CFA 53: Introduction to Fixed-Income Valuation

A portfolio manager is considering the purchase of a bond with a 5.5% coupon rate that pays interest annually and matures in three years. If the required rate of return on the bond is 5%, the price of the bond per 100 of par value is closest to: 98.65. 101.36. 106.43. B is correct. The bond price is closest to 101.36. The price is determined in the following manner: PV=PMT(1+r)1+PMT(1+r)2+PMT+FV(1+r)3 where: PV = present value, or the price of the bond PMT = coupon payment per period FV = future value paid at maturity, or the par value of the bond r = market discount rate, or required rate of return per period PV=5.5(1+0.05)1+5.5(1+0.05)2+5.5+100(1+0.05)3 PV = 5.24 + 4.99 + 91.13 = 101.36 A bond with two years remaining until maturity offers a 3% coupon rate with interest paid annually. At a market discount rate of 4%, the price of this bond per 100 of par value is closest to: 95.34. 98.00. 98.11. C is correct. The bond price is closest to 98.11. The formula for calculating the price of this bond is: PV=PMT(1+r)1+PMT+FV(1+r)2 where: PV = present value, or the price of the bond PMT = coupon payment per period FV = future value paid at maturity, or the par value of the bond r = market discount rate, or required rate of return per period PV=3(1+0.04)1+3+100(1+0.04)2=2.88+95.23=98.11 An investor who owns a bond with a 9% coupon rate that pays interest semiannually and matures in three years is considering its sale. If the required rate of return on the bond is 11%, the price of the bond per 100 of par value is closest to: 95.00. 95.11. 105.15. A is correct. The bond price is closest to 95.00. The bond has six semiannual periods. Half of the annual coupon is paid in each period with the required rate of return also being halved. The price is determined in the following manner: PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+PMT(1+r)4+PMT(1+r)5+PMT+FV(1+r)6 where: PV = present value, or the price of the bond PMT = coupon payment per period FV = future value paid at maturity, or the par value of the bond r = market discount rate, or required rate of return per period PV=4.5(1+0.055)1+4.5(1+0.055)2+4.5(1+0.055)3+4.5(1+0.055)4+4.5(1+0.055)5+4.5+1 00(1+0.055)6 PV = 4.27 + 4.04 + 3.83 + 3.63 + 3.44 + 75.79 = 95.00 A bond offers an annual coupon rate of 4%, with interest paid semiannually. The bond matures in two years. At a market discount rate of 6%, the price of this bond per 100 of par value is closest to: 93.07. 96.28. 96.33. B is correct. The bond price is closest to 96.28. The formula for calculating this bond price is: PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+PMT+FV(1+r)4 where: PV = present value, or the price of the bond PMT = coupon payment per period FV = future value paid at maturity, or the par value of the bond r = market discount rate, or required rate of return per period PV=2(1+0.03)1+2(1+0.03)2+2(1+0.03)3+2+100(1+0.03)4 PV = 1.94 + 1.89 + 1.83 + 90.62 = 96.28 A bond offers an annual coupon rate of 5%, with interest paid semiannually. The bond matures in seven years. At a market discount rate of 3%, the price of this bond per 100 of par value is closest to: 106.60. 112.54. 143.90. B is correct. The bond price is closest to 112.54.The formula for calculating this bond price is: PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+⋯+PMT+FV(1+r)14 where: PV = present value, or the price of the bond PMT = coupon payment per period FV = future value paid at maturity, or the par value of the bond r = market discount rate, or required rate of return per period PV=2.5(1+0.015)1+2.5(1+0.015)2+2.5(1+0.015)3+⋯+2.5(1+0.015)13+2.5+100(1+0.01 5)14 PV = 2.46 + 2.43 + 2.39 + ... + 2.06 + 83.21 = 112.54 A zero-coupon bond matures in 15 years. At a market discount rate of 4.5% per year and assuming annual compounding, the price of the bond per 100 of par value is closest to: 51.30. 51.67. 71.62. B is correct. The price of the zero-coupon bond is closest to 51.67. The price is determined in the following manner: PV=100(1+r)N where: PV = present value, or the price of the bond r = market discount rate, or required rate of return per period N = number of evenly spaced periods to maturity PV=100(1+0.045)15 PV = 51.67 Consider the following two bonds that pay interest annually: Bond Coupon Rate Time-to-Maturity A 5% 2 years B 3% 2 years At a market discount rate of 4%, the price difference between Bond A and Bond B per 100 of par value is closest to: 3.70. 