Laurence Booth
Sean Cleary
11
Forwards, Futures, and Swaps
LEARNING OBJECTIVES
11.1 Describe forward contracts and identify the associated payoffs with
long and short positions in forward contracts.
11.2 Explain how simple forward contracts are priced.
11.3 Describe futures contracts and explain why futures contracts can be
viewed as the public market version of forward contracts.
11.4 Describe the mechanics of simple swap structures, including
interest rate swaps and currency swaps.
11.5 Explain how the credit default swap market contributed to the
financial crisis.
11.6 Explain how the general principles of forward contracts can be
applied to fixed income securities.
11.1 FORWARD CONTRACTS
• Derivative securities have price behaviour that is derived from some
underlying asset
• Derivative securities have either linear payoffs, such as forwards,
futures, and swaps, or non-linear payoffs, such as options (Chapter 12)
• Derivatives offer corporations the tools to manage pre-defined risks
and/or capitalize on comparative advantages
• Risks that can be mitigated through derivatives include:
– Foreign exchange risk
– Credit risk
– Interest rate risk
• Because it costs the firm money to engage in derivative positions, the
costs of these practices can be though of as an insurance premium the
firm is willing to pay to reduce (or hedge) its overall exposure to risk
Booth • Cleary – 3rd Edition
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11.1 FORWARD CONTRACTS
• A spot contract establishes a price today for immediate delivery of an
asset, with the immediacy of the delivery depending on the nature of the
underlying asset
• A forward contract establishes a price today for future delivery on an
asset, and can be specified for almost any future date because forward
contracts are customized contracts between two parties
• Table 11-1 illustrates foreign exchange quotes for spot and future delivery
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11.1 FORWARD CONTRACTS
• Like all derivative securities, forwards can be used for:
– Hedging purposes by firms willing to mitigate exposure to specific risks
– Speculating on the future value of some asset in an attempt to profit
• But, in Canada, banks only sell forward contracts for legitimate
business purposes (i.e., for hedging, not for speculation) and only
up to a company’s approved credit limit
• Forward contracts are bank instruments that must be fulfilled
• There is no organized exchange for trading them and instead they
are traded over-the-counter (OTC)
• Forwards require that the customer have a banking relationship and
involves credit risk for the bank when investors suffer losses
• Since forwards are customized instruments, they can be tailored to
any specific date in the future and for any amount of money
Booth • Cleary – 3rd Edition
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11.1 FORWARD CONTRACTS
• To speculate on a forward contract requires that an investor not own the
underlying asset; this is a “naked” position, where the investor is exposed
to changes in the value of the underlying asset
• Hedging using a forward contract requires that the investor have an
opposite exposure to the contract; this is a “covered” position
• Naked positions expose investors to changes in the value of the underlying
asset
• Long positions are where investors own an asset in the hopes that it will
increase in value and the investor gains by its capital appreciation
• Short positions are where investors owe something. They borrow an asset,
sell it and hope to buy it back at a lower price later. Investors short assets
when they expect the underlying asset to depreciate in price.
• Credit (or counterparty) risk is the risk that a borrower will not fulfill the
contract or make a required payment
• Exposure is the extent to which value is affected by an external event,
such as a change in exchange rates
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11.1 FORWARD CONTRACTS
• Figure 11-1 shows the payoff of a naked or uncovered long position in the
U.S. dollar
• Equation 11-1 shows the profit or loss from a long position as the
difference between the future spot price and the forward price multiplied
by the number of contracts held:
Profit (loss) from long position  ST  F  n
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11.1 FORWARD CONTRACTS
• Figure 11-2 shows the payoff of a short position in the U.S. dollar
•
Equation 11-2 shows the profit or loss from a short position as the
difference between the forward price and the future spot price multiplied
by the number of contracts held:
Profit (loss) from long position  F  ST  n
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11.1 FORWARD CONTRACTS
• Figure 11-3 shows the payoffs when a firm with long U.S. dollar exposure
buys a forward contract to sell U.S. dollars forward for Canadian dollars;
the combined position is the sum of the two previous diagrams
• Regardless of what happens to the Canada-U.S. exchange rate, the
company is locked in (or covered, or hedged) against any future
fluctuations in the exchange rate
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11.1 FORWARD CONTRACTS
Interest Rate Parity (IRP) Revisited
• Equations 11-3 and 11-4 express the IRP condition, originally
discussed in Appendix 6A:
1  k domestic 
F 1  k domestic

 F  S

S 1  k foreign
 1  k foreign 
• Example: if the one-year euro interest rate is 3.5%, the one-year
Canadian interest rate is 5%, and today’s spot rate is 1 euro =
C$1.50, what is the one-year forward exchange rate?
