Chapter 11 - Commodity Forwards and Futures (FRM Part 1 - Book 3)
Chapter 11 - Commodity Forwards and Futures
Chapter 11 - Commodity Forwards and Futures
1. Which of the following is a significant difference between commodities and financial assets?
A. Commodities generally do not have any associated storage costs.
B. Financial assets require special care and insurance.
C. Commodities have significant storage costs, unlike financial assets.
D. Financial assets incur transportation costs, whereas commodities do not.
Commodities typically require storage, special care, and insurance, which incur additional costs. Financial assets, on the other hand, do not involve storage costs.
2. Which of the following is true regarding the transport costs associated with commodities?
A. Commodities have no transport costs associated with them.
B. Commodities' prices often depend on their location due to transport costs.
C. Financial assets face significant transportation costs, unlike commodities.
D. Transport costs for commodities are generally the same worldwide.
The price of commodities often varies based on their location because transporting them can be costly. Financial assets, however, do not have transport costs.
3. What is the primary way shorting costs for commodities are expressed?
A. As a lease rate
B. As a fee charged by the broker
C. As an interest rate
D. As a trading commission
The shorting costs for commodities are often expressed as a lease rate, which may be higher than the shorting fees for financial assets.
4. How do financial assets typically generate returns compared to commodities?
A. Financial assets only provide price returns, similar to commodities.
B. Commodities provide both price and income returns.
C. Commodities offer returns based on price trends and their mean-reverting nature.
D. Financial assets typically provide returns based on risk, unlike commodities.
Financial assets usually provide returns based on risk, including both price and income returns. In contrast, commodities provide only price returns, with price trends often reverting to the mean.
5. Why do agricultural commodities experience seasonal fluctuations in prices?
A. Because demand is seasonal and production is constant throughout the year
B. Because they are highly dependent on international trade only
C. Because production is seasonal while demand remains relatively constant
D. Because they cannot be stored and must be sold immediately
Agricultural commodities are produced seasonally, but demand is stable throughout the year. This mismatch causes seasonal price fluctuations.
6. What impact does a good harvest expectation have on commodity futures prices?
A. Prices are expected to decrease
B. Prices remain unaffected
C. Prices are expected to increase significantly
D. Prices depend only on demand, not on harvest
A good harvest increases supply, which typically leads to an expectation of lower prices for agricultural commodities.
7. Which of the following factors is considered a key determinant of agricultural commodity futures prices?
A. Rate of inflation
B. Interest rate fluctuations
C. Gold prices
D. Weather conditions
Weather conditions greatly impact agricultural production, making them a key factor influencing commodity futures prices.
8. Why is storage cost relevant to agricultural commodity futures pricing?
A. Because demand for storage facilities is limited
B. Because commodities must be stored due to seasonal production and constant demand
C. Because financial institutions charge high interest on commodity trading
D. Because futures contracts do not include delivery costs
Since production is seasonal but consumption is steady, agricultural commodities must be stored, making storage (and interest) costs crucial to futures pricing.
9. Which of the following political factors can impact agricultural commodity futures prices?
A. Import or export restrictions
B. Monetary policy changes
C. National elections
D. Government job programs
Government-imposed import or export restrictions can directly impact the supply and price of agricultural commodities, affecting futures prices.
10. Unlike agricultural commodities, what factor does NOT impact the pricing of metals?
A. Inventory levels
B. Seasonal weather changes
C. Cost of extraction
D. Foreign exchange rates
Metal prices are not affected by season or weather unlike agricultural commodities, though factors like inventory and extraction costs do affect pricing.
11. Why might an investor prefer to use long forward contracts for metals instead of buying and holding them physically?
A. To avoid storage costs and because physical holdings do not earn lease payments
B. Due to seasonal price benefits
C. Because physical metals degrade quickly
D. As physical ownership requires a trading license
Holding physical metals involves storage costs and does not provide lease returns, making synthetic exposure via forward contracts more attractive.
