- Which of the following statements regarding bond credit risk is true?
Answer: A downgrade of a corporate bond from A to BBB will generally reduce the bond's price and raise its yield to maturity because investors will demand a wider credit spread.
Credit ratings and credit spreads. A downgrade from A to BBB signals greater default risk, so investors demand a wider credit spread; the bond's price falls and its yield to maturity rises. The statement that a BB-rated bond is investment grade is wrong: investment grade begins at BBB (Baa3 on Moody's scale), so BB is a high-yield, non-investment-grade rating. The statement that credit spreads widen during economic expansions is wrong: spreads typically narrow during expansions as default risk falls and widen during recessions. The statement that credit risk is the risk of price decline from rising market interest rates describes interest-rate risk, which is measured by duration; credit risk is the risk of loss from issuer default or credit deterioration.
- An investor in the 32% federal income tax bracket, with no state income tax, is comparing two equally rated 10-year bonds trading at par: a municipal bond with a 3.4% coupon and a taxable corporate bond with a 4.6% coupon. What is the municipal bond's tax-equivalent yield?
Answer: 5.00%
Tax-equivalent yield = tax-free yield ÷ (1 − marginal tax rate) = 3.4% ÷ (1 − 0.32) = 3.4% ÷ 0.68 = 5.0%. Because 5.0% exceeds the 4.6% coupon on the comparable taxable bond, the municipal bond offers the higher after-tax return. The 2.31% figure multiplies 3.4% by (1 − 0.32), which converts a taxable yield into an after-tax yield and inverts the tax-equivalent formula. The 2.58% figure divides by (1 + 0.32) instead of by (1 − 0.32). The 4.49% figure multiplies 3.4% by 1.32, using 1 + tax rate rather than 1 − tax rate.
- Which of the following statements regarding bond duration is true?
Answer: For two bonds with identical maturity and yield to maturity, the lower-coupon bond has the longer duration and the greater interest-rate sensitivity.
Duration principles. Duration is the weighted-average time to receipt of a bond's cash flows and a measure of interest-rate sensitivity. Holding maturity and yield to maturity constant, a lower coupon lengthens duration because less cash flow is received before maturity; the longer duration gives the greater percentage price change for a given change in yield. The statement that a shorter-maturity bond has the longer duration is reversed: with coupon and yield held constant, shorter maturity shortens duration. The statement that duration increases when yield to maturity rises is reversed: higher yields discount distant cash flows more heavily, which lowers duration. Duration equals time to maturity only for a zero-coupon bond; a fixed-coupon bond's duration is less than its maturity because coupon payments are received before maturity.
- A $1,000 par bond carries an 8% coupon, matures in 10 years, and is currently priced at $1,100. The bond is callable at par in 5 years. Using the approximation formula, the yield to call is closest to:
Answer: 5.71%
Concept: Yield to call approximation formula. The yield to call is calculated as (Annual coupon + (Call price - Current price) / Years to call) divided by ((Call price + Current price) / 2). Here, that is (80 + (1000 - 1100) / 5) / ((1000 + 1100) / 2) = (80 - 20) / 1050 = 60 / 1050 = 5.71%. The 6.67% option is the yield to maturity, which amortizes the premium over the full 10-year maturity rather than the 5-year call period. The 7.27% option is the current yield (80 / 1100), which ignores the capital loss from the premium. The 8.00% option is simply the coupon rate and does not reflect the bond's market price or call feature.
- An investor is comparing four noncallable corporate bonds of comparable credit quality, each trading at par. Which bond's price is most sensitive to a 50-basis-point change in market yields?
Answer: 20-year bond with a 2% coupon
Duration — the measure of price sensitivity to a yield change — increases with longer maturity and decreases with a higher coupon. The 20-year bond with a 2% coupon has the longest maturity and the lowest coupon, so it has the highest duration and the largest percentage price move for a given yield change. The other 20-year bond carries an 8% coupon; its larger periodic cash flows reduce duration relative to the low-coupon bond of the same maturity. The 5- and 10-year bonds have shorter maturities and therefore shorter durations, so their prices are less sensitive regardless of the coupon.
