andytrader

Which of the following statements about the market yield environment is most accurate?

A) As yields increase, bond prices rise, the price curve flattens, and further increases in yield have a smaller effect on bond prices.

B) For a given change in interest rates, bond price sensitivity is lowest when market yields are already high.

C) Positive convexity applies to the percentage price change, not the absolute dollar price change.

---

The price volatility of noncallable (option-free) bonds is inversely related to the level of market yields. In other words, when the yield level is high, bond price volatility is low and vice versa.
The statement beginning with, As yields increase. . . should continue . . .bond prices fall. Positive convexity (bond prices increase faster than they decrease for a given change in yield) applies to both absolute dollar changes and percentage changes.

andytrader

Consider a bond with a duration of 5.61 and a convexity of 21.92. Which of the following is closest to the estimated percentage price change in the bond for a 75 basis point decrease in interest rates?

A) 4.33%.

B) 4.21%.

C) 4.12%.

---

The estimated percentage price change is equal to the duration effect plus the convexity effect. The formula is: [–duration × (Δy)] + [convexity × (Δy)2]. Therefore, the estimated percentage price change is: [–(5.61)(–0.0075)] + [(21.92)(-0.0075)2] = 0.042075 + 0.001233 = 0.043308 = 4.33%.

andytrader

A bond has a convexity of 25.72. What is the approximate percentage price change of the bond due to convexity if rates rise by 150 basis points?

A) 0.71%.

B) 0.26%.

C) 0.58%.

---

The convexity effect, or the percentage price change due to convexity, formula is: convexity × (Δy)2. The percentage price change due to convexity is then: (25.72)(0.015)2 = 0.0058.

andytrader

A bond has a modified duration of 6 and a convexity of 62.5. What happens to the bond's price if interest rates rise 25 basis points? It goes:

A) down 15.00%.

B) up 1.46%.

C) down 1.46%.

---

∆P = [(-MD × ∆y) + (convexity) × (∆y)2] × 100
∆P = [(-6 × 0.0025) + (62.5) × (0.0025)2] × 100 = -1.461%

andytrader

A bond has a modified duration of 7 and convexity of 50. If interest rates decrease by 1%, the price of the bond will most likely:

A) increase by 6.5%.

B) increase by 7.5%.

C) decrease by 7.5%.

---

Percentage Price Change = –(duration) (∆i) + convexity (∆i)2
therefore
Percentage Price Change = –(7) (–0.01) + (50) (–0.01)2=7.5%.

andytrader

A bond has a modified duration of 6 and a convexity of 62.5. What happens to the bond's price if interest rates rise 25 basis points? It goes:

A) up 4.00%.

B) down 1.46%.

C) down 15.00%.

---

ΔP/P = (-)(MD)(Δi) +(C) (Δi)2
= (-)(6)(0.0025) + (62.5) (0.0025)2 = -0.015 + 0.00039 = - 0.01461

andytrader

A bond’s duration is 4.5 and its convexity is 43.6. If interest rates rise 100 basis points, the bond’s percentage price change is closest to:

A) -4.50%.

B) -4.94%.

C) -4.06%.

---

Recall that the percentage change in prices = Duration effect + Convexity effect = [-duration × (change in yields)] + [convexity × (change in yields)2] = (-4.5)(0.01) + (43.6)(0.01)2 = -4.06%. Remember that you must use the decimal representation of the change in interest rates when computing the duration and convexity adjustments.

andytrader

If a bond has a convexity of 120 and a modified duration of 10, what is the convexity adjustment associated with a 25 basis point interest rate decline?

A) -2.875%.

B) +0.075%.

C) -2.125%.

---

Convexity adjustment: +(C) (Δi)2
Con adj = +(120)(-0.0025)(-0.0025) = +0.000750 or 0.075%

andytrader

One major difference between standard convexity and effective convexity is:

A) effective convexity is Macaulay's duration divided by [1 + yield/2].

B) effective convexity reflects any change in estimated cash flows due to embedded bond options.

C) standard convexity reflects any change in estimated cash flows due to embedded options.

---

The calculation of effective convexity requires an adjustment in the estimated bond values to reflect any change in estimated cash flows due to the presence of embedded options. Note that this is the same process used to calculate effective duration.

andytrader

William Morgan, CFA, manages a fixed-income portfolio that contains several bonds with embedded options. Morgan would like to evaluate the sensitivity of his portfolio to large interest rate changes and will therefore use a convexity measure in addition to duration. The convexity measure that will best estimate the price sensitivity of Morgan’s portfolio is:

A) modified convexity.

B) either effective or modified convexity.

C) effective convexity.

---

Effective convexity is the appropriate measure because it takes into account changes in cash flows due to embedded options, while modified convexity does not.