Professional Finance Education


Risks associated with investing in bonds (Reading 54)



Exercise Problems:

1. An investor purchases a 5% coupon bond maturing in 15 years for par value. Immediately after purchase, the yield required by the market increases. The investor would then most likely have to sell the bond at:

A. par.

B. a discount.

C. a premium.

 


Ans: B;

B is correct because the bond would sell below par or at a discount if the yield required by the market rises above the coupon rate. Because the bond initially was purchased at par, the coupon rate equals the yield required by the market. Subsequently, if yields rise above the coupon, the bond’s market price would fall below par.

2. Given two otherwise identical bonds, when interest rates rise, the price of Bond A declines more than the price of Bond B. Compared to Bond B, Bond A most likely:

A. is callable.

B. has a lower coupon.

C. has a shorter maturity.


Ans: B;

Since Bond A declines more than the price of Bond B when interest rates rise, Bond A has greater price sensitivity to changes in interest rates and thus greater interest rate risk/duration than Bond B.

B is correct. The lower the coupon rate, the greater the bond’s price sensitivity to changes in interest rates.

A in not correct. The presence of an embedded option decreases the bond’s price sensitivity to changes in interest rates.

C is not correct. The longer the maturity, the greater the bond’s price sensitivity to changes in interest rates.

 

3. An analyst is evaluating the two bonds below:


Bond A

Bond B

Coupon

6.90%

8.25%

Maturity

Oct 29, 2022

Nov 5, 2022

Callable

No

No

Price

$102.17

$102.39

Yield

6.60%

7.90%

Compared with Bond A, Bond B most likely will have:

A. less interest rate risk and more reinvestment risk.

B. more interest rate risk and less reinvestment risk.

C. less interest rate risk and less reinvestment risk.

 


Ans: A;

Since both securities have essentially the same maturity, all else the same, the bond with the lower coupon rate will have a higher sensitivity to changes in interest rates. Therefore, Bond B will have less interest rate risk.

The higher the yield on the bond, the more the reinvestment risk, because the investor must be able to reinvest at the same yield. Therefore, Bond B will have more reinvestment risk.

4. When interest rates fall, the price of a callable bond will:

A. rise more than an option-free bond.

B. rise less than an option-free bond.

C. fall less than an option-free bond.


Ans: B;

The call feature limits the upside price movement of a bond when interest rates fall. The price of a callable bond will not rise above the call price, which leads to that the value of a callable bond will be less sensitive to interest rate changes than an otherwise option-free bond. Therefore B is the correct answer. When interest rates fall, the price of a callable bond will rise less than an option-free bond.

 

5. If market interest rates rise, the price of a callable bond, compared to an otherwise identical option-free bond, will most likely decrease by:

A. more than the option-free bond.

B. the same amount as the option-free bond.

C. less than the option-free bond.


Ans: C;

Value of a callable bond

= Value of an option-free bond – Value of the call

As interest rates rise, the value of the call decreases by a decreasing amount.

Therefore, as interest rates rise, the value of a callable bond decreases by a less amount than an option-free bond.

 

6. For a 10-year floating-rate security, if market interest rates change by 1%, the change in the value of the security will most likely be:

A. zero.

B. related to the security’s coupon reset frequency.

C. similar to an otherwise identical fixed-rate security.

 


Ans: B;

B is correct. Change in the value of the security corresponding to a 1% change in market interest rates is termed as duration. The problem is asking for the duration of a 10-year floating-rate security. The duration of a floating-rate security is equal to the fraction of a year until the next reset date, therefore related to the security’s coupon reset frequency.

7. Duration is most accurate as a measure of interest rate risk for a bond portfolio when the slope of the yield curve:

A. increases.

B. decreases.

C. stays the same.

 


Ans: C;

C is correct because duration measures the change in bond’s price if the yields for all maturities change by the same amount; that is, it assumes the slope of the yield curve stays the same.




8. One reason why the duration of a portfolio of bonds does not properly reflect that portfolio’s yield curve risk is that the duration measure:

A. ignores differences in coupon rates across bonds.

B. assumes all the bonds have the same discount rate.

C. assumes all yields change by the same amount.

 


Ans: C;

C is correct because duration assumes that yields change by the same amount across all maturities.