12. Which of the following is a key reason for relatively stable global prices for crude oil?
A. Its limited usage globally
B. Complex pricing mechanisms
C. Ease of transport and relatively constant global demand
D. High seasonal consumption variations
Crude oil is easy to transport and has a more constant global demand, making its long-term price relatively stable.
13. Why do natural gas prices vary geographically?
A. Due to international regulation
B. Due to stable production year-round
C. Because it is a renewable energy source
D. Because of high storage and transportation costs
Natural gas is costly to store and transport, which causes its prices to vary by region.
14. What is the main reason electricity prices are more volatile than prices of other commodities?
A. Due to long-term storage contracts
B. Because electricity cannot be stored and must be used immediately
C. Due to weather dependency alone
D. Because prices are globally fixed
Electricity cannot be stored, so prices are determined instantly by supply and demand, leading to higher volatility.
15. Which of the following correctly pairs a commodity with its demand characteristics?
A. Natural gas – seasonal demand
B. Crude oil – highly seasonal demand
C. Electricity – constant demand
D. Metals – no demand fluctuations
Natural gas has seasonal demand, increasing in winter due to heating needs and in summer for electricity generation.
16. For which type of commodity are storage and preservation costs most impactful in determining futures pricing?
A. Agricultural commodities
B. Electricity
C. Industrial metals
D. Processed fuels
Agricultural goods require climate-controlled storage and often involve spoilage risk, making storage a crucial cost.
17. Which of the following best reflects the behavior of commodity prices over time?
A. They usually revert to a long-term average price.
B. They generate fixed interest income.
C. Their transport costs are minimal across geographies.
D. Their risk-return profile mimics that of equities.
Commodities are known for mean-reverting behavior and do not typically offer income returns like dividends or interest.
18. Weather derivatives are primarily priced based on:
A. Rainfall levels
B. Heating and cooling degree day metrics
C. Wind speed and humidity levels
D. Sunshine duration
Weather derivatives use HDD and CDD, which are computed from daily average temperatures across a given period.
19. Which of these commodities has the most unpredictable futures prices due to nonstorability?
A. Natural gas
B. Crude oil
C. Metals
D. Electricity
Since electricity cannot be stored, its pricing is highly sensitive to real-time supply and demand conditions.
20. What is a synthetic forward position on a commodity composed of?
A. A long commodity forward contract and a long zero-coupon bond
B. A long commodity forward contract and a short bond
C. A short forward and a long physical commodity
D. A short forward and a short bond
A synthetic forward replicates the payoff of a long commodity position by using a long forward and a long bond maturing at the forward price.
21. Why is the forward price not necessarily equal to the expected future spot price?
A. Due to government intervention
B. Because markets are inefficient
C. Because of arbitrage strategies
D. Because the forward price uses the risk-free rate, while the expected spot price uses a risk-adjusted rate
The forward price is discounted using the risk-free rate, while the expected spot price must be discounted at a risk-adjusted rate (α), creating a pricing bias.
22. What does the equation F0,T = E(ST) × [(1 + r)/(1 + α)]T illustrate?
A. The unbiased estimation of forward prices
B. The law of one price
C. The bias in forward pricing due to risk premium
D. The concept of backwardation
The equation shows that forward prices are a biased estimate of the expected spot price, adjusted for the difference between the risk-free rate and the risk-adjusted rate (α).
23. If there is no arbitrage, what is the forward price F0,T of a commodity in terms of the spot price S0?
A. F0,T = S0 / (1 + r)T
B. F0,T = S0(1 + r)T
C. F0,T = S0(1 + α)T
D. F0,T = S0(1 + r − α)T
Under no-arbitrage conditions, the forward price equals the spot price compounded at the risk-free rate over the time period.
24. What does the term r − α represent in the forward price equation?
A. Carrying cost
B. Inflation differential
C. Risk premium
D. Arbitrage return
The difference between the risk-free rate (r) and the risk-adjusted rate (α) reflects the commodity’s risk premium.