3.77. 4.00. B is correct. The price difference between Bonds A and B is closest to 3.77. One method for calculating the price difference between two bonds with an identical term to maturity is to use the following formula: PV=PMT(1+r)1+PMT(1+r)2 where: PV = price difference PMT = coupon difference per period r = market discount rate, or required rate of return per period In this case the coupon difference is (5% - 3%), or 2%. PV=2(1+0.04)1+2(1+0.04)2=1.92+1.85=3.77 Bond Price Coupon Rate Time-to-Maturity A 101.886 5% 2 years B 100.000 6% 2 years C 97.327 5% 3 years Which bond offers the lowest yield-to-maturity? Bond A Bond B Bond C A is correct. Bond A offers the lowest yield-to-maturity. When a bond is priced at a premium above par value the yield-to-maturity (YTM), or market discount rate is less than the coupon rate. Bond A is priced at a premium, so its YTM is below its 5% coupon rate. Bond B is priced at par value so its YTM is equal to its 6% coupon rate. Bond C is priced at a discount below par value, so its YTM is above its 5% coupon rate. Bond Price Coupon Rate Time-to-Maturity A 101.886 5% 2 years B 100.000 6% 2 years C 97.327 5% 3 years Which bond will most likely experience the smallest percent change in price if the market discount rates for all three bonds increase by 100 basis points? Bond A Bond B Bond C B is correct. Bond B will most likely experience the smallest percent change in price if market discount rates increase by 100 basis points. A higher-coupon bond has a smaller percentage price change than a lower-coupon bond when their market discount rates change by the same amount (the coupon effect). Also, a shorter-term bond generally has a smaller percentage price change than a longer-term bond when their market discount rates change by the same amount (the maturity effect). Bond B will experience a smaller percent change in price than Bond A because of the coupon effect. Bond B will also experience a smaller percent change in price than Bond C because of the coupon effect and the maturity effect. Bond Price Coupon Rate Time-to-Maturity A 101.886 5% 2 years B 100.000 6% 2 years C 97.327 5% 3 years Suppose a bond's price is expected to increase by 5% if its market discount rate decreases by 100 basis points. If the bond's market discount rate increases by 100 basis points, the bond price is most likely to change by: 5%. less than 5%. more than 5%. B is correct. The bond price is most likely to change by less than 5%. The relationship between bond prices and market discount rate is not linear. The percentage price change is greater in absolute value when the market discount rate goes down than when it goes up by the same amount (the convexity effect). If a 100 basis point decrease in the market discount rate will cause the price of the bond to increase by 5%, then a 100 basis point increase in the market discount rate will cause the price of the bond to decline by an amount less than 5%. Bond Coupon Rate Maturity (years) A 6% 10 B 6% 5 C 8% 5 All three bonds are currently trading at par value. Relative to Bond C, for a 200 basis point decrease in the required rate of return, Bond B will most likely exhibit a(n): equal percentage price change. greater percentage price change. smaller percentage price change. B is correct. Generally, for two bonds with the same time-to-maturity, a lower coupon bond will experience a greater percentage price change than a higher coupon bond when their market discount rates change by the same amount. Bond B and Bond C have the same time-to-maturity (5 years); however, Bond B offers a lower coupon rate. Therefore, Bond B will likely experience a greater percentage change in price in comparison to Bond C. Bond Coupon Rate Maturity (years) A 6% 10 B 6% 5 C 8% 5 All three bonds are currently trading at par value. Which bond will most likely experience the greatest percentage change in price if the market discount rates for all three bonds increase by 100 basis points? Bond A Bond B Bond C A is correct. Bond A will likely experience the greatest percent change in price due to the coupon effect and the maturity effect. For two bonds with the same time-to- maturity, a lower-coupon bond has a greater percentage price change than a higher- coupon bond when their market discount rates change by the same amount. Generally, for