Chapter 19 - Interest Rate Futures (FRM Part 1 - Book 3)
Chapter 19 - Interest Rate Futures
Chapter 19 - Interest Rate Futures
1. Which day count convention is typically used for U.S. Treasury bonds?
A. 30/360
B. Actual/360
C. Actual/Actual
D. 360/365
U.S. Treasury bonds typically use the Actual/Actual day count convention, which accounts for the actual number of days in both the coupon period and the settlement period.
2. Which day count convention is typically used for U.S. corporate and municipal bonds?
A. Actual/Actual
B. Actual/360
C. 360/365
D. 30/360
U.S. corporate and municipal bonds typically use the 30/360 day count convention, where each month is assumed to have 30 days, and the year has 360 days.
3. Which day count convention is typically used for U.S. money-market instruments like Treasury bills?
A. 30/360
B. Actual/360
C. Actual/Actual
D. 360/365
U.S. money-market instruments, such as Treasury bills, use the Actual/360 day count convention, where the actual number of days is used in the numerator, but the denominator assumes 360 days in a year.
4. When calculating accrued interest for a bond, which formula is used?
A. Accrued interest = coupon × # of days from last coupon to the settlement date / # of days in coupon period
B. Accrued interest = coupon × # of days from settlement date to maturity / # of days in coupon period
C. Accrued interest = coupon × # of days in the coupon period / # of days in the settlement period
D. Accrued interest = coupon × # of days from issue date to settlement date / # of days in coupon period
The formula for calculating accrued interest is: Accrued interest = coupon × # of days from last coupon to the settlement date / # of days in coupon period.
5. Which of the following markets typically use the Actual/360 day count convention?
A. U.S. Treasury bonds
B. U.S. money-market instruments (Treasury bills)
C. U.S. corporate and municipal bonds
D. Eurobonds
The Actual/360 day count convention is typically used for U.S. money-market instruments like Treasury bills, where the interest is calculated with a 360-day year.
1. What is the main difference between the clean price and the dirty price of a U.S. Treasury bond?
A. The clean price includes accrued interest, while the dirty price does not.
B. The dirty price includes accrued interest, while the clean price does not.
C. The clean price is quoted based on a $100 par value, while the dirty price is quoted in fractions.
D. The dirty price is always lower than the clean price.
The dirty price (also called the cash price or invoice price) includes the clean price plus any accrued interest. The clean price, in contrast, only reflects the present value of the bond without accrued interest.
2. Which of the following formulas correctly relates the clean price to the dirty price of a U.S. Treasury bond?
A. Clean price = dirty price + accrued interest
B. Clean price = dirty price − accrued interest
C. Dirty price = clean price − accrued interest
D. Accrued interest = dirty price − clean price
The clean price is calculated by subtracting the accrued interest from the dirty price (or cash price). This means the clean price only reflects the present value of the bond, excluding any interest that has accumulated.
3. How is the accrued interest for a U.S. Treasury bond calculated?
A. Accrued interest = coupon × # of days from settlement date to maturity / # of days in coupon period
B. Accrued interest = coupon × # of days from issue date to settlement date / # of days in coupon period
C. Accrued interest = coupon × # of days from last coupon to the settlement date / # of days in coupon period
D. Accrued interest = coupon × # of days from settlement date to the last coupon date / # of days in coupon period
Accrued interest is calculated as the coupon rate times the number of days that have passed since the last coupon payment, divided by the total days in the coupon period.
4. If the quoted price of a U.S. Treasury bond is 95-05 (i.e., 95 5/32 or 95.15625), how do you calculate the dirty price if the accrued interest is $2.50?
A. Dirty price = 95.15625 + 2.50
B. Dirty price = 95.15625 − 2.50
C. Dirty price = 95.15625 × 2.50
D. Dirty price = 95.15625 × 100
The dirty price is the quoted price (clean price) plus the accrued interest. Therefore, the dirty price would be 95.15625 + 2.50 = 97.65625.