- A portfolio manager compares a 10-year non-callable corporate bond with a 10-year callable corporate bond. Both bonds have the same coupon rate, credit quality, and current yield to maturity. If market interest rates fall significantly, which of the following statements correctly explains the difference in the bonds' price behavior?
Answer: The callable bond will appreciate less because the embedded call option limits the price increase as rates fall.
Concept: Effective duration and embedded options. A callable bond has negative convexity. When market interest rates fall, the embedded call option moves into the money, increasing the chance that the issuer will call the bond and cap its price appreciation. Therefore, the callable bond appreciates less than an identical non-callable bond. The statement that it appreciates more assumes positive convexity, which option-free and putable bonds have but callable bonds lose as rates fall. The statement that both appreciate equally ignores the significant impact of the call option on the bond's effective duration. The statement that the callable bond depreciates is incorrect because a decline in rates still raises its price, just at a slower rate than a non-callable bond.
- An investor is evaluating an 8% coupon, 12-year corporate bond with a $1,000 par value. The bond is callable at $1,030 in five years and currently trades at $1,100. Which of the following statements is correct?
Answer: The nominal yield is the highest of the four yield measures and the yield to call is the lowest.
Nominal yield = 8%. Current yield = $80 ÷ $1,100 = 7.27%. For a premium bond, nominal yield > current yield > yield to maturity. Because the market price of $1,100 exceeds the $1,030 call price, the issuer will likely call the bond, and the yield to call (approximately 6.2%) falls below the yield to maturity (approximately 6.8%). The full ordering is nominal (8%) > current (7.27%) > YTM (6.8%) > YTC (6.2%). The statement that the yield to call exceeds the yield to maturity would hold only if the call price were above the bond's amortized value at the call date; here the investor pays $1,100 and would receive only $1,030 at the call, and the $70 loss at call lowers the call-based return below the yield to maturity. The current yield is below, not above, the nominal yield for a premium bond. The yield to call, not the yield to maturity, is the lowest of the four measures.
- Which of the following statements regarding bond yield measures is true?
Answer: For a callable bond purchased at a premium while interest rates are falling, yield to call is generally lower than yield to maturity, and it is the more meaningful measure for the investor.
Bond yield measures (current yield, yield to maturity, and yield to call). A callable bond purchased at a premium while rates are falling is likely to be called, so yield to call is the more meaningful measure; yield to call is generally lower than yield to maturity for a premium callable bond because the bond is redeemed at the call price rather than at par, creating a capital loss that is realized sooner. The statement that a discount bond's yield to call is generally lower than its yield to maturity is reversed: because the call price is above the discount market price, yield to call is generally higher than yield to maturity for a discount bond. The statement that a premium bond's current yield is lower than its yield to maturity is also reversed: for a premium bond, current yield exceeds yield to maturity because the premium amortizes down to par as the bond ages. The statement that yield to maturity is the better measure for a premium callable bond in a falling-rate environment is wrong: once a call appears likely, yield to call is the yield investors should evaluate because the bond's full contractual life probably will not run.
- An investor owns a 10-year fixed-coupon corporate bond rated A that has just been downgraded to BBB by a major rating agency. The bond's contractual cash flows are unchanged, and there is no change in general market interest rates. Which of the following best describes the most direct effect on the bond in the secondary market?
Answer: The bond's yield spread over Treasuries widens and its market price falls.
A downgrade increases the default-risk premium investors demand, so the bond's required yield rises; its yield spread over Treasuries widens and, with contractual cash flows fixed and general interest rates unchanged, its market price falls. The spread is not unchanged merely because the promised payments are fixed; the market now discounts those promised payments at a higher required yield. Because the required yield rises, the bond's yield to maturity rises relative to the comparable Treasury yield rather than falling below it. Macaulay duration is a present-value-weighted measure of the time to cash flows; a higher discount rate reduces the relative weight of the distant final payment, tending to shorten duration, not increase it.
- An investor holds a 5-year, $1,000 par value corporate bond with a 5% coupon, trading at $950. Which of the following correctly ranks the bond's yield measures from lowest to highest?