the same coupon rate, a longer-term bond has a greater percentage price change than a shorter-term bond when their market discount rates change by the same amount. Relative to Bond C, Bond A and Bond B both offer the same lower coupon rate of 6%; however, Bond A has a longer time-to-maturity than Bond B. Therefore, Bond A will likely experience the greater percentage change in price if the market discount rates for all three bonds increase by 100 basis points. An investor considers the purchase of a 2-year bond with a 5% coupon rate, with interest paid annually. Assuming the sequence of spot rates shown below, the price of the bond is closest to: Time-to-Maturity Spot Rates 1 year 3% 2 years 4% 101.93. 102.85. 105.81. A is correct. The bond price is closest to 101.93. The price is determined in the following manner: PV=PMT(1+Z1)1+PMT+FV(1+Z2)2 where: PV = present value, or the price of the bond PMT = coupon payment per period FV = future value paid at maturity, or the par value of the bond Z1 = spot rate, or the zero-coupon yield, for Period 1 Z2 = spot rate, or the zero-coupon yield, for Period 2 PV=5(1+0.03)1+5+100(1+0.04)2 PV = 4.85 + 97.08 = 101.93 A 3-year bond offers a 10% coupon rate with interest paid annually. Assuming the following sequence of spot rates, the price of the bond is closest to: Time-to-Maturity Spot Rates 1 year 8.0% 2 years 9.0% 3 years 9.5% 96.98. 101.46. 102.95. B is correct. The bond price is closest to 101.46. The price is determined in the following manner: PV=PMT(1+Z1)1+PMT(1+Z2)2+PMT+FV(1+Z3)3 where: PV = present value, or the price of the bond PMT = coupon payment per period FV = future value paid at maturity, or the par value of the bond Z1 = spot rate, or the zero-coupon yield, or zero rate, for period 1 Z2 = spot rate, or the zero-coupon yield, or zero rate, for period 2 Z3 = spot rate, or the zero-coupon yield, or zero rate, for period 3 PV=10(1+0.08)1+10(1+0.09)2+10+100(1+0.095)3 PV = 9.26 + 8.42 + 83.78 = 101.46 Bond Coupon Rate Time-to-Maturity Time-to-Maturity Spot Rates X 8% 3 years 1 year 8% Y 7% 3 years 2 years 9% Z 6% 3 years 3 years 10% All three bonds pay interest annually. Based upon the given sequence of spot rates, the price of Bond X is closest to: 95.02. 95.28. 97.63. B is correct. The bond price is closest to 95.28. The formula for calculating this bond price is: PV=PMT(1+Z1)1+PMT(1+Z2)2+PMT+FV(1+Z3)3 where: PV = present value, or the price of the bond PMT = coupon payment per period FV = future value paid at maturity, or the par value of the bond Z1 = spot rate, or the zero-coupon yield, or zero rate, for period 1 Z2 = spot rate, or the zero-coupon yield, or zero rate, for period 2 Z3 = spot rate, or the zero-coupon yield, or zero rate, for period 3 PV=8(1+0.08)1+8(1+0.09)2+8+100(1+0.10)3 PV = 7.41 + 6.73 + 81.14 = 95.28 Bond Coupon Rate Time-to-Maturity Time-to-Maturity Spot Rates X 8% 3 years 1 year 8% Y 7% 3 years 2 years 9% Z 6% 3 years 3 years 10% All three bonds pay interest annually. Based upon the given sequence of spot rates, the price of Bond Y is closest to: 87.50. 92.54. 92.76. C is correct. The bond price is closest to 92.76. The formula for calculating this bond price is: PV=PMT(1+Z1)1+PMT(1+Z2)2+PMT+FV(1+Z3)3 where: PV = present value, or the price of the bond PMT = coupon payment per period FV = future value paid at maturity, or the par value of the bond Z1 = spot rate, or the zero-coupon yield, or zero rate, for period 1 Z2 = spot rate, or the zero-coupon yield, or zero rate, for period 2 Z3 = spot rate, or the zero-coupon yield, or zero rate, for period 3 PV=7(1+0.08)1+7(1+0.09)2+7+100(1+0.10)3 PV = 6.48 + 5.89 + 80.39 = 92.76 Bond Coupon Rate Time-to-Maturity Time-to-Maturity Spot Rates X 8% 3 years 1 year 8% Y 7% 3 years 2 years 9% Z 6% 3 years 3 years 10% All three bonds pay interest annually. Based upon the given sequence of spot rates, the yield-to-maturity of Bond Z is closest to: 9.00%. 9.92%. 