Reading 69: Introduction to the Measurement of Interest R

答案和详解如下：

1.Consider the following two statements about putable bonds:

Statement #1: As yields fall, the price of putable bonds will rise less quickly than similar option-free bonds (beyond a critical point) due to the decrease in value of the embedded put option.

Statement #2: As yields rise, the price of putable bonds will fall more quickly than similar option-free bonds (beyond a critical point) due to the increase in value of the embedded put option.

You should:

A)   agree with statement #1 and disagree with statement #2.

B)   agree with statement #1 and agree with statement #2.

C)   disagree with statement #1 and agree with statement #2.

D)   disagree with statement #1 and disagree with statement #2.

The correct answer was D)

Both statements are false. As yields fall, the value of the embedded put option in a putable bond decreases and (beyond a critical point) the putable bond behaves much the same as an option-free bond. As yields rise, the value of the embedded put option increases and (beyond a critical point) the putable bond decreases in value less quickly than a similar option-free bond.

2.At a market rate of 7 percent, a $1,000 callable par value bond is priced at $910, while a similar bond that is non-callable is priced at $960. What is the value of the embedded call option?

A)   $40.

B)   $50.

C)   $30.

D)   $90.

The correct answer was B)

The value of the embedded call option is simply stated as: 

value of the straight bond component – callable bond value = value of embedded call option.

$960 – $910 = $50

3.If interest rates fall, the:

A)   callable bond's price rises faster than that of a noncallable but otherwise identical bond.

B)   callable bond's price rises more slowly than that of a noncallable but otherwise identical bond.

C)   value of call option embedded in the callable bond falls.

D)   value of call option embedded in the callable bond may either fall or rise.

The correct answer was B)

When a callable bond's yield falls to a certain point, when the yields fall the price will increase at a decreasing rate.  Compare this to a noncallable bond where, as the yield falls the price rises at an increasing rate. 

4.A $1,000 face, 10-year, 8.00 percent semi-annual coupon, option-free bond is issued at par (market rates are thus 8.00 percent). Given that the bond price decreased 10.03 percent when market rates increased 150 basis points (bp), which of the following statements is TRUE? If market yields:

A)   decrease by 150bp, the bond's price will decrease by more than 10.03%.

B)   decrease by 150bp, the bond's price will increase by 10.03%.

C)   increase by 100bp, the bond's price will decrease by more than 10.03%.

D)   decrease by 150bp, the bond's price will increase by more than 10.03%.

The correct answer was D)

All other choices are false because of positive convexity - bond prices rise faster than they fall. Positive convexity applies to both dollar and percentage price changes. 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. For a 100bp increase, the price decrease would be less than that for a 150bp increase.

5.Which of the following bonds is likely to exhibit the greatest volatility due to interest rate changes? A bond with a:

A)   low coupon and a long maturity.

B)   low coupon and a short maturity.

C)   high coupon and a long maturity.

D)   high coupon and a short maturity.

The correct answer was A)

There are three features that determine the magnitude of the bond price volatility:

(1) The lower the coupon, the greater the bond price volatility.
(2) The longer the term to maturity, the greater the price volatility.
(3) The lower the initial yield, the greater the price volatility.

So the bond with a low coupon and long maturity will have the greatest price volatility.