25. What is the primary goal of a cash-and-carry arbitrage transaction?
A. To reduce storage costs
B. To avoid spot market exposure
C. To earn riskless profit from overpriced futures
D. To gain from currency fluctuations
Cash-and-carry arbitrage seeks to earn a riskless profit when the futures price is above the no-arbitrage price by exploiting cost-of-carry pricing.
26. In a carry market, what does the forward price formula F0,T = (S0 + U) × (1 + r)T include?
A. Spot price, storage costs, and interest rate
B. Only interest rate
C. Income and depreciation
D. Insurance and spoilage costs only
The formula includes spot price (S₀), storage costs (U), and interest rate (r) over time T.
27. What component is subtracted from the spot price if storage costs are negative?
A. Spoilage
B. Income
C. Rent
D. Loan charges
When storage costs are negative, they are treated as income (I), which is subtracted from the spot price in the formula.
28. What action is taken at the start of a cash-and-carry arbitrage?
A. Sell the commodity in spot market
B. Short the underlying asset
C. Borrow money and short a futures contract
D. Borrow funds, buy the commodity, and sell futures
At initiation, the arbitrageur borrows funds, buys the commodity at spot, and sells a futures contract.
29. When is the arbitrage profit realized in a cash-and-carry transaction?
A. At futures contract expiration
B. Immediately upon buying the commodity
C. After the interest is paid
D. When storage cost is zero
Profit is realized when the commodity is delivered against the futures contract and the borrowed money (plus interest) is repaid.
30. If the forward price is lower than the no-arbitrage price, which arbitrage opportunity exists?
A. Cash-and-carry arbitrage
B. Currency arbitrage
C. Reverse cash-and-carry arbitrage
D. Covered interest arbitrage
Reverse cash-and-carry arbitrage is used when futures are underpriced relative to no-arbitrage price.
31. Which of the following best describes reverse cash-and-carry arbitrage?
A. Buying the commodity, selling futures
B. Selling the commodity short and buying futures
C. Borrowing the commodity and storing it
D. Shorting futures and holding cash
Reverse cash-and-carry arbitrage involves short selling the commodity, investing proceeds, and buying it back at a lower futures price.
32. When is reverse cash-and-carry arbitrage profitable?
A. When the futures price is lower than the no-arbitrage price
B. When the spot price is greater than the futures price
C. When interest rates are zero
D. When storage costs are negative
Reverse arbitrage profits arise when futures are underpriced compared to the no-arbitrage price.
33. What is the first step in a reverse cash-and-carry arbitrage strategy?
A. Buy commodity and sell futures
B. Deliver commodity in spot market
C. Sell commodity short
D. Hold the commodity till expiration
The first step is to short sell the commodity and invest the proceeds at the risk-free rate.
34. In the formula F0,T = S0 × [(1 + r)/(1 + δ)]T, what does δ represent?
A. Dividend yield
B. Storage cost
C. Depreciation rate
D. Lease rate
The lease rate (δ) represents the return an investor earns by lending a commodity.
35. From the commodity borrower's perspective, the lease rate is:
A. The dividend yield on the commodity
B. The cost of borrowing the commodity
C. The profit from arbitrage
D. The forward margin
Lease rate is seen as the borrowing cost of the commodity by the borrower.
36. Which of the following describes the convenience yield?
A. The cost of borrowing a commodity
B. The income earned by lending a commodity
C. The nonmonetary benefit of holding excess inventory of a commodity
D. The risk-free rate of return on a commodity
The convenience yield is the nonmonetary benefit a business derives from holding excess inventory to avoid stockouts.
37. The forward price with a convenience yield is calculated as:
A. F0,T = (S0 + U) × [(1 + r) / (1 + Y)]T
B. F0,T = (S0 × (1 + Y))
C. F0,T = (S0 + U) × [(1 + δ) / (1 + r)]T
D. F0,T = (S0 + U) × [(1 + r) / (1 + Y)]T
The formula with the convenience yield adjusts for the nonmonetary benefit of holding the commodity.
