Chapter 10 - Pricing Financial Forwards and Futures (FRM Part 1 - Book 3)
Chapter 10 - Pricing Financial Forwards and Futures
Chapter 10 - Pricing Financial Forwards and Futures
1. Which of the following is considered an investment asset?
A. Natural gas
B. Crude oil
C. Stocks
D. Petrol
Investment assets are held for investment purposes by many investors. Stocks are a prime example of financial investment assets.
2. What is the primary use of consumption assets?
A. Trading for profit
B. Personal or industrial consumption
C. Tax-saving investments
D. Issuing bonds
Consumption assets are typically held for consumption rather than investment. Examples include oil and natural gas.
3. What is the goal of a short seller?
A. Sell high now, buy low later
B. Buy low now, sell high later
C. Hold assets long-term
D. Avoid market volatility
In short selling, the goal is to profit from a price drop — sell now at a high price and buy back later at a lower price.
4. What obligation does a short seller have regarding dividends?
A. Receive all dividends
B. Ignore dividends
C. Share dividends with the broker
D. Pay all dividends to the lender
A short seller is required to pay any dividends on the borrowed shares to the lender.
5. A stock is short sold at ₹30. Later, it’s bought back at ₹20. What is the net profit per share (ignoring all fees and dividends)?
A. ₹20
B. ₹10
C. ₹5
D. ₹0
The short seller sold at ₹30 and bought back at ₹20, resulting in a profit of ₹10 per share.
6. What does the variable 'S' represent in the forward pricing model?
A. Spot price of the underlying asset
B. Forward price of the contract
C. Risk-free interest rate
D. Time to maturity
In the model, 'S' stands for the spot price of the underlying asset at time t = 0.
7. Which formula correctly represents the forward price with no income or yield?
A. F = S × (1 - r)^T
B. F = S ÷ (1 + r)^T
C. F = S × (1 + r)^T
D. F = S + rT
The forward price is derived by compounding the spot price with the risk-free rate over time T: F = S × (1 + r)^T.
8. What happens if the forward price F is greater than S × (1 + r)T?
A. Arbitrageurs sell the asset and lend the proceeds
B. Arbitrageurs sell the forward and buy the asset
C. No arbitrage opportunity exists
D. Arbitrageurs buy both the forward and the asset
If F > S × (1 + r)^T, arbitrageurs can lock in profit by selling the overpriced forward and buying the asset with borrowed funds.
9. In a no-arbitrage condition, what must be true about the forward price?
A. F > S × (1 + r)^T
B. F < S × (1 + r)^T
C. F = S × r × T
D. F = S × (1 + r)^T
In a no-arbitrage market, the forward price must equal the compounded spot price: F = S × (1 + r)^T.
10. What does the variable 'I' represent in the forward pricing model with income?
A. Interest earned by the forward holder
B. Present value of income (cash flows) from the underlying asset
C. Implied rate of return
D. Inflation adjustment
In the formula, 'I' refers to the present value of all known income or cash flows from the asset during the contract term.
11. Which of the following is the correct formula for forward pricing with income?
A. F = (S + I) × (1 + r)^T
B. F = S × (1 + r)^T + I
C. F = (S − I) × (1 + r)^T
D. F = S × (1 + r)^T − I
When the asset generates known income, the forward price is calculated as F = (S − I) × (1 + r)^T.
12. Why is the income deducted from the spot price when calculating forward price?
A. Because the forward contract holder does not receive the income
B. To reflect future tax obligations
C. To account for price volatility
D. Because the forward contract includes dividend reinvestment
The forward contract holder doesn’t receive interim income, so the present value of income is subtracted from the spot price.
13. If the asset pays income during the life of a forward contract, how does it affect arbitrage opportunities?
A. No adjustment is needed; arbitrage works the same
B. Arbitrage is not possible if income is present
C. Arbitrage only works if income is reinvested
D. Arbitrage must account for the income by using the adjusted formula
Arbitrage remains possible, but the present value of income from the asset must be considered in the forward pricing formula.
14. What does the variable 'q' represent in the forward pricing model with dividends?
A. Quantity of the asset
B. Quarterly compounding rate
C. Annually compounded dividend yield
D. Forward contract quantity
The variable 'q' in the formula refers to the annually compounded dividend yield of the underlying asset.
15. Which of the following formulas correctly represents the forward price when the asset pays a known annual dividend yield?
A. F = S × (1 + r + q)T
B. F = S × [(1 + r) / (1 + q)]T
C. F = S × (1 + r − q)T
D. F = (S − q) × (1 + r)T
The forward price is adjusted for dividend yield using the formula F = S × [(1 + r) / (1 + q)]T.
16. Why is the forward price adjusted downward when the asset pays a dividend?
A. To adjust for inflation expectations
B. Because interest rates are lower during dividend payments
C. To reflect spot price volatility
D. Because the forward holder does not receive the dividend
Since the forward contract holder doesn’t receive dividends, the forward price is adjusted to reflect the lower value of holding the asset.
