Baran

 

6、For a given change in yields, the difference between the actual change in a bond’s price and that predicted using the duration measure will be greater for:

A) a bond with greater convexity.

B) a short-term bond.

C) inverse convexity.

D) a bond with less convexity.

Baran

 

The correct answer is A

 

Duration is a linear measure of the relationship between a bond’s price and yield. The true relationship is not linear as measured by the convexity. When convexity is higher, duration will be less accurate in predicting a bond’s price for a given change in interest rates. Short-term bonds generally have low convexity.

Baran

 

7、Convexity is more important when rates are:

A) unstable.

B) high.

C) low.

D) depends on whether the note is selling at a premium or a discount.

Baran

 

The correct answer is A

 

Since interest rates and the price of bonds are inversely related, unstable interest rates will lead to larger price fluctuations in bonds. The larger the change in the price of a bond the more error will be introduced in determining the new price of the bond if only duration is used because duration assumes the price yield relationship is linear when in fact it is a curved convex line. If duration alone is used to price the bond, the curvature of the line magnifies the error introduced by yield changes, and makes the convexity adjustment even more important.

Baran

 

AIM 6: Estimate, given the DV01, the duration and the convexity of a fixed income security, the price change of a security.

1、A 12-year, 8 percent semiannual coupon bond with $100 par value currently trades at $78.75 and has an effective duration of 9.8 years and a convexity of 130.0. What is the price of the bond if the yield falls by 150 basis points?

A) $91.48. 

B) $67.17. 

C) $86.47. 

D) $95.43.

Baran

 

The correct answer is A

 

Percentage price change = [(-) (effective duration)( Δy)]+[(1/2)(convexity)( Δy)2]

= [(-)(9.80)(-0.015)]+[(0.5)(130)(-0.015)2] = 16.16

Estimated price = 78.75(1+0.1616) = $91.48

Baran

 

2、Estimated price changes using only duration tend to:

A) overestimate the increase in price that occurs with a decrease in yield for large changes in yield.

B) underestimate the decrease in price that occurs with an increase in yield for large changes in yield.

C) underestimate the increase in price that occurs with a decrease in yield for large changes in yield. 

D) overestimate the increase in price that occurs with a decrease in yield for small changes in yield.

Baran

 

The correct answer is C

 

For large changes in yield, duration underestimates the increase in price that occurs with a decrease in yield, and overestimates the decrease in price that occurs with an increase in yield. For small changes in yield, the estimated price change and actual price change are very close to the same.

Baran

 

3、A bond has an effective duration of 7.5 and a convexity of 104.0. If yields rise by 82 bps, the price of the bond will:

A) increase by 6.50%.

B) decrease by 5.80%.   

C) increase by 6.15%. 

D) decrease by 6.15%.   

Baran

 

The correct answer is B

 

%DPrice = [–7.5 ′ 0.0082 ′ 100] ? [(1/2) ′ 104 ′ 0.00822 ′ 100] = –5.80%.