5. What is the correct formula for calculating the clean price of a U.S. Treasury bond?
A. Clean price = quoted price + accrued interest
B. Clean price = dirty price − accrued interest
C. Clean price = accrued interest − dirty price
D. Clean price = quoted price − dirty price
The clean price is calculated by subtracting the accrued interest from the dirty price (or cash price). This gives the value of the bond excluding the accrued interest.
1. How is the discount rate for a U.S. Treasury bill calculated?
A. Discount rate = (100 − Y) × n / 360
B. Discount rate = 360 × (100 − Y) / n
C. Discount rate = Y × 360 / (100 − n)
D. Discount rate = (100 − Y) / 360 × n
The discount rate for a U.S. Treasury bill is calculated using the formula:
Discount rate = (360 × (100 − Y)) / n, where Y is the cash price and n is the number of days to maturity.
2. What does the discount rate of a U.S. Treasury bill represent?
A. The price of the T-bill
B. The total interest earned on the T-bill
C. The annualized discount from the face value of the T-bill
D. The maturity value of the T-bill
The discount rate represents the annualized discount from the face value of the T-bill, expressed as a percentage. It is calculated using the formula involving the face value, cash price, and the number of days to maturity.
3. If a U.S. Treasury bill has a cash price of $98 and 180 days to maturity, what is the discount rate?
A. 3.78%
B. 3.56%
C. 4.00%
D. 4.12%
Using the formula Discount rate = (360 × (100 − Y)) / n, we plug in the values:
Y = 98, n = 180. The discount rate = (360 × (100 − 98)) / 180 = 3.78%.
4. Which of the following best describes the relationship between the discount rate and the actual yield on a U.S. Treasury bill?
A. The discount rate equals the actual yield earned on the T-bill.
B. The discount rate is an annualized rate based on the discount from the face value, which is different from the actual yield earned on the T-bill.
C. The discount rate is lower than the actual yield earned on the T-bill.
D. The actual yield equals the price of the T-bill at maturity.
The discount rate is an annualized rate based on the face value and the price difference, while the actual yield reflects the return on investment considering the purchase price. The two rates are not always the same.
5. What is the formula for calculating the annualized yield on a U.S. Treasury bill, given its price?
A. Yield = (100 − Y) / Y × (360 / n)
B. Yield = Y / (100 − Y) × (360 / n)
C. Yield = (100 − Y) / Y × (360 / n)
D. Yield = Y / (100 − Y) × (n / 360)
The annualized yield of a T-bill is calculated by dividing the discount from the face value (100 − Y) by the purchase price (Y), then multiplying by 360/n, where n is the number of days to maturity.
1. How is the cash received by the short position in a Treasury bond futures contract calculated?
A. Cash received = QFP × CF
B. Cash received = QFP × AI
C. Cash received = (QFP × CF) − AI
D. Cash received = (QFP × CF) + AI
The cash received by the short position is calculated as (QFP × CF) + AI, where QFP is the quoted futures price, CF is the conversion factor for the bond delivered, and AI is the accrued interest since the last coupon date.
2. What does the conversion factor (CF) represent in the context of a Treasury bond futures contract?
A. The price received by the long position for the Treasury bond
B. The total accrued interest on the Treasury bond
C. The price received by the short position for the bond delivered
D. The yield of the Treasury bond delivered
The conversion factor (CF) defines the price received by the short position of the contract for the Treasury bond delivered.
3. How does the rounding down of time to maturity affect the conversion factor for longer-term Treasury notes?
A. It is rounded down to the nearest three months to calculate the conversion factor.
B. It is rounded down to the nearest year to calculate the conversion factor.
C. It is rounded down to the nearest month to calculate the conversion factor.
D. There is no rounding down for longer-term Treasury notes.
For longer-term Treasury notes (10-year or longer), the rounding down of time to maturity is done to the nearest three months when calculating the conversion factor.
4. How are conversion factors calculated for shorter-period Treasury notes, such as 2-year or 5-year notes?
A. Conversion factors are calculated using the maturity date of the bond.
B. Conversion factors are based on the nearest quarter year for maturity.
C. Conversion factors are calculated based on the quoted futures price.
D. Conversion factors are rounded down to the nearest month for Treasury notes with shorter periods.
For Treasury notes with shorter periods (such as 2-year or 5-year), the rounding down of time to maturity is done to the nearest month when calculating the conversion factor.