17. What happens if the forward price is greater than S × [(1 + r) / (1 + q)]T?
A. Arbitrageurs will sell the forward and buy the asset
B. Arbitrageurs will buy the forward and short the asset
C. Arbitrage opportunities do not exist in this scenario
D. The forward price must be increased
If the forward is overpriced, arbitrageurs can profit by selling the forward and buying the asset, earning a riskless gain.
18. What is the initial value of a forward contract?
A. Positive value
B. Negative value
C. Zero value
D. Undefined value
The initial value of a forward contract is zero at inception since no obligation has been created yet.
19. How is the value of a long forward contract on an asset with no cash flows calculated?
A. Value = S − [K / (1 + r)T]
B. Value = S + [K / (1 + r)T]
C. Value = S − I − [K / (1 + r)T]
D. Value = [S / (1 + q)T] − [K / (1 + r)T]
The value of a long forward contract with no cash flows is calculated as: S − [K / (1 + r)T].
20. How is the value of a forward contract adjusted when the underlying asset has cash flows?
A. Value = S − [K / (1 + r)T] + I
B. Value = S − I + [K / (1 + r)T]
C. Value = S − I − [K / (1 + r)T]
D. Value = [S / (1 + q)T] − [K / (1 + r)T]
When cash flows are involved, the value of the forward contract becomes: S − I − [K / (1 + r)T], where I is the present value of the cash flows.
21. What is the formula for the value of a forward contract on an asset with an annual dividend yield (q)?
A. Value = S − [K / (1 + r)T] + q
B. Value = [S / (1 + q)T] − [K / (1 + r)T]
C. Value = S × [(1 + r) / (1 + q)]T
D. Value = S × [(1 + q) / (1 + r)]T
For an asset with an annual dividend yield (q), the value of the forward contract is given by: [S / (1 + q)T] − [K / (1 + r)T].
22. What is the primary difference between forward contracts and futures contracts?
A. Futures contracts are settled once at maturity, while forwards are settled daily.
B. Forward contracts are traded on exchanges, whereas futures are not.
C. Futures contracts have no marking-to-market requirement, while forwards do.
D. Futures contracts are marked-to-market daily, whereas forward contracts are settled only at maturity.
The key difference is that futures contracts are marked-to-market daily, while forward contracts are settled only at maturity.
23. When interest rates are known or change predictably, what is the relationship between forward and futures prices?
A. Futures prices are always higher than forward prices.
B. Forward prices are always higher than futures prices.
C. Forward and futures prices are approximately equal.
D. The difference between forward and futures prices is always significant.
When interest rates are known or predictable, forward and futures prices are approximately equal, as the impact of interest rate changes is minimal.
24. Why would a long futures contract be priced slightly higher than a long forward contract when asset prices are positively correlated to interest rates?
A. The daily marking-to-market of futures allows immediate reinvestment of gains at a higher interest rate.
B. Futures contracts have more flexible delivery dates than forwards.
C. Futures contracts do not account for changes in interest rates.
D. Futures contracts do not recognize asset price changes as they happen.
When asset prices are positively correlated to interest rates, the daily marking-to-market in futures allows for immediate reinvestment of gains at a higher interest rate, making futures slightly more desirable than forwards.
25. How do futures contracts differ from forward contracts in terms of delivery dates?
A. Futures contracts have no fixed delivery date, while forward contracts have multiple options.
B. Futures contracts have one fixed delivery date, while forward contracts may have a choice of delivery dates.
C. Futures contracts have a choice of delivery dates, whereas forward contracts have one delivery date.
D. Futures contracts do not have delivery dates, while forward contracts have multiple options.
Futures contracts offer a choice of delivery dates, whereas forward contracts have a single fixed delivery date.
26. According to the Interest Rate Parity (IRP), what is the relationship between the forward exchange rate (F) and the spot exchange rate (S)?
A. F = S × (1 + rXXX) / (1 + rYYY)
B. F = S × [(1 + rYYY) / (1 + rXXX)]T
C. F = S × [(1 + rXXX) / (1 + rYYY)]
D. F = S × [(1 + rYYY) / (1 + rXXX)]
According to IRP, the forward exchange rate (F) is related to the spot exchange rate (S) and the interest rate differential between the domestic and foreign currencies as: F = S × [(1 + rYYY) / (1 + rXXX)]T.
27. In the IRP condition, what does the variable 'T' represent?
A. Time to maturity of the forward contract in years
B. Time in days before the forward exchange rate is settled
C. Total interest rate differential between the two currencies
D. The amount of time the foreign currency deposit is held
In the IRP formula, 'T' represents the time to maturity of the forward contract in years.
28. What is the primary assumption underlying the Interest Rate Parity (IRP) condition?
A. There are no transaction costs or restrictions on the currency market.
B. The foreign exchange market is completely inefficient.
C. The interest rates in different countries are independent of each other.
D. The IRP condition is a no-arbitrage relationship.
The IRP condition assumes a no-arbitrage relationship, meaning there are no opportunities for riskless profits through arbitrage in the foreign exchange market.
29. How is the interest rate differential between the domestic currency (YYY) and foreign currency (XXX) represented in the IRP condition?
