Baran

 

AIM 5: Define and compute convexity, and interpret the convexity of a fixed income security, given a change in yield and the resulting change in price.

 

1、If a 12-year, 8 percent annual coupon bond with $100 par value is currently selling at par what is the convexity of the bond?

A) 57.0. 

B) 98.0. 

C) 100.5. 

D) 78.0.

Baran

 

The correct answer is D

 

Since the bond is selling at par, it’s yield = coupon rate = 8%.

V0 = Par = 100.

For convexity, change in yield used in calculations is arbitrary – so we use 100 bps in our calculations below.

I/Y = 7.00; FV = 100; N = 12; PMT = 0.08 x 100 = 8; PV = V- = 107.94

I/Y = 9.00; FV = 100; N = 12; PMT = 0.08 x 100 = 8; PV = V+ = 92.84

convexity = (107.94+92.84-200)/(100x0.012)= 78

Baran

 

2、Which of the following statements describe a property of bond convexity? Convexity:

  I.  increases as yields increase.

 II.  increases with the square of maturity.

III.  measures the rate of change in duration.

IV.  increases if the coupon on a bond is increased.

A) II and III only.   

B) I and III only.

C) II and IV only. 

D) III and IV only.

Baran

 

The correct answer is A

 

Convexity is inversely related to yield and is indirectly related to the coupon rate on a bond. Convexity is the second derivative of price with respect to yield, which means that convexity measures the rate of change in duration. Convexity increases with the square of maturity.

Baran

 

3、Why is convexity a good thing for a bond holder? Because when compared to a low convexity bonds a high convexity bond:

A) is usually underpriced. 

B) has better price changes regardless of the direction of the yield change. 

C) is more sensitive to interest rate changes, increasing the potential payoff. 

D) has improved estimation of price changes.

Baran

 

The correct answer is B

 

Relative to a bonds with low convexity, the price of a bond with high convexity will increase more when rates decline and decrease less when rates rise.

Baran

 

4、How does the convexity of a bond influence the yield on the bond? All else the same, for a bond with high convexity investors will require:

A) a lower yield. 

B) a higher yield. 

C) the same yield as for a low convexity bond. 

D) a higher or lower yield depending on the bond's duration.

Baran

 

The correct answer is A

 

Convexity is to the advantage of the bond holder because a high-convexity bond's price will decrease less when rates increase and will increase more when rates decrease than a low-convexity bond's price.

Baran

 

5、With respect to an option-free bond, when interest-rate changes are large, the duration measure will overestimate the:

A) associated change in the bond's rating.

B) final bond price from a given increase in interest rates.

C) fall in a bond's price from a given increase in interest rates.

D) increase in a bond's price from a given increase in interest rates.

Baran

 

The correct answer is C

 

When interest rates increase by 50-100 basis points or more, the duration measure overestimates the decrease in the bond’s price.