11.93% B is correct. The yield-to-maturity is closest to 9.92%. The formula for calculating the price of Bond Z is: PV=PMT(1+Z1)1+PMT(1+Z2)2+PMT+FV(1+Z3)3 where: PV = present value, or the price of the bond PMT = coupon payment per period FV = future value paid at maturity, or the par value of the bond Z1 = spot rate, or the zero-coupon yield, or zero rate, for period 1 Z2 = spot rate, or the zero-coupon yield, or zero rate, for period 2 Z3 = spot rate, or the zero-coupon yield, or zero rate, for period 3 PV=6(1+0.08)1+6(1+0.09)2+6+100(1+0.10)3 PV = 5.56 + 5.05 + 79.64 = 90.25 Using this price, the bond's yield-to-maturity can be calculated as: PV=PMT(1+r)1+PMT(1+r)2+PMT+FV(1+r)3 90.25=6(1+r)1+6(1+r)2+6+100(1+r)3 r = 9.92% Bond dealers most often quote the: flat price. full price. full price plus accrued interest. A is correct. Bond dealers usually quote the flat price. When a trade takes place, the accrued interest is added to the flat price to obtain the full price paid by the buyer and received by the seller on the settlement date. The reason for using the flat price for quotation is to avoid misleading investors about the market price trend for the bond. If the full price were to be quoted by dealers, investors would see the price rise day after day even if the yield-to-maturity did not change. That is because the amount of accrued interest increases each day. Then after the coupon payment is made the quoted price would drop dramatically. Using the flat price for quotation avoids that misrepresentation. The full price, flat price plus accrued interest, is not usually quoted by bond dealers. Accrued interest is included in not added to the full price and bond dealers do not generally quote the full price. Bond G, described in the exhibit below, is sold for settlement on 16 June 2014. Annual Coupon 5% Coupon Payment Frequency Semiannual Interest Payment Dates 10 April and 10 October Maturity Date 10 October 2016 Day Count Convention 30/360 Annual Yield-to-Maturity 4% The full price that Bond G will settle at on 16 June 2014 is closest to: 102.36. 103.10. 103.65. B is correct. The bond's full price is 103.10. The price is determined in the following manner: As of the beginning of the coupon period on 10 April 2014, there are 2.5 years (5 semiannual periods) to maturity. These five semiannual periods occur on 10 October 2014, 10 April 2015, 10 October 2015, 10 April 2016 and 10 October 2016. PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+PMT(1+r)4+PMT+FV(1+r)5 where: PV = present value PMT = coupon payment per period FV = future value paid at maturity, or the par value of the bond r = market discount rate, or required rate of return per period PV=2.5(1+0.02)1+2.5(1+0.02)2+2.5(1+0.02)3+2.5(1+0.02)4+2.5+100(1+0.02)5 PV = 2.45 + 2.40 + 2.36 + 2.31 + 92.84 = 102.36 The accrued interest period is identified as 66/180. The number of days between 10 April 2014 and 16 June 2014 is 66 days based on the 30/360 day count convention. (This is 20 days remaining in April + 30 days in May + 16 days in June = 66 days total). The number of days between coupon periods is assumed to be 180 days using the 30/360 day convention. PVFull = PV × (1 + r)66/180 PVFull = 102.36 × (1.02)66/180 = 103.10 Bond G, described in the exhibit below, is sold for settlement on 16 June 2014. Annual Coupon 5% Coupon Payment Frequency Semiannual Interest Payment Dates 10 April and 10 October Maturity Date 10 October 2016 Day Count Convention 30/360 Annual Yield-to-Maturity 4% The accrued interest per 100 of par value for Bond G on the settlement date of 16 June 2014 is closest to: 0.46. 0.73. 0.92. C is correct. The accrued interest per 100 of par value is closest to 0.92. The accrued interest is determined in the following manner: The accrued interest period is identified as 66/180. The number of days between 10 April 2014 and 16 June 2014 is 66 days based on the 30/360 day count convention. (This is 20 days remaining in April + 30 days in May + 16 days in June = 66 days total). The number of days between coupon periods is assumed to be 180 days using the 30/360 day convention. Accruedinterest=tT×PMT where: t = number of days from the last coupon payment to the settlement date T = number of days in the coupon period t/T = fraction of the coupon period that has gone by since the last payment PMT = coupon payment per period Accruedinterest=66180×5.002=0.92 Bond G, described in the exhibit below, is sold for settlement on 16 June 2014. Annual Coupon 5% Coupon Payment Frequency Semiannual Interest Payment Dates 10 April and 10 October Maturity Date 10 October 2016 Day Count Convention 30/360 Annual Yield-to-Maturity 4% The flat price for Bond G on the settlement date of 16 June 2014 is closest to: 102.18. 103.10. 