5. What is the primary effect of the yield curve's level and shape on the cheapest-to-deliver (CTD) Treasury bond decision?
A. A flat yield curve will have no impact on the CTD decision.
B. A steep yield curve increases the price of the long-end bonds, making them more attractive for delivery.
C. A steep yield curve decreases the price of the long-end bonds, making them less attractive for delivery.
D. A flat yield curve makes short-term bonds more attractive for delivery.
A steep yield curve typically increases the price of long-end bonds, making them more attractive for delivery in the cheapest-to-deliver (CTD) Treasury bond decision.
21. How is the cash received by the short position in a Treasury bond futures contract calculated?
A. Cash received = (QFP × CF) − AI
B. Cash received = (Quoted bond price + AI)
C. Cash received = (QFP × CF) + (Quoted bond price)
D. Cash received = (QFP × CF) + AI
The cash received by the short position in a Treasury bond futures contract is calculated as (QFP × CF) + AI, where QFP is the quoted futures price, CF is the conversion factor for the bond delivered, and AI is the accrued interest since the last coupon date.
22. What is the primary goal when determining the cheapest-to-deliver (CTD) bond?
A. Maximizing the bond price
B. Minimizing the conversion factor
C. Minimizing the cost of delivering the bond
D. Maximizing the yield
The CTD bond minimizes the cost of delivering the bond, which is calculated as quoted bond price − (QFP × CF).
23. Which type of bonds tend to be the cheapest to deliver when yields are greater than 6%?
A. High-coupon, short-maturity bonds
B. Low-coupon, long-maturity bonds
C. High-coupon, long-maturity bonds
D. Low-coupon, short-maturity bonds
When yields are greater than 6%, the cheapest-to-deliver (CTD) bonds tend to be low-coupon, long-maturity bonds.
24. Which type of bonds are typically the cheapest to deliver when yields are less than 6%?
A. High-coupon, short-maturity bonds
B. Low-coupon, long-maturity bonds
C. High-coupon, long-maturity bonds
D. Low-coupon, short-maturity bonds
When yields are less than 6%, the cheapest-to-deliver (CTD) bonds tend to be high-coupon, short-maturity bonds.
25. How does the yield curve's shape affect the cheapest-to-deliver (CTD) bond decision?
A. A flat yield curve makes long-term bonds more attractive for delivery.
B. A downward sloping yield curve makes long-term bonds more attractive for delivery.
C. A steep yield curve makes short-term bonds more attractive for delivery.
D. An upward sloping yield curve makes long-term bonds more attractive for delivery.
When the yield curve is upward sloping, the cheapest-to-deliver (CTD) bonds tend to have longer maturities.
26. How does the wild card play impact the short position in a Treasury bond futures contract?
A. It allows the short position to deliver the bond at any time during the delivery month, increasing delivery costs.
B. It allows the short position to choose the lowest yield bond for delivery.
C. It allows the short position to choose the delivery date and potentially reduce delivery costs.
D. It forces the short position to deliver the bond at the specified settlement price.
The wild card play gives the short position the ability to choose the delivery date and potentially reduce delivery costs if bond prices fall after the settlement price at 2:00 pm.
27. What is the primary reason the short position may accept a lower delivery price in a Treasury bond futures contract?
A. Because the futures price is always set higher than the bond price.
B. Because of the benefits available to the short position, such as the wild card play.
C. Because the long position receives fewer benefits in the futures contract.
D. Because the short position cannot influence the delivery price.
The short position may accept a lower delivery price due to the various benefits it enjoys, such as the wild card play and the ability to choose the delivery date, which reduce the delivery cost.
28. What is the formula for calculating the theoretical futures price of a bond with known cash flows, using annual compounding?
