Clearing-house guarantee reduces counter-party risk


Valuation of Forwards and Futures

What Determines Forward and Futures Prices?

  • Forward/futures prices ultimately linked to future spot prices
  • Notation:

    Contract Spot at t
    		 Forward Futures
    Price S_t F_{t,T} H_{t,T}

  • Ignore differences between forward and futures price for now
    F_{t,T} \approx. H_{t, T}
  • Two ways to buy the underlying asset for date-T delivery
    1. Buy a forward or futures contract with maturity date T
    2. Buy the underlying asset and store it until T
Date Forward Contract
Outright Asset Purchase
0
  • Pay $0 for contract with forward price $F0,T
  • Borrow $S0
  • Pay $S0 for Asset
T
  • Pay $F0,T
  • Own asset
  • Pay back $S0(1+r)T
  • ƒPay cumulative storage costs (if any)
  • ƒDeduce cumulative" convenience yield" (if any)
  • ƒOwn asset
Total Cost at T
  $F0,T $S0(1+r)T   +  net storage costs

F_{0,T} \approx. H_{0, T} = (1+r_f)^T S_0 + FV_T (net storage costs)

\dfrac{F_{0,T}}{(1+r)^t}  \approx. \dfrac{H_{0, T}}{(1+r)^T} = S_0 + PV_0 (net storage costs)


Date Forward Contract
Outright Asset Purchase
t
  • Pay $0 for contract with forward price $Ft,T
  • Borrow $St
  • Pay $St for Asset
T
  • Pay $Ft,T
  • Own asset
  • Pay back $St(1+r)T-t
  • ƒPay cumulative storage costs (if any)
  • ƒDeduce cumulative" convenience yield" (if any)
  • ƒOwn asset
Total Cost at T
  $Ft,T $S0(1+r)T-t   +  net storage costs

F_{t,T} \approx. H_{t, T} = (1+r_f)^{T-t} S_t + FV_T (net storage costs)

\dfrac{F_{t,T}}{(1+r)^{T-t}}  \approx. \dfrac{H_{t, T}}{(1+r)^{T-t}} = S_t + PV_t (net storage costs)

What Determines Forward/Futures Prices?

  • Difference between the two methods:
    – Costs (storage for commodities, not financials)
    – Benefits (convenience for commodities, dividends for financials)
  • By no arbitrage (Principal P1), these two methods must cost the same

Gold

  • Easy to store (negligible costs of storage)
  • No dividends or benefits
  • Two ways to buy gold for T
    – Buy now for S tand hold until T
    – Buy forward at t, pay Ft,T at T and take delivery at T
  • No-arbitrage requires that
F_{t,T} \approx. H_{t, T} = (1+r_f)^{(T-t)} S_t


Gasoline
  • Costly to store (let c be percentage cost per period)
  • Convenience yield does exist (let ybe percentage yield per period)
  • Not for long-term investment (like gold), but for future use
  • Two ways to buy gasoline for T
    – Buy now for S tand hold until T
    – Buy forward at t, pay Ft,T at T and take delivery at T
  • No-arbitrage requires that
F_{t,T} \approx. H_{t, T} = (1+r_f + c - y)^{(T-t)} S_t

Financials

  • Let underlying be a financial asset
    – No cost to store (the underlying asset)
    – Dividend or interest on the underlying
  • Example: Stock index futures
    – Underlying are bundles of stocks, e.g., S&P, Nikkei, etc.
    – Futures settled in cash (no delivery)
    – Let the annualized dividend yield be d; then

    F_{t,T} \approx. H_{t, T} = (1+r_f -d)^{(T-t)} S_t

Example:

  • Gold quotes on 2001.08.02 are
  • Spot price (London fixing) $267.00/oz
  • October futures (CMX) $269.00/oz
  • What is the implied interest rate?
F=S_0(1+r_f)^{2/12}
r_f= ( F/S_0)^6 −1 = 4.58%

Example:

  • Gasoline quotes on 2001.08.02:
  • Spot price is 0.7760
  • Feb 02 futures price is 0.7330
  • 6-month interest rate is 3.40%
  • What is the annualized net convenience yield (net of storage costs)?
0.7330=(0.7760)(1+0.0340−y)^{6/12}

y= 1 .0340− (\dfrac{0.7330}{0.7760})^2 = 14.18%

Example:

  • The S&P 500 closed at 1,220.75 on 2001.08.02
  • The S&P futures maturing in December closed at 1,233.50
  • Suppose the T-bill rate is 3.50%
  • What is the implied annual dividend yield?
d  = [1+r_f - (f/S_0)^{12/4}]
= [1 + 0.0350 - (1233.50/1220.75)^3] = 0.33%

Applications

Index Futures Have Many Advantages

  • Since underlying asset is a portfolio, trading in the futures market is easier than trading in cash market
  • Futures prices may react quicker to macroeconomic news than the  index itself
  • Index futures are very useful for:
    • Hedging market risk in block purchases and underwriting
    • Creating synthetic index fund
    • Portfolio insurance

Example:

You have $1 million to invest in the stock market and you have decided to
invest in the S&P 500. How should you do this?
  • One way is to buy the S&P 500 in the cash market:
    – Buy the 500 stocks, weights proportional to their market caps
  • Another way is to buy S&P futures:
    – Put the money in your margin account
    – Assuming the S&P 500 is at 1,000 now, number of contract to buy: (value of a futures contract is $250 times the S&P 500 index)
    \dfrac{$1,000,000}{250 \times 1,000} = 4

Example (cont):

  • As the S&P index fluctuates, the future value of your portfolio (in $MM) is given by the following table (ignoring interest payments and  dividends):

    S & P 500
    		 Cash Portfolio
    		  Futures Portfolio
    900
    1,000
    1,100
    		 $0.90
    $1.00
    $1.10
    		  $0.90
    $1.00
    $1.10

  • Suppose you a diversified portfolio of large-cap stocks worth $5MM and are now worried about equity markets and would like to reduce  your exposure by 25% - how could you use S&P 500 futures to  implement this hedge?
    – (Short) sell5 S&P 500 futures contracts (why 5?)
  • Compare hedged and unhedgedportfolio (in $MM):

    S & P 500
    		 Cash Portfolio
    		  Cash Plus Futures Portfolio
    900
    1,000
    1,100
    		 $4.50
    $5.00
    $5.50
    		  $4.50 + $0.125= $4.625
    $5.00
    $5.50 - $0.125 = $5.375
  • Fluctuations have been reduced
  • As if 25% of the portfolio has been shifted to cash

Extensions and Qualifications

  • Interest-rate, bond, and currency futures are extremely popular
  • Single-stock futures are gaining liquidity
  • Volatility futures recently launched (VIX)

Key Points

  • Forward and futures contracts are zero-NPV contracts when initiated
  • After initiation, both contracts may have positive/negative NPV
  • Futures contracts are "marked to market" every day
  • Futures and forwards are extremely liquid
  • Hedging and speculating are important applications of futures/forwards