104.02. A is correct. The flat price of 102.18 is determined by subtracting the accrued interest (from question 20) from the full price (from question 19). PVFlat = PVFull - Accrued Interest PVFlat = 103.10 - 0.92 = 102.18 Matrix pricing allows investors to estimate market discount rates and prices for bonds: with different coupon rates. that are not actively traded. with different credit quality. B is correct. For bonds not actively traded or not yet issued, matrix pricing is a price estimation process that uses market discount rates based on the quoted prices of similar bonds (similar times-to-maturity, coupon rates, and credit quality). When underwriting new corporate bonds, matrix pricing is used to get an estimate of the: required yield spread over the benchmark rate. market discount rate of other comparable corporate bonds. yield-to-maturity on a government bond having a similar time-to-maturity. A is correct. Matrix pricing is used in underwriting new bonds to get an estimate of the required yield spread over the benchmark rate. The benchmark rate is typically the yield-to-maturity on a government bond having the same, or close to the same, time-to-maturity. The spread is the difference between the yield-to-maturity on the new bond and the benchmark rate. The yield spread is the additional compensation required by investors for the difference in the credit risk, liquidity risk, and tax status of the bond relative to the government bond. In matrix pricing, the market discount rates of comparable bonds and the yield-to- maturity on a government bond having a similar time-to-maturity are not estimated. Rather they are known and used to estimate the required yield spread of a new bond. A bond with 20 years remaining until maturity is currently trading for 111 per 100 of par value. The bond offers a 5% coupon rate with interest paid semiannually. The bond's annual yield-to-maturity is closest to: 2.09%. 4.18%. 4.50%. B is correct. The formula for calculating this bond's yield-to-maturity is: PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+⋯+PMT(1+r)39+PMT+FV(1+r)40 where: PV = present value, or the price of the bond PMT = coupon payment per period FV = future value paid at maturity, or the par value of the bond r = market discount rate, or required rate of return per period 111=2.5(1+r)1+2.5(1+r)2+2.5(1+r)3+⋯+2.5(1+r)39+2.5+100(1+r)40 r = 0.0209 To arrive at the annualized yield-to-maturity, the semiannual rate of 2.09% must be multiplied by two. Therefore, the yield-to-maturity is equal to 2.09% × 2 = 4.18%. The annual yield-to-maturity, stated for with a periodicity of 12, for a 4-year, zero- coupon bond priced at 75 per 100 of par value is closest to: 6.25%. 7.21%. 7.46%. B is correct. The annual yield-to-maturity, stated for a periodicity of 12, is 7.21%. It is calculated as follows: PV=FV(1+r)N 75=(100(1+r)4×12) 10075=(1+r)48 1.33333 = (1 + r)48 [1.33333]1/48 = [(1 + r)48]1/48 1.3 = (1 + r) 1.00601 = (1 + r) 1.00601 - 1 = r 0.00601 = r r × 12 = 0.07212, or approximately 7.21% A 5-year, 5% semiannual coupon payment corporate bond is priced at 104.967 per 100 of par value. The bond's yield-to-maturity, quoted on a semiannual bond basis, is 3.897%. An analyst has been asked to convert to a monthly periodicity. Under this conversion, the yield-to-maturity is closest to: 3.87%. 4.95%. 7.67%. A is correct. The yield-to-maturity, stated for a periodicity of 12 (monthly periodicity), is 3.87%.The formula to convert an annual percentage rate (annual yield-to- maturity) from one periodicity to another is as follows: (1+APRmm)m=(1+APRnn)n (1+0.)2=(1+APR1212)12 (1.01949)2=(1+APR1212)12 1.03935=(1+APR1212)12 (1.03935)1/12=[(1+APR1212)12]1/12 1.00322=(1+APR1212) 1.00322−1=(APR1212) APR12 = 0.00322 × 12 = 0.03865, or approximately 3.87%. A bond with 5 years remaining until maturity is currently trading for 101 per 100 of par value. The bond offers a 6% coupon rate with interest paid semiannually. The bond is first callable in 3 years, and is callable after that date on coupon dates according to the following schedule: End of Year Call Price 3 102 4 101 5 100 The bond's annual yield-to-maturity is closest to: 2.88%. 5.77%. 