A. F₀ = (S₀ − I) × (1 + r)^T
B. F₀ = S₀ × (1 + r)^T
C. F₀ = S₀ − I × r × T
D. F₀ = S₀ + I × e^rT
The cost-of-carry model adjusts the spot price by the present value of known income and compounds the result at the risk-free rate. Hence, F₀ = (S₀ − I) × (1 + r)^T.
29. What does 'I' represent in the futures pricing formula F₀ = (S₀ − I) × (1 + r)^T?
A. Interest accrued on the bond
B. Inflation factor
C. Present value of cash flow
D. Internal rate of return
'I' refers to the present value of known cash flows (such as coupons) from the bond, which reduces the spot price in futures pricing.
30. Under continuous compounding, what is the correct form of the futures pricing formula?
A. F₀ = (S₀ + I) × e^rT
B. F₀ = S₀ × e^rT − I
C. F₀ = S₀ − I × e^rT
D. F₀ = (S₀ − I) × e^rT
With continuous compounding, the futures price is calculated as F₀ = (S₀ − I) × e^rT, where e^rT reflects exponential growth at the risk-free rate.
31. What is the role of the Conversion Factor in Treasury bond futures contracts?
A. It adjusts for inflation over the bond’s life
B. It standardizes different bonds to a common benchmark
C. It adjusts the spot price for interest payments
D. It converts accrued interest into annual yield
The conversion factor adjusts for differences between the delivered bond and the notional bond, allowing comparison on a standardized basis.
32. In Treasury bond futures pricing, what must be added to the clean price of a bond to obtain the full price?
A. Accrued interest
B. Conversion factor
C. Present value of future coupons
D. Inflation adjustment
The full (or invoice) price of a bond includes the clean price plus accrued interest since the last coupon payment.
33. Which of the following is a key difference between Eurodollar futures and forward-rate agreements (FRAs)?
A. Eurodollar futures are settled only at the end of the contract
B. Eurodollar futures pay interest at the end of the three months
C. Eurodollar futures settle daily, while FRAs settle only at the end of the contract
D. Eurodollar futures are not based on LIBOR
Eurodollar futures settle daily, while forward-rate agreements (FRAs) are settled only at the end of the contract. Additionally, Eurodollar futures pay interest at the beginning of the contract.
34. What is the minimum price change or "tick" for a Eurodollar futures contract?
A. 1 basis point, or $25 per $1 million contract
B. 10 basis points, or $250 per $1 million contract
C. 0.5 basis points, or $12.50 per $1 million contract
D. 0.1 basis points, or $2.50 per $1 million contract
The minimum price change, or "tick," for a Eurodollar futures contract is 1 basis point, which equals $25 for each $1 million contract.
35. Which of the following best describes a Eurodollar futures contract?
A. A forward contract that settles at the end of the contract
B. A futures contract based on the price of crude oil
C. A futures contract on U.S. Treasury bond prices
D. A cash-settled futures contract based on three-month LIBOR
A Eurodollar futures contract is a cash-settled futures contract based on the three-month LIBOR, used to manage short-term interest rate risks.
36. In Eurodollar futures, what is the face amount of the underlying Eurodollar deposit?
A. $500,000
B. $1 million
C. $5 million
D. $10 million
The face amount of the underlying Eurodollar deposit is $1 million, which is used for calculating the futures contract value.
37. How is the Eurodollar futures contract different from a Forward Rate Agreement (FRA) in terms of interest payment timing?
A. Eurodollar futures pay interest at the end of the contract, while FRAs pay interest at the beginning
B. Eurodollar futures and FRAs both pay interest at the same time
C. Eurodollar futures pay interest at the beginning of the contract, while FRAs pay at the end
D. Eurodollar futures and FRAs have no interest payments
Eurodollar futures pay interest at the beginning of the contract, while FRAs pay interest at the end of the contract.
38. What is the effect of convexity adjustment on Eurodollar futures contracts?
A. It reduces the actual forward rate to be lower than the implied forward rate
B. It increases the futures rate compared to the forward rate
C. It eliminates any differences between the actual and implied forward rates
D. It reduces the difference between the actual forward rate and the implied forward rate from futures contracts
The convexity adjustment reduces the difference between the actual forward rate and the implied forward rate from futures contracts. It ensures that long-dated futures contracts imply forward rates that are closer to actual rates.