1  k domestic 
 1.05 
F  S
 $1.522
  1.50 

1.035 
 1  k foreign 
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11.1 FORWARD CONTRACTS
• Interest rate parity is a special case for pricing forward contracts
• The general condition is that investors can create a forward position in a
storable commodity by buying it spot and holding it for future delivery
• The only difference between the spot price (S) and the forward price (F)
should be the cost of carry, which is interest costs on financing the
purchase and storage costs of the commodity
• Commodities are things that can be traded based solely on price, because
they are undifferentiated and do not require physical examination
• Storage costs are the price charged for holding a commodity for future
delivery
• Convenience yield is the benefit or premium derived from holding the
asset rather than holding a derivative
• Cost of carry is the total cost of buying a commodity spot and then
carrying it or effecting physical delivery when the forward contract expires
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11.1 FORWARD CONTRACTS
Pricing Forward Contracts
• Equation 11-5, the commodity pricing model, expresses the
relationship between cost of carry, spot price and forward price:
F = (1 + c) × S
• where:
c = the cost of carry as a percentage of S over the period
• Example: Find the forward price for a one-year forward contract for
a metal that is selling for $90 spot, if storage costs are $5 for the
year and financing costs are 10% per year.
S = $90, c = (0.1 × $90 + $5) / $90 = 0.1556
F = (1 + c) × S = (1.1556) × $90 = $104
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11.2 FUTURES CONTRACTS
• Futures contracts are a standardized exchange-traded contract in
which the seller agrees to deliver a commodity to the buyer at
some point in the future
• Organized futures exchanges with standardized futures contracts:
– Reduce credit risk by (1) having a clearing corporation act as
counterparty in all transactions, (2) having margin requirements and
(3) marking to market for daily resettlement
– Allow the contract features and volumes to be reported
– Allow the futures positions to be liquid, executing offsetting
transactions to cancel the futures positions, increasing the flexibility in
their use
• The term of a futures contract is set by individual exchanges:
– Delivery months are: March, June, September, and December
– Underlying assets are standardized so that even if delivery rarely takes
place, investors know what they’re getting
– The notional amount is standardized for each contract
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11.2 FUTURES CONTRACTS
• For financial futures, most exchanges follow the lead of a major
exchange like the Chicago Mercantile Exchange (CME) Group
• Western barley and canola futures trade on ICE Canada (an
exchange)
• Major financial futures contracts like those for bankers’ acceptances
(BAX), two and 10 year Government of Canada bonds (CGZ) and the
S&P/TSX 60 Index (SXF) trade on the Montreal Exchange
• Exchanges develop the market in futures contracts and there is
significant competition among exchanges which is a source of
innovation:
– New types of contracts are developed
– As interest declines or needs change, some types cease to be traded
• Interest in financial futures has grown substantially as companies
increasingly hedge their risk exposures through these instruments
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11.2 FUTURES CONTRACTS
• Commodity futures, such as traditional agricultural products (corn, wheat,
hogs, etc.), energy products and base metals
• Financial futures, such as the S&P index, bankers’ acceptances, bonds
• Other futures, such as weather derivatives, contracts on real estate,
contracts on the consumer price index (CPI) to hedge inflation
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11.2 FUTURES CONTRACTS
• The process of marking to market helps to limit exposure to credit
risk for the exchange
• All futures contracts are marked to market at the end of each day
• Therefore, all profits and losses on a futures contract are credited to
investors’ accounts each day in order to calculate their equity
positions
• If the equity position increases, these profits can be withdrawn
• But, if the equity position drops below a maintenance margin,
which is usually 75% of the initial margin, the investor will receive a
margin call and be forced to contribute more money to increase the
equity position back to the maintenance level
• If a margin call is not met in a timely manner, a position can be
liquidated to cover the shortfall
Booth • Cleary – 3rd Edition
© John Wiley & Sons Canada, Ltd.
