READING 58 YIELD-BASED BOND CONVEXITY AND PORTFOLIO PROPERTIES Flashcards
(22 cards)
Which of the following best describes the shape of the price-yield relationship for an option-free bond?
A. Linear and downward sloping
B. Convex and upward sloping
C. Convex and downward sloping
Correct Answer: C
Explanation:
The price-yield relationship for an option-free bond is convex and downward sloping—as yield increases, price decreases, but at a decreasing rate.
A is incorrect because the relationship is not linear.
B is incorrect because the curve is downward, not upward sloping.
What is the key reason that modified duration underestimates bond price increases when yields fall?
A. It assumes flat yield curves
B. It ignores the time value of money
C. It does not account for convexity
Correct Answer: C
Explanation:
Modified duration is a linear approximation and does not capture the curvature (convexity) of the price-yield relationship.
A is irrelevant; yield curve shape isn’t the issue here.
B is incorrect; time value of money is already factored into duration.
Which of the following bond characteristics increases convexity, all else equal?
A. Shorter maturity
B. Higher coupon rate
C. Lower yield to maturity
Correct Answer: C
Explanation:
Convexity increases with longer maturity, lower coupon, and lower YTM.
A and B are incorrect because shorter maturity and higher coupon both reduce convexity.
What does convexity measure in the context of bonds?
A. The probability of default
B. The linear sensitivity of price to yield changes
C. The curvature of the price-yield relationship
Correct Answer: C
Explanation:
Convexity measures the second-order effect—how much the bond price curve bends as yield changes.
A is related to credit risk, not convexity.
B describes duration, not convexity.
When estimating bond price changes using duration and convexity, what role does convexity play?
A. It cancels out the duration effect
B. It adjusts the duration estimate for larger yield changes
C. It estimates price for callable bonds only
Correct Answer: B
Explanation:
Convexity refines the duration estimate for better accuracy, especially with larger changes in yield.
A is false—convexity does not cancel duration.
C is incorrect—convexity applies to all bonds, not just callable ones.
A bond with higher convexity will:
A. Gain more in price when yields fall and lose more when yields rise
B. Lose less in price when yields rise and gain less when yields fall
C. Gain more when yields fall and lose less when yields rise
Correct Answer: C
Explanation:
Positive convexity benefits bondholders: more gain when yields fall, less loss when yields rise.
A is incorrect—it applies to bonds with negative convexity.
B is incorrect because gain is not less with higher convexity.
Why is convexity always positive for option-free bonds?
A. Future coupons are reinvested
B. Bond prices are inversely related to yields
C. Longer maturity cash flows have higher sensitivity
Correct Answer: C
Explanation:
Positive convexity arises because later cash flows are more sensitive to yield changes, increasing curvature.
A is unrelated to convexity directly.
B is true but explains price-yield slope, not convexity.
Which of the following statements is true regarding money duration?
A. It measures price sensitivity as a percentage
B. It is duration multiplied by full bond price
C. It only applies to zero-coupon bonds
Correct Answer: B
Explanation:
Money duration = Modified Duration × Full Price—gives price change in currency units.
A is false—that’s percent duration.
C is incorrect—it applies to any bond.
What happens to convexity when a bond’s time to maturity increases?
A. It decreases
B. It remains constant
C. It increases
Correct Answer: C
Explanation:
Longer maturity = more convexity because future cash flows are more sensitive.
A and B contradict this.
Which best describes the relationship between convexity and duration?
A. They both increase with higher coupon rates
B. Convexity captures changes that duration cannot
C. Duration is derived from convexity
Correct Answer: B
Explanation:
Convexity adds accuracy to duration estimates for nonlinear price-yield changes.
A is false—higher coupon reduces both.
C is incorrect—convexity is not a base for duration.
Why is convexity adjustment the same for both yield increases and decreases?
A. It is always a negative value
B. It is based on the square of yield change
C. It depends only on coupon rate
Correct Answer: B
Explanation:
Because convexity uses (Δy)^2, its effect is always positive, regardless of direction.
A is false—it’s positive.
C is unrelated to the sign of the adjustment.
Which of the following is NOT a characteristic that increases a bond’s convexity?
A. Lower coupon
B. Higher YTM
C. Longer maturity
Correct Answer: B
Explanation:
Higher YTM decreases present value of distant cash flows, reducing convexity.
A and C both increase convexity.
Why are price estimates using only duration often inaccurate for large changes in yield?
A. Duration assumes constant interest rates
B. Duration does not account for bond pricing formula
C. Duration is a linear approximation of a nonlinear curve
Correct Answer: C
Explanation:
Duration is linear, but bond price-yield relationship is convex (curved).
A and B are unrelated or incorrect.
The convexity of a zero-coupon bond is generally:
A. Negative
B. Zero
C. Positive
Correct Answer: C
Explanation:
Even though zero-coupon bonds have no interim cash flows, they still have positive convexity.
A and B are incorrect.
In bond analysis, the term “first-order effect” refers to:
A. Convexity
B. Modified duration
C. Yield spread
Correct Answer: B
Explanation:
Duration = first-order measure of interest rate sensitivity.
A is second-order.
C is not related.
A bond with a greater number of dispersed cash flows will generally have:
A. Higher modified duration and lower convexity
B. Higher convexity and possibly same duration
C. Lower duration and lower convexity
Correct Answer: B
Explanation:
More spread-out cash flows = greater convexity, even if duration is the same.
A and C misstate the relationship.
The concept of “money convexity” is best described as:
A. Percentage price change for a bond
B. Convexity expressed in currency terms
C. Convexity for money market instruments
Correct Answer: B
Explanation:
Money convexity = convexity × bond’s full price (in dollars or SAR).
A and C are incorrect.
If a bond’s price increases more than predicted by duration, this is most likely due to:
A. Negative convexity
B. Interest rate risk
C. Positive convexity
Correct Answer: C
Explanation:
Positive convexity explains why the bond price rises more than duration predicts when yields fall.
A would underperform.
B is too general.
Which statement best summarizes the role of convexity in bond pricing?
A. It eliminates the need for duration
B. It adjusts duration estimates for better accuracy
C. It is only used for callable bonds
Correct Answer: B
Explanation:
Convexity enhances duration-based estimates, especially for larger yield changes.
A and C are false.
Which of the following is most accurate about a bond with positive convexity?
A) Positive changes in yield lead to positive changes in price.
B) Price increases and decreases at a faster rate than the change in yield.
C)
Price increases when yields drop are greater than price decreases when yields rise
by the same amount.
Correct Answer: C
Explanation:
A convex price/yield graph has a larger increase in price as yield decreases than the
decrease in price when yields increase.
A $1,000 face, 10-year, 8.00% semi-annual coupon, option-free bond is issued at par (market
rates are thus 8.00%). Given that the bond price decreased 10.03% when market rates
increased 150 basis points (bp),if market yields decrease by 150 bp, the bond’s price will:
A) decrease by more than 10.03%.
B) increase by more than 10.03%.
C) increase by 10.03%.
Correct Answer: B
Explanation:
Because of positive convexity, (bond prices rise faster than they fall) for any given absolute
change in yield, the increase in price will be more than the decrease in price for a fixed-
coupon, noncallable bond. As yields increase, bond prices fall, and the price curve gets
flatter, and changes in yield have a smaller effect on bond prices. As yields decrease, bond
prices rise, and the price curve gets steeper, and changes in yield have a larger effect on
bond prices. Here, for an absolute 150bp change, the price increase would be more than
the price decrease.