Answer: Nominal yield (5%) < current yield (5.26%) < yield to maturity
Current yield = annual interest ÷ market price = $50 ÷ $950 = 5.26%. For a bond trading at a discount, the yield measures rank nominal yield < current yield < yield to maturity: the investor earns the $50 discount as price appreciation in addition to the coupon, so the yield to maturity is the highest measure and the current yield exceeds the 5% coupon. The ordering that places the yield to maturity below the current yield is the premium-bond hierarchy applied to a discount bond. The ordering with the yield to maturity between the nominal and current yields misstates the ranking because the yield to maturity must be the highest of the three. The ordering that puts the current yield below the nominal yield is reversed for a discount bond, where the current yield must exceed the coupon.
- A bond has a Macaulay duration of 7.0 years, a yield to maturity of 6.0%, and a convexity of 15. If market interest rates increase by 100 basis points, which of the following best approximates the bond's percentage price change?
Answer: -6.53%
Concept: Modified duration and convexity. The modified duration is calculated as Macaulay duration divided by (1 + yield to maturity), or 7.0 / 1.06 = 6.6038 years. The first-order price change from a 100 basis point (1.0%) rate increase is -6.6038% 1.00 = -6.6038%. The convexity adjustment is +0.5 15 * (0.01)2 = 0.075%. Combining these gives -6.6038% + 0.075% = -6.5288%, approximately -6.53%. The -6.60% option ignores the convexity adjustment. The -7.00% option applies the Macaulay duration directly without converting to modified duration. The -6.93% option incorrectly converts the Macaulay duration using 1.01 as the divisor instead of the bond's actual yield factor of 1.06. - A $1,000 par bond with a 7% coupon is priced at $1,050 and matures in 10 years. The bond's current yield and approximate yield to maturity are, respectively:
Answer: 6.67% and 6.34%
Concept: Yield measures for a premium bond. Current yield is the annual coupon divided by the market price, which is 70 / 1050 = 6.67%. The approximate yield to maturity is calculated as (Annual coupon + (Par value - Price) / Years to maturity) divided by ((Par value + Price) / 2), which is (70 - 5) / 1025 = 65 / 1025 = 6.34%. Because the bond is priced at a premium, the premium is gradually amortized against the coupon income over the bond's life, so the yield to maturity is lower than the current yield. The option listing 6.34% and 6.67% reverses the two figures. The option listing 7.00% incorrectly uses the coupon rate as the current yield. The option listing 6.67% and 7.00% mistakenly uses the coupon rate as the yield to maturity.
- A 2-year corporate bond with a $1,000 par value and a 10% annual coupon is priced to yield 10%, so it trades at par. If market yields rise by 50 basis points, approximately what percentage price change would modified duration predict?
Answer: −0.87%
Macaulay duration = [1 × (100 ÷ 1.10) + 2 × (1,100 ÷ 1.10²)] ÷ 1,000 = (90.91 + 1,818.18) ÷ 1,000 = 1.91 years. Modified duration = 1.91 ÷ 1.10 = 1.74. Approximate percentage price change = −modified duration × change in yield = −1.74 × 0.005 = −0.87%. The −0.95% figure uses Macaulay duration (1.91 years) directly without dividing by 1 + yield to obtain modified duration. The −1.00% figure substitutes the 2-year maturity for the duration. The −1.74% figure applies the modified duration to a 100-basis-point move instead of the 50-basis-point move stated in the stem.
- An investor owns a 15-year corporate bond with a 7% coupon, a modified duration of 9.0, and a current market price of $1,120. If the bond's yield to maturity increases by 60 basis points, the bond's price will most likely move to approximately:
Answer: $1,060
Modified duration. The approximate percentage price change equals the negative of modified duration times the change in yield: percentage price change ≈ -9.0 × 0.006 = -0.054, or -5.4%. That is a decline of about $60.48, so the price moves to about $1,060. The 15-year maturity and 7% coupon are distractors; modified duration already summarizes the bond's interest-rate sensitivity. The $1,180 result treats the price as rising, reversing the sign of the yield change. The $1,066 result applies the 5.4% change to the $1,000 par value instead of the $1,120 market price. The $1,113 result applies only the 60-basis-point change (0.6%) to the price and omits the duration multiplier.