38. What does the convenience yield explain about forward prices?
A. Why forward prices may be lower than the pure spot plus storage costs
B. Why forward prices cannot be lower than storage costs
C. Why forward prices always increase over time
D. Why forward prices only depend on the risk-free rate
The convenience yield can reduce the forward price below the sum of spot price and storage costs due to the value of holding the commodity.
39. In the forward price formula with convenience yield, what does Y represent?
A. The risk-free rate
B. The storage cost of the commodity
C. The annualized convenience yield
D. The lease rate for the commodity
Y represents the annualized convenience yield, which accounts for the nonmonetary benefits of holding the commodity.
40. When the convenience yield is positive, the forward price will be:
A. Higher than the spot price plus storage costs
B. Lower than the spot price plus storage costs
C. Equal to the spot price plus storage costs
D. Dependent only on the risk-free rate
A positive convenience yield reduces the forward price because it represents the value of holding inventory.
41. What does normal backwardation imply in the context of futures pricing?
A. The futures price will exceed the expected future spot price
B. There is no correlation between the futures price and the spot price
C. The futures price will be lower than the expected future spot price
D. The spot price will exceed the futures price
Normal backwardation occurs when futures prices are lower than the expected future spot price, often due to a positive correlation with the underlying asset.
42. In the case of contango, what happens to the futures price relative to the expected future spot price?
A. The futures price is equal to the expected future spot price
B. The futures price is higher than the expected future spot price
C. The futures price is lower than the expected future spot price
D. The futures price is unrelated to the expected future spot price
Contango occurs when futures prices are higher than the expected future spot price, typically due to negative correlation between the asset’s returns and the market.
43. If the correlation between the return on the market and the underlying asset is positive, which of the following is true?
A. The futures price will be equal to the spot price at maturity
B. The expected future spot price will be lower than the futures price
C. The expected future spot price will exceed the futures price (normal backwardation)
D. The expected future spot price will be independent of the futures price
A positive correlation means the futures return should exceed the risk-free return, leading to normal backwardation, where the futures price is lower than the expected spot price.
44. The equation P = F / (1 + r)T is used to calculate:
A. The spot price of the commodity
B. The expected return on futures
C. The forward price of a commodity
D. The present value of the futures price
The formula calculates the present value of the futures price, accounting for the risk-free rate over time to maturity.
45. In a market with zero correlation between futures returns and the market, the expected future spot price will:
A. Always exceed the futures price
B. Be equal to the futures price
C. Always be lower than the futures price
D. Be unrelated to the futures price
With zero correlation, there is no systematic risk, and the expected future spot price will be equal to the futures price.
46. Why do agricultural commodities tend to fluctuate seasonally?
A. Because their production is stable throughout the year
B. Because their production is seasonal, while demand is relatively constant
C. Because demand for agricultural products is highly seasonal
D. Because weather has no impact on agricultural production
Agricultural commodities experience seasonal price fluctuations due to the seasonal nature of their production while demand remains relatively stable.
47. How do commodity metals differ from agricultural commodities in terms of pricing?
A. They are more sensitive to weather patterns
B. Their pricing is not affected by the season or weather conditions
C. They are less sensitive to fluctuations in supply compared to agricultural commodities
D. Their prices are mostly driven by agricultural demand
Commodity metals' prices are not impacted by seasonal changes or weather conditions, unlike agricultural commodities whose prices are affected by these factors.
48. What is a unique characteristic of electricity as an energy commodity?
A. It is a storable commodity with stable pricing
B. Its price is influenced only by seasonal demand
C. It can be easily transported over long distances
D. It is non-storable and its price is set by demand and supply at a specific time
Electricity is non-storable, meaning its price is determined by demand and supply at the specific time of use, unlike other energy products that can be stored.
49. Why does the price of natural gas vary geographically?
A. Because natural gas is always in high demand globally
B. Because it is easily storable and transportable
C. Due to high transportation costs and geographical limitations on storage
D. Because it has no seasonal demand fluctuations
The price of natural gas can vary geographically due to high transportation costs and its expensive storage requirements, which limit its availability in some regions.