39. What is the formula for calculating the convexity adjustment in Eurodollar futures?
The convexity adjustment is calculated using the formula: Forward rate = Futures rate − (½ × Ïƒ2 × T1 × T2), where σ is the standard deviation, T1 is the maturity of the futures contract, and T2 is the time to the maturity of the rate underlying the contract.
40. As the maturity (T1) of a Eurodollar futures contract increases, what happens to the convexity adjustment?
A. The convexity adjustment increases
B. The convexity adjustment decreases
C. The convexity adjustment remains unchanged
D. The convexity adjustment becomes irrelevant
As the maturity (T1) of a Eurodollar futures contract increases, the convexity adjustment increases, leading to a larger difference between actual forward rates and those implied by futures.
41. In the convexity adjustment formula for Eurodollar futures, what does T2 represent?
A. The maturity in years of the futures contract
B. The time to the maturity of the rate underlying the contract
C. The time to maturity of the futures contract and underlying rate
D. The time to the maturity of the rate underlying the contract, in years
T2 represents the time to the maturity of the rate underlying the contract, which is typically 90 days for Eurodollar futures.
42. What effect does an increase in the standard deviation (σ) have on the convexity adjustment for Eurodollar futures?
A. It decreases the convexity adjustment
B. It increases the convexity adjustment
C. It has no effect on the convexity adjustment
D. It reverses the effect of the convexity adjustment
An increase in the standard deviation (σ) leads to a larger convexity adjustment, as volatility is a key component in the adjustment formula.
43. What is the purpose of using convexity-adjusted Eurodollar futures to produce a LIBOR spot curve?
A. To calculate the forward rate between T1 and T2
B. To estimate the interest rate for a single future period
C. To generate a curve representing the future spot rates for LIBOR
D. To determine the discount factor for Eurodollar futures contracts
The purpose of using convexity-adjusted Eurodollar futures to produce a LIBOR spot curve is to generate a curve that represents the future spot rates (LIBOR zero curve), which can be derived from the forward rates implied by the futures contracts.
44. In the equation for the forward rate between T1 and T2, what does the term "R1" represent?
A. The forward rate between T1 and T2
B. The spot rate corresponding to T1 periods
C. The forward rate between T2 and T3
D. The interest rate implied by the Eurodollar futures contract
"R1" represents the spot rate corresponding to the time period T1. It is the initial spot rate used to calculate the forward rate between T1 and T2.
45. What does the equation for forward rate in Eurodollar futures help to calculate?
A. The LIBOR rate for a single period
B. The spot rate at time T2
C. The forward rate between two periods, T1 and T2
D. The interest rate volatility over a given time period
The equation for forward rate in Eurodollar futures helps to calculate the forward rate between two periods, T1 and T2, by using the spot rates for those periods.
46. How can the next LIBOR spot rate (R2) be calculated based on the forward rate and the first spot rate (R1)?
A. By subtracting the forward rate from the spot rate
B. By multiplying the forward rate by the spot rate
C. By adding the forward rate to the spot rate
D. By solving the rearranged forward rate equation: R2 = RForward (T2 − T1) + R1 T1 / T2
The next LIBOR spot rate (R2) can be calculated by solving the rearranged equation for the forward rate: R2 = RForward (T2 − T1) + R1 T1 / T2, where RForward is the forward rate between T1 and T2.
47. What is the end result of calculating the LIBOR spot curve using the forward rate equation?
A. The discount factor for LIBOR rates
B. The interest rate for a given future period
C. The generated LIBOR spot (zero) curve
D. The forward rate for each future contract
The end result of calculating the LIBOR spot curve using the forward rate equation is the generated LIBOR spot (zero) curve, which represents the spot rates for different maturities.