5.94%. B is correct. The yield-to-maturity is 5.77%. The formula for calculating this bond's yield-to-maturity is: PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+⋯+PMT(1+r)9+PMT+FV(1+r)10 where: PV = present value, or the price of the bond PMT = coupon payment per period FV = future value paid at maturity, or the par value of the bond r = market discount rate, or required rate of return per period 101=3(1+r)1+3(1+r)2+3(1+r)3+⋯+3(1+r)9+3+100(1+r)10 r = 0.02883 To arrive at the annualized yield-to-maturity, the semiannual rate of 2.883% must be multiplied by two. Therefore, the yield-to-maturity is equal to 2.883% × 2 = 5.77% (rounded). A bond with 5 years remaining until maturity is currently trading for 101 per 100 of par value. The bond offers a 6% coupon rate with interest paid semiannually. The bond is first callable in 3 years, and is callable after that date on coupon dates according to the following schedule: End of Year Call Price 3 102 4 101 5 100 The bond's annual yield-to-first-call is closest to: 3.12%. 6.11%. 6.25%. C is correct. The yield-to-first-call is 6.25%. Given the first call date is exactly three years away, the formula for calculating this bond's yield-to-first-call is: PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+⋯+PMT(1+r)5+PMT+FV(1+r)6 where: PV = present value, or the price of the bond PMT = coupon payment per period FV = call price paid at call date r = market discount rate, or required rate of return per period 101=3(1+r)1+3(1+r)2+3(1+r)3+⋯+3(1+r)5+3+102(1+r)6 r = 0.03123 To arrive at the annualized yield-to-first-call, the semiannual rate of 3.123% must be multiplied by two. Therefore, the yield-to-first-call is equal to 3.123% × 2 = 6.25% (rounded). A bond with 5 years remaining until maturity is currently trading for 101 per 100 of par value. The bond offers a 6% coupon rate with interest paid semiannually. The bond is first callable in 3 years, and is callable after that date on coupon dates according to the following schedule: End of Year Call Price 3 102 4 101 5 100 The bond's annual yield-to-second-call is closest to: 2.97%. 5.72%. 5.94%. C is correct. The yield-to-second-call is 5.94%. Given the second call date is exactly four years away, the formula for calculating this bond's yield-to-second-call is: PV=PMT(1+r)1+PMT(1+r)2+PMT(1+r)3+⋯+PMT(1+r)7+PMT+FV(1+r)8 where: PV = present value, or the price of the bond PMT = coupon payment per period FV = call price paid at call date r = market discount rate, or required rate of return per period 101=3(1+r)1+3(1+r)2+3(1+r)3+⋯3(1+r)7+3+101(1+r)8 r = 0.0297 To arrive at the annualized yield-to-second-call, the semiannual rate of 2.97% must be multiplied by two. Therefore, the yield-to-second-call is equal to 2.97% × 2 = 5.94%. A bond with 5 years remaining until maturity is currently trading for 101 per 100 of par value. The bond offers a 6% coupon rate with interest paid semiannually. The bond is first callable in 3 years, and is callable after that date on coupon dates according to the following schedule: End of Year Call Price 3 102 4 101 5 100 The bond's yield-to-worst is closest to: 2.88%. 5.77%. 6.25%. B is correct. The yield-to-worst is 5.77%. The bond's yield-to-worst is the lowest of the sequence of yields-to-call and the yield-to-maturity. From above, we have the following yield measures for this bond: Yield-to-first-call: 6.25% Yield-to-second-call: 5.94% Yield-to-maturity: 5.77% Thus, the yield-to-worst is 5.77%. A two-year floating-rate note pays 6-month Libor plus 80 basis points. The floater is priced at 97 per 100 of par value. Current 6-month Libor is 1.00%. Assume a 30/360 day-count convention and evenly spaced periods. The discount margin for the floater in basis points (bps) is closest to: 180 bps. 236 bps. 420 bps. B is correct. The discount or required margin is 236 basis points. Given the floater has a maturity of two years and is linked to 6-month Libor, the formula for calculating discount margin is: PV=(Index+QM)×FVm(1+Index+DMm)1+(Index+QM)×FVm(1+Index+DMm)2+⋯+(Inde x+QM)×FVm+FV(1+Index+DMm)4 where: PV = present value, or the price of the floating-rate note = 97 Index = reference rate, stated as an annual percentage rate = 0.01 QM = quoted margin, stated as an annual percentage rate = 0.0080 FV = future value paid at maturity, or the par value of the bond = 100 m = periodicity of the floating-rate note, the number of payment periods per year = 2 DM = discount margin, the required margin stated as an annual percentage rate Substituting given values in: 97=(0.01+0.0080)×1002(1+0.01+DM2)1+(0.01+0.0080)×1002(1+0.01+DM2)2+⋯+(0.01 +0.0080)×1002+100(1+0.01+DM2)4 97=0.90(1+0.01+DM2)1+0.90(1+0.01+DM2)2+0.90(1+0.01+DM2)3+0.90+100(1+0.01+ DM2)4 To calculate DM, begin by solving