READING 52 FIXED-INCOME BOND VALUATION: PRICES AND YIELDS Flashcards
(19 cards)
A 5-year bond with a par value of $1,000 has a 6% annual coupon rate. If the yield to maturity (YTM) is 6%, what is the bond’s price relative to its par value?
A. Trades at a discount
B. Trades at par
C. Trades at a premium
Correct Answer: B
Explanation:
When the coupon rate (6%) equals the YTM (6%), the bond’s price equals its par value ($1,000). This occurs because the present value of the cash flows (discounted at 6%) matches the par value, reflecting no premium or discount.
A (Discount) is incorrect as it applies when YTM > coupon rate.
C (Premium) is incorrect as it applies when YTM < coupon rate.
A 5-year bond with a par value of $1,000 has an 8% annual coupon rate. If the YTM is 6%, what is the bond’s likely price behavior?
A. Trades below par
B. Trades at par
C. Trades above par
Correct Answer: C
Explanation:
When the coupon rate (8%) exceeds the YTM (6%), the bond trades above par (at a premium). The higher coupon payments increase the present value of cash flows when discounted at a lower YTM, pushing the price above $1,000 (e.g., approximately $1,080).
A (Below par) is incorrect as it occurs when YTM > coupon rate.
B (At par) is incorrect as it occurs when YTM = coupon rate.
A 5-year bond with a par value of $1,000 has a 6% annual coupon rate. If the YTM rises to 8%, how will the bond’s price compare to its par value?
A. Equal to par
B. Less than par
C. Greater than par
Correct Answer: B
Explanation:
When the YTM (8%) exceeds the coupon rate (6%), the bond trades below par (at a discount). The higher discount rate reduces the present value of cash flows, lowering the price below $1,000 (e.g., approximately $920).
A (Equal to par) is incorrect as it occurs when YTM = coupon rate.
C (Greater than par) is incorrect as it occurs when YTM < coupon rate.
A bond with a par value of $1,000 and a 7% annual coupon rate currently trades at $1,050. What can be inferred about the relationship between the coupon rate and YTM?
A. Coupon rate is less than YTM
B. Coupon rate equals YTM
C. Coupon rate is greater than YTM
Correct Answer: C
Explanation:
A price of $1,050 (above par) indicates the bond trades at a premium, which occurs when the coupon rate (7%) is greater than the YTM. The higher coupon payments increase the present value, driving the price above par.
A (Less than YTM) is incorrect as it would result in a discount price.
B (Equals YTM) is incorrect as it would result in a price equal to par.
A 5-year bond with a par value of $1,000 has a 5% annual coupon rate and trades at $950. Explain the relationship between the coupon rate and YTM.
A. YTM is less than the coupon rate
B. YTM equals the coupon rate
C. YTM is greater than the coupon rate
Correct Answer: C
Explanation:
A price of $950 (below par) indicates the bond trades at a discount, which occurs when the YTM is greater than the coupon rate (5%). The higher YTM reduces the present value of cash flows, lowering the price below $1,000.
A (YTM < coupon rate) is incorrect as it would result in a premium price.
B (YTM = coupon rate) is incorrect as it would result in a price equal to par.
If a bond’s coupon rate is 4% and its YTM is 4%, what is the expected purchase price relative to its $1,000 par value?
A. $900
B. $1,000
C. $1,100
Correct Answer: B
Explanation:
When the coupon rate (4%) equals the YTM (4%), the bond’s purchase price equals its par value ($1,000). The present value of the cash flows discounted at 4% matches the par value, indicating no premium or discount.
A ($900) is incorrect as it suggests a discount, which occurs when YTM > coupon rate.
C ($1,100) is incorrect as it suggests a premium, which occurs when YTM < coupon rate.
A bond with a par value of $1,000 and a 9% annual coupon rate trades at $1,020. Which statement best describes the YTM?
A. YTM is equal to 9%
B. YTM is less than 9%
C. YTM is greater than 9%
Correct Answer: B
Explanation:
A price of $1,020 (above par) indicates a premium, which occurs when the YTM is less than the coupon rate (9%). A lower YTM increases the present value of cash flows, raising the price above $1,000.
A (YTM = 9%) is incorrect as it would result in a price equal to par.
C (YTM > 9%) is incorrect as it would result in a discount price.
A bond with a par value of $1,000 and a 6% annual coupon rate trades at $980. What is the likely relationship between the coupon rate and YTM?
A. Coupon rate exceeds YTM
B. Coupon rate equals YTM
C. Coupon rate is less than YTM
Correct Answer: C
Explanation:
A price of $980 (below par) indicates a discount, which occurs when the YTM exceeds the coupon rate (6%). A higher YTM decreases the present value of cash flows, lowering the price below $1,000.
A (Exceeds YTM) is incorrect as it would result in a premium price.
B (Equals YTM) is incorrect as it would result in a price equal to par.