A. As (1 + rXXX) / (1 + rYYY)
B. As (rXXX - rYYY)
C. As (rYYY - rXXX)
D. As (rYYY + rXXX)
In the IRP condition, the interest rate differential is represented as (rYYY - rXXX), where rYYY is the interest rate for the domestic currency and rXXX is the interest rate for the foreign currency.
30. The Interest Rate Parity condition is equivalent to which previous equation?
A. Equation 3 with rXXX replacing q
B. Equation 1 with rYYY replacing q
C. Equation 4 with rYYY replacing q
D. Equation 2 with rXXX replacing q
The IRP condition is equivalent to Equation 3 with rXXX replacing q. The interest rate differential between domestic and foreign currencies is represented as rYYY - rXXX.
31. How are stock index futures valued in relation to forward contracts?
A. They are valued similarly to futures contracts that do not pay dividends.
B. They are valued similarly to forward contracts that pay dividends.
C. They are valued based on the present value of future dividends.
D. They are valued based on the interest rates of the domestic country.
Stock index futures are valued similarly to forward contracts that pay dividends, with the futures price being calculated using Equation 3, considering the average dividend yield (q).
32. When arbitrage opportunities arise in stock index futures, which of the following is true?
A. If the futures price is greater than the theoretical value, short the stocks and go long the futures contract.
B. If the futures price is lower than the theoretical value, short the futures contract and go long the stocks.
C. If the futures price is greater than the theoretical value, short the futures contract and go long the underlying stocks.
D. Arbitrage opportunities do not exist in stock index futures markets.
If the futures price is greater than the theoretical value, an arbitrage profit is generated by shorting the futures contracts and going long the underlying stocks.
33. What type of investors typically perform index arbitrage when the futures price is higher than the theoretical value?
A. Pension funds
B. Corporations holding short-term investments
C. Hedge funds specializing in commodities
D. Individual retail investors
Pension funds are typically involved in index arbitrage when the futures price is higher than the theoretical value, as they hold portfolios of index stocks.
34. How is index arbitrage typically implemented in the market?
A. By buying the futures contract and holding until maturity
B. By purchasing call options on the index
C. By trading the futures contract manually without technology
D. By program trading, where a computer sends out trades for stocks and futures contemporaneously
Index arbitrage is implemented through program trading, where a computer sends out all necessary trades for the stocks in the index simultaneously with the trading of the futures contract.
35. What is the main objective of index arbitrage?
A. To predict future movements of stock prices
B. To maintain the pricing relationship between the index and its futures
C. To speculate on market volatility
D. To reduce the cost of hedging positions in stock indexes
The main objective of index arbitrage is to maintain the pricing relationship between the index and its futures, ensuring that any mispricing is corrected.
36. How do interest rates affect the desirability of a long futures contract compared to a long forward contract?
A. Long futures contracts become more desirable as interest rates rise.
B. Long futures contracts become less desirable as interest rates fall.
C. Long futures contracts become less desirable as interest rates rise due to the immediate recognition of losses.
D. There is no relationship between interest rates and the desirability of futures contracts.
When interest rates rise, a loss from an asset price decrease will be recognized immediately with futures contracts, making them less desirable compared to forward contracts, where losses are delayed.
37. Why are forward contracts often more desirable than futures contracts when there are losses on the underlying asset?
A. Forward contracts allow immediate recognition of losses, unlike futures contracts.
B. Forward contracts allow for a delay in recognizing losses, making them more desirable when there are losses.
C. Forward contracts have lower settlement costs compared to futures contracts.
D. Futures contracts allow for a delay in recognizing losses, making them more desirable in this case.
Forward contracts allow a delay in recognizing losses compared to futures contracts, which have daily settlement. This makes forwards more desirable when there are losses.
38. What is the main difference between forward contracts and futures contracts in terms of settlement?
A. Forward contracts are settled daily, while futures contracts are settled at the end of the contract.
B. Futures contracts are settled monthly, while forward contracts are settled daily.
C. Futures contracts are settled daily, while forward contracts are settled at the end of the contract.
D. There is no difference in settlement between forwards and futures contracts.
The main difference is that futures contracts are settled daily, while forward contracts are settled at the end of the contract.
39. Why do forward and futures prices often appear to be very close to each other?
A. They are based on different underlying assets.
B. The path of interest rates is often unpredictable, which leads to similar pricing for both contracts.
C. Forward contracts are more liquid than futures contracts.
D. Futures contracts are generally less expensive than forwards due to their daily settlement feature.
Forward and futures prices are often very close to each other because the path of interest rates is unpredictable, which makes both contracts similarly priced in practice.
40. Which of the following is true regarding the pricing relationship between forward and futures contracts?
A. Futures contracts are priced significantly higher than forward contracts at all times.
B. Forward contracts are always priced higher than futures contracts due to settlement differences.
C. Forward and futures prices are often very close to each other, and price differences are usually negligible.
D. Futures contracts have larger price differences than forward contracts because of daily settlement.
Forward and futures prices are often very close to each other due to the unpredictable nature of interest rates, and the price differences are generally negligible.