for the discount rate per period: 97=0.90(1+r)1+0.90(1+r)2+0.90(1+r)3+0.90+100(1+r)4 r = 0.0168 Now, solve for DM: 0.01+DM2=0.0168 DM = 0.0236 The discount margin for the floater is equal to 236 basis points. n analyst evaluates the following information relating to floating rate notes (FRNs) issued at par value that have 3-month Libor as a reference rate: Floating Rate Note Quoted Margin Discount Margin X 0.40% 0.32% Y 0.45% 0.45% Z 0.55% 0.72% Based only on the information provided, the FRN that will be priced at a premium on the next reset date is: FRN X. FRN Y. FRN Z. A is correct. FRN X will be priced at a premium on the next reset date because the quoted margin of 0.40% is greater than the discount or required margin of 0.32%. The premium amount is the present value of the extra or "excess" interest payments of 0.08% each quarter (0.40% - 0.32%). FRN Y will be priced at par value on the next reset date since there is no difference between the quoted and discount margins. FRN Z will be priced at a discount since the quoted margin is less than the required margin. A 365-day year bank certificate of deposit has an initial principal amount of USD 96.5 million and a redemption amount due at maturity of USD 100 million. The number of days between settlement and maturity is 350. The bond equivalent yield is closest to: 3.48%. 3.65%. 3.78%. C is correct. The bond equivalent yield is closest to 3.78%. It is calculated as: AOR=(YearDays)×(FV−PVPV) where: PV = present value, principal amount, or the price of the money market instrument FV = future value, or the redemption amount paid at maturity including interest Days = number of days between settlement and maturity Year = number of days in the year AOR = add-on rate, stated as an annual percentage rate (also, called bond equivalent yield). AOR=()×(100−96.596.5) AOR = 1.04286 × 0.03627 AOR = 0.03783 or approximately 3.78% The bond equivalent yield of a 180-day banker's acceptance quoted at a discount rate of 4.25% for a 360-day year is closest to: 4.31%. 4.34%. 4.40%. C is correct. The bond equivalent yield is closest to 4.40%. The present value of the banker's acceptance is calculated as: PV=FV×(1−DaysYear×DR) where: PV = present value, or price of the money market instrument FV = future value paid at maturity, or face value of the money market instrument Days = number of days between settlement and maturity Year = number of days in the year DR = discount rate, stated as an annual percentage rate PV=100×(1−DaysYear×DR) PV=100×(1−×0.0425) PV = 100 × (1 - 0.02125) PV = 100 × 0.97875 PV = 97.875 The bond equivalent yield (AOR) is calculated as: AOR=(YearDays)×(FV−PVPV) where: PV = present value, principal amount, or the price of the money market instrument FV = future value, or the redemption amount paid at maturity including interest Days = number of days between settlement and maturity Year = number of days in the year AOR = add-on rate (bond equivalent yield), stated as an annual percentage rate AOR=()×(100−PVPV) AOR=()×(100−97.87597.875) AOR = 2.02778 × 0.02171 AOR = 0.04402, or approximately 4.40% Note that the PV is calculated using an assumed 360-day year and the AOR (bond equivalent yield) is calculated using a 365-day year. Which of the following statements describing a par curve is incorrect? A par curve is obtained from a spot curve. All bonds on a par curve are assumed to have different credit risk. A par curve is a sequence of yields-to-maturity such that each bond is priced at par value. B is correct. All bonds on a par curve are assumed to have similar, not different, credit risk. Par curves are obtained from spot curves and all bonds used to derive the par curve are assumed to have the same credit risk, as well as the same periodicity, currency, liquidity, tax status, and annual yields. A par curve is a sequence of yields-to- maturity such that each bond is priced at par value. A yield curve constructed from a sequence of yields-to-maturity on zero-coupon bonds is the: par curve. spot curve. forward curve. B is correct. The spot curve, also known as the strip or zero curve, is the yield curve constructed from a sequence of yields-to-maturities on zero-coupon bonds. The par curve is a sequence of yields-to-maturity such that each bond is priced at par value. The forward curve is constructed using a series of forward rates, each having the same timeframe. The rate, interpreted