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11.2 FUTURES CONTRACTS
Trading/Hedging with Futures Contracts
• Suppose a fixed-income portfolio manager holds a diversified
bond portfolio comprised primarily of Government of Canada
bonds
• The portfolio manager expects interest rates will rise, which
will cause the value of his portfolio to fall because bond prices
will fall
• The manager can hedge this interest rate risk by:
1. Selling bonds and holding cash until the threat of rising rates
passes or until rates actually rise, and then repurchase the
devalued bonds.
2. Sell long term bonds and replace them with shorter maturity
bonds, reducing the portfolio’s duration and mitigating the
market value losses if interest rates actually do rise.
Booth • Cleary – 3rd Edition
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11.2 FUTURES CONTRACTS
Trading/Hedging with Futures Contracts
• The manager can hedge this interest rate risk by:
3. Hold the portfolio unchanged and use a short hedge, a
short position in a government bond futures contract, so
the losses in the market value of the portfolio will be
offset by the gains on the short hedge contract. This
avoids the transaction costs and portfolio disruption of
the other two options. But, if the hedge cannot be
perfectly constructed, the portfolio will still have basis
risk because losses on the portfolio may not be exactly
offset by the short hedge.
Booth • Cleary – 3rd Edition
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11.2 FUTURES CONTRACTS
Forwards versus Futures
• Although forward and future contracts serve the same
purpose, forwards offer more flexibility because they are
customized contracts that trade OTC
• Forwards, however, also face more risk, including credit and
liquidity risk.
• Table 11-3 summarizes a comparison of forwards and futures
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11.3 SWAPS
• A swap is an agreement between two parties, called
counterparties, to exchange cash flows in the future
• Swaps are not traded on formal exchanges which guarantee
performance, but instead through dealers or over-thecounter, and there is credit risk
• Swaps have also evolved into bank instruments with banks or
swap dealers serving as intermediaries
• Comparative advantage is a benefit that one firm has relative
to another; for example, the ability to manage a type of risk
better than another firm
• Interest rate swaps and currency swaps are a common types
of swap
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11.3 SWAPS
Interest Rate Swaps
• An interest rate swap is an exchange of interest payments on a notional
principal amount in which borrows switch loan rates
• Often this involves trading fixed payments for variable rate payments
• A plain vanilla interest rate swap occurs when a fixed-for-floating interest
rate swap is denominated in one currency
• Table 11-4 illustrates a plain vanilla interest rate swap between
counterparties A and B and is structured to benefit both parties equally
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11.3 SWAPS
• Counterparties to a swap are often unequal partners to the contract; for
example, one party may be AAA-rated while the other is BBB-rated
• Any credit risk is borne by the higher-rated counterparty, so the AAA-rated
party may have to honour both its own obligations and those of the BBBrated party if the lower-rated party defaults
• Counterparties can control credit risk by using:
– Set-off rights in the swap agreement allowing the other party to stop
making payments in the event of a default
– Net payments so that, instead of exchanging total interest amounts,
only the difference between the two streams are exchanged and
structuring the payments into sub-periods (e.g., every six months)
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11.3 SWAPS
• Currency swaps require exchange of all cash flows and permit firms
to adjust their foreign exchange exposure
• This actually increases credit risk, but presents opportunities
• The first swap was a currency swap between IBM Corporation and
the World Bank, motivated by comparative advantage; both IBM
and the World Bank used it to raise new capital cheaply in a primary
market transaction
• Once swaps became standardized, it became possible to change the
nature of the institution’s liability stream constantly
• Today, currency swaps have become a bank market through their
links to the forward foreign exchange market
• Banks are capable of executing a secondary market transaction with
themselves as the counterparties because a currency swap can be
thought of as a series of forward transactions
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11.3 SWAPS
• Standardization has helped to grow the swap market