50. What role do weather derivatives play for energy companies?
A. They are used to predict seasonal demand fluctuations for agricultural commodities
B. They help hedge against weather-related pricing fluctuations in energy markets
C. They are used to control inventory costs for electricity
D. They are used for forecasting the production levels of commodity metals
Energy companies use weather derivatives to hedge against the impact of temperature changes on demand for energy products such as natural gas and electricity.
51. What is the first step in a cash-and-carry arbitrage at the initiation of the contract?
A. Borrow money to buy futures contracts
B. Borrow money for the term of the contract at market interest rates
C. Sell the underlying commodity at the spot price
D. Buy the underlying commodity at the futures price
In a cash-and-carry arbitrage, the first step is to borrow money at the market interest rate for the term of the contract to finance the purchase of the underlying commodity.
52. What happens at the expiration of a cash-and-carry arbitrage contract?
A. The loan is not repaid, and profits are realized
B. The futures contract is bought back at a higher price
C. The commodity is sold back at the spot price
D. The commodity is delivered, and the loan plus interest is repaid
At the expiration of the contract, the commodity is delivered to settle the futures contract, and the loan, along with any interest, is repaid.
53. When does normal backwardation occur in futures markets?
A. When the futures price is equal to the spot price
B. When the futures price exceeds the expected future spot price
C. When the futures price is below the expected future spot price
D. When the futures price is above the current spot price
Normal backwardation occurs when the futures price is below the expected future spot price, typically because traders expect the price to rise.
54. What does the term "contango" describe in the context of futures pricing?
A. A situation where futures prices are below the spot price
B. A situation where futures prices are equal to the spot price
C. A situation where futures prices are lower than expected future spot prices
D. A situation where futures prices are above the expected future spot price
Contango occurs when the futures price is above the expected future spot price, reflecting the cost of carry and expectations of price increases.
55. Which of the following is true for a cash-and-carry arbitrage strategy?
A. The strategy is used when futures prices are expected to decrease
B. The strategy involves selling the underlying commodity and buying futures contracts
C. The strategy involves buying the commodity at the spot price and selling futures contracts
D. The strategy is not used for arbitrage opportunities
In a cash-and-carry arbitrage strategy, an investor buys the underlying commodity at the spot price and sells the corresponding futures contract.
56. Which commodity typically has the highest storage costs due to its nature?
A. Metals
B. Electricity
C. Natural gas
D. Agricultural products
Natural gas has very high storage costs due to the complexity of storage and its potential for indefinite storage, making it the most costly compared to other commodities.
57. What is a characteristic of commodity prices regarding their behavior over time?
A. Commodity prices are highly volatile without any patterns
B. Commodity prices always increase over time
C. Commodity prices tend to be mean-reverting
D. Commodity prices do not follow any economic patterns
Commodities tend to revert back to an average value over time, a concept known as mean reversion. This means that after periods of fluctuation, commodity prices usually return to their long-term average.
58. Which of the following is a primary cost associated with investing in commodities?
A. Interest rate costs
B. Dividends
C. Currency exchange fees
D. Storage and transportation costs
Commodities can incur significant storage and transportation costs. These costs do not apply to financial assets, which typically do not have storage or transportation expenses.
59. What does the lease rate of a commodity represent?
A. The interest rate charged by the government
B. The cost of borrowing financial assets
C. The cost of borrowing a commodity based on supply and demand
D. The dividend paid by a commodity
The lease rate is the cost a borrower incurs for borrowing a commodity, similar to the interest on a financial loan. The lease rate can vary based on commodity supply and demand.
60. What happens to lease rates as the supply of a commodity available for borrowing increases?
A. Lease rates increase significantly
B. Lease rates remain constant
C. Lease rates generally fall
D. Lease rates become negative
As the supply of a commodity available for borrowing increases, the lease rate tends to fall because the increased availability reduces scarcity and the cost of borrowing.