48. What is the main goal of a duration-based hedge strategy in the context of interest rate futures?
A. To maximize the portfolio’s return by increasing its duration
B. To eliminate the impact of changing interest rates on the portfolio's value
C. To create a position with a zero duration, making the portfolio insensitive to yield changes
D. To adjust the portfolio value to match the futures contract's value
The primary objective of a duration-based hedge is to create a combined position that has a zero duration, thus making the portfolio insensitive to changes in interest rates.
49. In the duration-based hedge ratio formula, what does the negative sign indicate?
A. The investor should long both the portfolio and the futures contract
B. The futures position should be in the same direction as the portfolio
C. The futures position should be the opposite of the original position
D. The portfolio value should be increased to match the futures contract value
The negative sign indicates that the futures position should be the opposite of the portfolio position. If the portfolio is long, the futures position must be short.
50. What does the duration-based hedge ratio formula help to calculate?
A. The number of futures contracts required to hedge the portfolio
B. The total value of the futures contract needed for the hedge
C. The optimal amount of capital needed to hedge the portfolio
D. The future value of the portfolio after the hedge
The duration-based hedge ratio formula is used to calculate the number of futures contracts required to hedge the portfolio and eliminate the impact of yield changes.
51. In the duration-based hedge ratio formula, what does the term "DP" represent?
A. The duration of the futures contract at the hedging horizon
B. The duration of the portfolio at the hedging horizon
C. The present value of the portfolio
D. The value of the futures contract at the hedging horizon
"DP" represents the duration of the portfolio at the hedging horizon. It is a measure of the portfolio’s sensitivity to changes in interest rates.
52. When using the duration-based hedge ratio, if an investor is long on the portfolio, what action should they take with the futures contracts?
A. The investor should short the futures contracts
B. The investor should long the futures contracts
C. The investor should not take any action with futures contracts
D. The investor should short the portfolio and long the futures contracts
If the investor is long on the portfolio, they should short the futures contracts to hedge against interest rate movements and achieve a zero duration position.
53. What is one of the main limitations of using duration-based hedging strategies?
A. Duration-based hedging strategies are only effective for short-term interest rate changes
B. Duration-based hedging assumes that interest rates are constant over time
C. Duration-based hedging assumes that yield changes are linear, which is not accurate for large changes
D. Duration-based hedging can only be used for bonds with a low coupon rate
The main limitation of duration-based hedging is that it assumes yield changes are linear, which becomes less accurate when the changes are large or nonparallel.
54. How does the convexity of the price/yield relationship affect duration-based hedging strategies?
A. Convexity has no impact on duration-based hedging strategies
B. Convexity makes duration-based hedging more accurate for small interest rate changes
C. Convexity makes duration-based hedging less accurate for large interest rate changes
D. Convexity increases the effectiveness of duration-based hedging strategies for nonparallel shifts in the yield curve
Convexity makes the price/yield relationship nonlinear, which causes duration-based hedging to become less accurate as the size of interest rate changes increases.
55. Why does the assumption that all yield changes are perfectly correlated limit the effectiveness of duration-based hedging?
A. Because yield changes are always parallel and therefore do not affect the portfolio
B. Because the assumption that all yield changes are perfectly correlated does not hold in real markets where yield curves can shift in different ways
C. Because duration-based hedging can only be applied to non-correlated yield changes
D. Because perfectly correlated yield changes always result in losses in the portfolio
The assumption that all yield changes are perfectly correlated does not hold in real markets, where yield curves can experience nonparallel shifts, which reduces the effectiveness of duration-based hedging.
56. In what scenario would a duration-based hedge perform poorly?
A. When interest rates change by a small, parallel shift
B. When interest rates change by large, nonparallel shifts
C. When interest rates are completely predictable
D. When interest rate changes are perfectly correlated
Duration-based hedging strategies perform poorly when interest rates change in large, nonparallel shifts, as the linear assumption of duration becomes less accurate.
57. What does the use of duration as a risk measurement tool assume about interest rate changes?
A. Interest rate changes are always large and unpredictable
B. Interest rates will remain constant over time
C. Interest rate changes are perfectly linear and correlated
D. Interest rate changes have no impact on the portfolio
Duration assumes that interest rate changes are linear and perfectly correlated, which can be unrealistic in real market conditions.