• Interest rate swaps, like currency swaps, have also become a
bank market through standardization
– Floating rates are fixed against LIBOR (London Inter-Bank
Offer Rate)
– Fixed rates are fixed against the government bond rate,
with the choice of rate depending on whether it is a five
year, 10 year or other maturity contract and this becomes
the swap rate
• The swap rate is the rate of the fixed portion of a swap which
is used for quoting swaps
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11.3 SWAPS
• Interest rate swaps are found around the world
• Table 11-7 gives swap rates for the Euro, U.S. dollar, and Pound Sterling for
May 12, 2009
• Swap rates follow the full spectrum of the yield curve, from one year to 30
years, so interest rate exposure can be managed
• It also links swaps to forward rate agreements (FRAs)
• FRAs are agreements that use forward rates to manage a firm’s exposure
to interest rate risk by borrowing or lending at a specified future date at
an interest rate that is fixed today
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11.3 SWAPS
The Evolution of Swap Markets
• The integration of swap markets with the forward market has fuelled
expansion of the market
• Firms wanting to change a floating rate liability into a fixed rate
liability, for example, simply call their bank and execute an interest
rate swap as a secondary market transaction against a line of credit
• Creating swaps is a key component of the services provided by major
banks for their corporate clients
• Swap opportunities beyond interest rate and currency swaps also
exist, including the total return swap
• Total return swaps exchange an interest rate return for the total
return on an equity index plus or minus a spread
• The more specialized a swap is, the less tradable and the greater the
counterparty risk
• Only standardized swaps are done with banks
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11.5 THE FINANCIAL CRISIS AND THE
CREDIT DEFAULT SWAP MARKET
• A total return swap exchanges an interest rate return for the total return
on an equity index plus or minus a spread. For example, first an investor
could enter into an interest rate swap to convert fixed rate bond payments
into payments that vary with a float rate, such as LIBOR. Then, the investor
could enter a total return swap, paying LIBOR and receiving the total
return from an equity index such as the S&P 500 Index.
• The notional principal amount is usually at least $100 million for total
return swaps, so they are used almost exclusively by major financial
institutions and large funds.
• A credit default swap is a swap where one party makes a series of interest
payments and then gets compensated by the counterparty in the event of
default on the bond; it functions as default insurance on a bond.
– An example would be when the risk-free payments on a government
bond are swapped for the proceeds of a risky bond.
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11.5 THE FINANCIAL CRISIS AND THE
CREDIT DEFAULT SWAP MARKET
• There are two important differences between credit default swaps (CDS)
and insurance:
– The risk attached to regular insurance is usually random, and so by
pooling an insurer’s exposure can be made predictable. The risk
underlying CDS is economic or systematic risk which cannot
necessarily be made as predictable as regular insurance.
– The CDS market is part of the swap market (which is an over the
counter market), so everything depends on the counterparties to the
swap fulfilling their obligations. Insurance companies are heavily
regulated and required to keep reserves to ensure they can fulfill
promises.
• By 2007 the CDS market was worth US$45 trillion, or about three times
the value of the entire U.S. stock market.
• Many of the newer CDS contracts were based on securities tied to the U.S.
subprime mortgage market
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11.5 THE FINANCIAL CRISIS AND THE
CREDIT DEFAULT SWAP MARKET
• As the sub-prime market in the United States collapsed in 2007 and
2008, major issuers of CDS such as American International Group
(AIG) were burdened with fulfilling the contracts as a result of
default
• The very solvency of AIG came into question in fall 2008 and the
U.S. government provided funds from the Troubled Asset Relief
Program (TARP) to ensure the continuity of AIG’s counterparty
operations
• The failure of AIG also dealt a huge blow to the over-the-counter
(OTC) markets and there is currently pressure to force CDS to be
traded on organized exchanges for greater transparency and to
ensure that writers have to post margins, just like they would for
futures contracts, to ensure they can fulfill their contracts
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