9. A bond is selling for 98.6. It is estimated that the price will fall to 97.0if yields rise 30 bps and that the price will rise to 100.5 if yields fall 30 bps. Based on these estimates, the duration of the bond is closest:

A. 5.92.

B. 1.78

C. 2.96.


Ans: A;

Duration

=

==5.92

10. A fixed income portfolio manager owns a $4 million par value non-callable bond. The bond’s duration is 5.4 and the current market value is $4,125,000. The dollar duration of the bond is closest to:

A. 200,000.

B. 216,000.

C. 222,750.


Ans: C;

Dollar duration is the price change in dollars in response of a change in yield of 100 basis points (1%).

Dollar Duration = Duration 0.01Market Value

=5.40.01$4,125,000

=222,750

 

11. Compared with an otherwise identical amortizing security, a zero-coupon bond will most likely have:

A. less reinvestment risk and the same interest rate risk.

B. less reinvestment risk and more interest rate risk.

C. the same reinvestment risk and the same interest rate risk.


Ans: B;

Less reinvestment risk: An amortizing security is exposed to reinvestment risk since it receives periodic payments of both interest and principal that must be reinvested ; while a zero-coupon bond has no reinvestment risk since no cash flows are received that must be reinvested before maturity.

More interest rate risk: Because zero-coupon bonds do not have periodic cash flows, they have higher interest rate risk for a given maturity and a given change in market yields.

12. Two amortizing bonds have the same maturity date and same yield to maturity. The reinvestment risk for an investor holding the bonds to maturity is greatest for the bond that is:

A. a coupon bond selling at a discount to par as a result of market yields increasing after the bond was issued.

B. a zero-coupon bond.

C. a coupon bond selling at a premium to par.


Ans: C;

Reinvestment risk refers to the risk that interest rates will decline causing the future income expected from reinvesting coupon payments to decline. The higher the coupon being paid, the greater the reinvestment risk.

Because the two amortizing bonds have the same maturity date and the same yield to maturity, the bond selling at a premium must have a higher coupon rate and a higher amount requiring reinvestment and thus higher reinvestment risk.

 

13. An investor fears that economic conditions will worsen and the market prices of her portfolio of investment-grade corporate bonds will decrease more than her portfolio of government bonds. The investor’s fear is best described as a fear of:

A. downgrade risk.

B. default risk.

C. credit spread risk.


Ans: C;

A is not correct. Downgrade risk is the risk that a credit rating agency will lower a bond’s rating.

B is not correct. Default risk is the risk that the issuer not making timely interest and principal payments as promised.

C is the correct answer. Credit spread risk is the risk that the yield required in the market for a given rating can increase even while the yield on the Treasury security of similar maturity remains unchanged. Since the market prices of the investor’s portfolio of corporate bonds will decrease more than her portfolio of government bonds, the spreads on those bonds widens relative to default-free bonds. Thus the investor is concerned about credit spread risk.

 

14. For an A- rated corporate bond that has deteriorating fundamentals, but is expected to remain investment grade, the greatest risk is most likely:

A. liquidity risk.

B. default risk.

C. credit spread risk.

 


Ans: C;

Credit spread risk is correct since the bond is expected to see a widening of spreads as a result of deteriorating fundamentals and a potential downgrade but still remaining investment grade.

15. What risk does the bid-ask spread most closely measure:

A. Liquidity risk.

B. Credit spread risk.

C. Inflation risk.


Ans: A;

A is correct. Liquidity risk is the risk that the investor will have to sell a bond below its indicated value. The size of the spread between the bid price and the ask price is the primary measure of liquidity of the issue. If trading activity in a particular security declines, the bid-ask spread will widen, and the issue is considered less liquid.

 

16. All else equal, an increase in expected yield volatility is most likely to cause the price of a:

A. callable price to increase.

B. callable price to decrease.

C. putable price to decrease.


Ans: B;

An increase in expected yield volatility increases the values of both put options and call options.

However,

Value of a callable bond

= Value of an option-free bond – Value of the call

Note here the call option is retained by the issuer.

Value of a putable bond

= Value of an option-free bond + Value of the put

Note here the put option is owned by the bond holder.

Therefore, an increase in expected yield volatility will cause the price of a callable price to decrease and a putable price to increase. Therefore B is the correct answer.

 




17. A portfolio of option-free bonds is least likely to be exposed to:

A. yield curve risk.

B. volatility risk.

C. reinvestment risk


Ans: B;

Volatility risk is present for fixed-income securities that have embedded options. Changes in interest rate volatility affect the value of the embedded options and thus affect the values of securities with embedded options. By definition, option-free bonds are not affected by volatility risk.

 

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