Chapter 3 - Pricing of Futures Contracts (Done) Flashcards
What is arbitrage?
Academic or pure arbitrage refers
to the simultaneous purchase and
sale of instruments that are perfect
equivalents in the hope of taking
advantage of pricing discrepancies
between them to earn a risk-free
profit. Most real world arbitrage,
however, is not pure. There usually is
some element of risk.
What is backwardation?
Backwardation is when the current price of an underlying asset is higher than prices trading in the futures market. Backwardation can occur as a result of a higher demand for an asset currently than the contracts maturing in the coming months through the futures market.
What is basis with regards to futures contracts?
The difference between the current
cash price and the futures price.
BASIS = FUTURES PRICE - SPOT PRICE
What is cash-and-carry arbitrage?
Arbitrage that involves buying the
underlying asset and selling the
futures contract to take advantage of
a situation where futures are priced
higher than fair value.
What is a contango market?
A market where the forward or futures
price is higher than the spot price.
For commodity futures contracts,
contango markets are considered
normal as there is typically a cost to
carrying or holding a commodity.
What is convenience yield?
The benefit from owning the physical
commodity. The value of the benefit
is dependent upon the probability
of shortages of the commodity. If
the commodity is currently in short
supply and that shortage is expected
to continue, the convenience yield will
be high.
What is the concept of convergence with respect to futures?
The narrowing of the basis as a futures
contract nears expiration.
What is cost of carry?
Term associated with the cost of
holding a commodity or financial asset
until it is sold or delivered. The cost of
holding a commodity typically includes
financing, storage and insurance
charges. The cost of holding a financial
asset typically includes financing costs
less income received such as dividends
for stocks and interest for debt
instruments.
What is fair value of a futures contract?
If a futures contract is trading at a price
that reflects full carry, it is said to be
trading at fair or theoretical value.
What is an inverted market?
An inverted market shows futures prices that decrease over time, while a normal market sees futures prices that increase over time. A futures market is inverted if the spot price is higher for a contract that expires in one month than a contract that expires in four months.
What is a normal market?
A normal futures curve, or normal market, demonstrates that the cost to carry increases with time. An inverted futures curve, or inverted market, demonstrates that the prices for further out deliveries are less expensive than the current spot price.
What is reverse cash-and-carry arbitrage?
Arbitrage that involves buying the
futures contract and selling the
underlying asset to take advantage of a
situation where the futures contract is
underpriced relative to fair value.
What is a spot price?
The price of an asset on the spot
market.
Explain why futures differ from spot prices.
Futures prices represent the current price of the underlying asset adjusted for the cost of carry that arises from
delayed delivery of the asset.
Describe the basic cost-of-carry model and explain how it works.
- The cost of delayed settlement includes financing costs and storage and insurance costs. As well, any other
cash flows associated with owning the underlying asset must be considered. - The cost of carry model starts with the spot price of an asset and calculates the fair value futures price based
on these costs from the present until the maturity of the futures contract. The difference between a spot price
and a futures price is referred to as the basis.
Explain how arbitrage keeps futures prices in line with the basic cost-of-carry model.
As the only difference between buying in the futures market and buying in the spot market is the delayed
settlement, it stands to reason that futures prices should be the same as spot prices adjusted for the costs of
the delayed settlement.
If futures prices deviate significantly from fair value, market participants will either buy the “cheap” alternative,
sell the “expensive” alternative, or do both simultaneously. When participants buy and sell the same asset
simultaneously, it is referred to as arbitrage.
The collective actions of market participants attempting to buy low and sell high help keep spot and futures
prices in line with one another during a futures contract’s life.
Identify an arbitrage opportunity.
If a futures contract is trading at a price other than its fair value, an arbitrage opportunity may exist. In general,
the futures price must differ from its fair value price by more than the transaction costs involved in executing
the arbitrage before arbitrageurs will try to take advantage of the discrepancy.
Explain how to exploit an arbitrage opportunity.
- If the futures price is greater than its fair value price, the futures contract should be sold, and the underlying
asset should be bought in the cash market. This is known as cash-and-carry arbitrage. - If the futures price is lesser than its fair value, the futures contract should be bought and the underlying asset
should be sold short in the cash market. This is known as reverse cash-and-carry arbitrage.
Describe situations where the cost-of-carry model may not apply.
The cost-of-carry model applies to futures markets that display the following characteristics…
- ease of short selling;
- a large supply of the underlying interest;
- high storability;
- non-seasonal production or consumption (or both).
When these conditions exist, arbitrage is easy to implement, and futures prices will trade on the basis of fair
value as determined by the cost-of-carry model.
When these conditions do not exist, arbitrage may be very difficult or even impossible to implement. Futures
contracts based on these markets will trade more on the basis of expectations of the future spot price of the
underlying asset.
- Financial assets such as bonds and equities and precious metals are relatively easy to arbitrage as they share these characteristics.
- Agricultural and energy commodities are more difficult to arbitrage because they generally do not meet all of these characteristics. As result, the agriculture – and energy – related futures contracts trade more on the basis of expectations than carry.
Describe and calculate the basis of a futures contract.
The basis is a numerical measure of the difference between a cash price and a futures price.
As mentioned above, the basis is simply the difference between the spot price and the futures price.
Explain the concepts of normal market, inverted market, and convergence.
- A normal commodity futures market (also referred to as a contango market) is one where futures prices trade at
a premium to spot prices, reflecting all or at least some of the costs of carry. - An inverted commodity futures market (also referred to as a market in backwardation) is one where spot prices
are higher than futures prices. An inverted market places an increased value on owning the physical asset. This
value is known as a convenience yield. - Convergence is the process whereby futures prices gradually merge with cash prices as expiration of the
futures contract approaches.
Questions i) and ii) below pertain to copper futures and are based on the following information.
Annual financing rate 4%
Spot price of copper $3.60 per pound
Storage costs $0.005 per pound per month
Insurance $0.015 per pound per month
i. What are the total monthly carrying costs for copper?
a. 1.2¢ per pound.
b. 2.0¢ per pound.
c. 2.7¢ per pound.
d. 3.2¢ per pound.
ii. What is fair value for 3-month copper futures?
a. $3.504 per pound.
b. $3.660 per pound.
c. $3.696 per pound.
d. $3.744 per pound.
i. d. 3.2¢ per pound.
(($3.60 × 0.04 ÷ 12) + $0.015 + $0.005) × 100
Multiply by 100 to convert the answer to cents.
ii. c. $3.696 per pound.
$3.60 + ($0.032 × 3)
The $0.032 is the monthly costs calculated in Question i) above.
In a contango commodity futures market, would the basis narrow or widen as the futures expiration
approaches?
Regardless of the type of market (contango or inverted), the basis always narrows as futures expiration
approaches.
As a general rule, are futures prices more easily underpriced or overpriced relative to fair value?
Explain your answer.
Futures are generally more easily underpriced, due to the fact that for some commodities it is often difficult if
not impossible to do a reverse cash and carry arbitrage.