Which of the following best explains the relationship between a bond’s yield to maturity (YTM) and its price?
A. As YTM increases, bond prices increase.
B. As YTM increases, bond prices decrease.
C. Bond prices remain constant regardless of YTM changes.
Correct Answer: B
Explanation:
As YTM increases, the present value of the bond’s future cash flows decreases, leading to a lower bond price. This inverse relationship is fundamental in fixed income valuation.
Option A is incorrect: Price and yield move in opposite directions.
Option C is incorrect: Prices are directly affected by YTM fluctuations.
Which of the following bonds is most sensitive to changes in interest rates, assuming all else equal?
A. A 10-year, 8% coupon bond
B. A 10-year, 3% coupon bond
C. A 5-year, 3% coupon bond
Correct Answer: B
Explanation:
Lower coupon bonds are more sensitive to interest rate changes because a larger portion of their value comes from the final principal payment, which is more heavily discounted.
Option A is incorrect: Higher coupons make the bond less sensitive to rate changes.
Option C is incorrect: Although it has a low coupon, the shorter maturity reduces sensitivity.
All else equal, which bond will exhibit the highest price volatility in response to a 1% decrease in market interest rates?
A. 5-year, 6% coupon bond
B. 15-year, 6% coupon bond
C. 15-year, 3% coupon bond
Correct Answer: C
Explanation:
Price volatility is highest for long-term bonds with low coupons. This bond has both characteristics.
Option A is incorrect: Shorter maturity reduces sensitivity.
Option B is incorrect: Although it has long maturity, the higher coupon dampens price volatility.
A 6% annual coupon bond is trading at a premium. If the yield to maturity remains constant over time, what will happen to the bond’s price as it approaches maturity?
A. It will increase toward par.
B. It will decrease toward par.
C. It will remain constant.
Correct Answer: B
Explanation:
A bond trading at a premium (coupon > YTM) will gradually decline in price toward par as it nears maturity—this is known as the “pull to par” effect.
Option A is incorrect: Only discount bonds increase toward par.
Option C is incorrect: Prices of premium bonds don’t remain constant if YTM is lower than the coupon.
Which of the following best describes the concept of “convexity” in bond pricing?
A. Bond prices rise and fall by the same amount for equal yield changes.
B. Bond prices fall more sharply when yields increase than they rise when yields fall.
C. Bond prices increase more when yields fall than they decrease when yields rise by the same amount.
Correct Answer: C
Explanation:
Convexity refers to the curvature in the price-yield relationship. Bond prices gain more when yields drop than they lose when yields rise by the same amount.
Option A is incorrect: The price-yield relationship is not linear.
Option B is incorrect: It reverses the effect.
A 3-year, 6% coupon bond is priced at par. Which of the following must be true?
A. The bond’s YTM is 3%.
B. The bond’s YTM is 6%.
C. The bond’s YTM is 9%.
Correct Answer: B
Explanation:
A bond trades at par only when its coupon rate equals the YTM.
Option A is incorrect: If YTM < coupon, the bond would trade at a premium.
Option C is incorrect: If YTM > coupon, the bond would trade at a discount.
Assuming no change in yield, which of the following accurately describes the price behavior of a discount bond as it approaches maturity?
A. Its price increases toward par.
B. Its price remains below par.
C. Its price decreases further below par.
Correct Answer: A
Explanation:
A discount bond (YTM > coupon) will rise in value over time, converging toward par value at maturity.
Option B is incorrect: It doesn’t stay at a discount if yield remains constant.
Option C is incorrect: It doesn’t fall further; it rises toward 100.
A bond has a YTM greater than its coupon rate. Which of the following is most likely true?
A. The bond is trading at a premium.
B. The bond is trading at par.
C. The bond is trading at a discount.
Correct Answer: C
Explanation:
When the YTM > coupon rate, investors require a higher return, so the bond must be sold at a discount to be attractive.
Option A is incorrect: A premium bond has a coupon > YTM.
Option B is incorrect: Par pricing occurs only when coupon = YTM.
Which statement best explains why long-term bond prices are more sensitive to changes in YTM than short-term bonds?
A. Long-term bonds have smaller cash flows.
B. Long-term bonds have cash flows further in the future that are more heavily discounted.
C. Long-term bonds have higher default risk
Correct Answer: B
Explanation:
Distant cash flows are more sensitive to changes in discount rates (YTM), amplifying price volatility.
Option A is incorrect: Sensitivity is about time, not size.
Option C is not the primary reason related to interest rate sensitivity.
A 10-year, 8% bond is currently priced at 108.546. If the YTM rises to 12%, what will most likely happen to the bond’s price?
A. It will increase above 110.
B. It will decrease below 100.
C. It will remain at 108.546.
Correct Answer: B
Explanation:
An increase in YTM decreases the bond’s present value, especially for a bond priced above par.
Option A is incorrect: Prices fall when YTM increases.
Option C is incorrect: Prices don’t stay the same when YTM changes.
