[2008]Topic 29: Measures of Price Sensitivity Based on Parallel Yield Shifts相 percentage, following, all, interest, depends

Baran

 

AIM 1: Define and compute the yield-based DV01.

 

1、The magnitude of the percentage price change on a bond for a given change in interest rates depends on all of the following EXCEPT the:

A) volatility of interest rates.

B) coupon rate.

C) term to maturity.

D) initial yield. 

Baran

 

The correct answer is A

 

The volatility of interest rates will affect the frequency with which price changes are observed, but not the magnitude. All else equal, bond price sensitivity is higher for (a) lower coupon bonds; (b) longer term maturity bonds; and (c) lower the initial yield.

Baran

 

AIM 2: Discuss the differences in applying and interpreting the effective duration, modified duration and Macaulay duration.

 

1、A five-year bond selling at par and yielding 6 percent has a duration of 3.2 years. If interest rates rise one percent, what will be the market price of the bond?

A) 96.8.

B) 97.0.

C) 103.0.

D) 103.2.

Baran

 

The correct answer is A

 

Percent change in price = -(3.2) (0.01) = -3.2%. We are told the bond is currently selling at par, or 100. The new price will be 96.8.

Baran

 

2、One of the features of using only modified duration for estimating change in price is that the size of the estimated price change is:

A) the same for up or down movements in interest rates.

B) higher for an up move in interest rates as compared to a down move in interest rates.

C) lower for an up move in interest rates as compared to a down move in interest rates. 

D) higher for a callable bond as compared to an option-free bond.

Baran

 

The correct answer is A

 

Estimated price changes using only duration are symmetric for a change in interest rates. How the modified duration for a callable bond would compare with an otherwise identical option-free bond will depend upon the relevant range over which the measure would be calculated. If the relevant range includes a range in which the callable bond will experience price compression, the effective duration measure for the callable bond will be lower than for the option-free bond.

Baran

 

3、A 6-year, 5 percent annual coupon bond with $100 par value currently trades at par and has an effective duration of 4.25 years. What is the price change if the yield falls by 50 basis points?

A) 2.13%.

B) 4.25%.

C) -4.25%.

D) 6.38%.

Baran

 

The correct answer is A

 

Percentage price change = (-) (effective duration)( Δy)

= (-)(4.25)(-0.005) = 2.125%

Baran

 

4、Community Bank has a $5 million par value position in a bond with the following characteristics:

The bond is a 5-year, zero-coupon bond.

The bond is priced to yield 5%.

The historical mean change in daily yields is 0.0%.

The standard deviation in yield is 36 basis points.

The modified duration of the bond is closest to:

A) 4.395.

B) 2.524.

C) 5.000. 

D) 4.878.

Baran

 

The correct answer is D

 

The modified duration is:

Remember that while the Macaulay duration for a zero-coupon bond is the same as its maturity, an adjustment needs to be made for modified duration.