to be the incremental return for extending the time-to-maturity of an investment for an additional time period, is the: add-on rate. forward rate. yield-to-maturity. B is correct. The forward rate can be interpreted to be the incremental or marginal return for extending the time-to-maturity of an investment for an additional time period. The add-on rate (bond equivalent yield) is a rate quoted for money market instruments such as bank certificates of deposit and indices such as Libor and Euribor. Yield-to-maturity is the internal rate of return on the bond's cash flows—the uniform interest rate such that when the bond's future cash flows are discounted at that rate, the sum of the present values equals the price of the bond. It is the implied market discount rate. Time Period Forward Rate "0y1y" 0.80% "1y1y" 1.12% "2y1y" 3.94% "3y1y" 3.28% "4y1y" 3.14% All rates are annual rates stated for a periodicity of one (effective annual rates). The 3-year implied spot rate is closest to: 1.18%. 1.94%. 2.28%. B is correct. The 3 year implied spot rate is closest to 1.94%. It is calculated as the geometric average of the one-year forward rates: (1.0080 × 1.0112 × 1.0394) = (1 + z3)3 1.05945 = (1 + z3)3 [1.05945]1/3= [(1 + z3)3]1/3 1.01944 = 1 + z3 1.01944 - 1 = z3 0.01944 = z3, z3 = 1.944% or approximately 1.94% Time Period Forward Rate "0y1y" 0.80% "1y1y" 1.12% "2y1y" 3.94% "3y1y" 3.28% "4y1y" 3.14% All rates are annual rates stated for a periodicity of one (effective annual rates). The value per 100 of par value of a two-year, 3.5% coupon bond, with interest payments paid annually, is closest to: 101.58. 105.01. 105.82. B is correct. The value per 100 of par value is closest to105.01. Using the forward curve, the bond price is calculated as follows: 3.51.0080+103.5(1.0080×1.0112)=3.47+101.54=105.01 The spread component of a specific bond's yield-to-maturity is least likely impacted by changes in: its tax status. its quality rating. inflation in its currency of denomination. C is correct. The spread component of a specific bond's yield-to-maturity is least likely impacted by changes in inflation of its currency of denomination. The effect of changes in macroeconomic factors, such as the expected rate of inflation in the currency of denomination, is seen mostly in changes in the benchmark yield. The spread or risk premium component is impacted by microeconomic factors specific to the bond and bond issuer including tax status and quality rating. The yield spread of a specific bond over the standard swap rate in that currency of the same tenor is best described as the: I-spread. Z-spread. G-spread. A is correct. The I-spread, or interpolated spread, is the yield spread of a specific bond over the standard swap rate in that currency of the same tenor. The yield spread in basis points over an actual or interpolated government bond is known as the G-spread. The Z-spread (zero-volatility spread) is the constant spread such that is added to each spot rate such that the present value of the cash flows matches the price of the bond. Bond Coupon Rate Time-to-Maturity Price UK Government Benchmark Bond 2% 3 years 100.25 UK Corporate Bond 5% 3 years 100.65 Both bonds pay interest annually. The current three-year EUR interest rate swap benchmark is 2.12%. The G-spread in basis points (bps) on the UK corporate bond is closest to: 264 bps. 285 bps. 300 bps. B is correct. The G-spread is closest to 285 bps. The benchmark rate for UK fixed-rate bonds is the UK government benchmark bond. The Euro interest rate spread benchmark is used to calculate the G-spread for Euro-denominated corporate bonds, not UK bonds. The G-spread is calculated as follows: Yield-to-maturity on the UK corporate bond: 100.65=5(1+r)1+5(1+r)2+105(1+r)3,r=0.04762or476bps Yield-to-maturity on the UK government benchmark bond: 100.25=2(1+r)1+2(1+r)2+102(1+r)3,r=0.01913or191bps The G-spread is 476 - 191 = 285 bps. A corporate bond offers a 5% coupon rate and has exactly 3 years remaining to maturity. Interest is paid annually. The following rates are from the benchmark spot curve: Time-to-Maturity Spot Rate 1 year 4.86% 2 years 4.95% 3 years 5.65% The bond is currently trading at a Z-spread of 234 basis points. The value of the bond is closest to: 92.38. 98.35. 106.56. A is correct. The value of the bond is closest to 92.38. The calculation is: PV=PMT(1+z1+Z)1+PMT(1+z2+Z)2+PMT+FV(1+z3+Z)3=5(1+0.0486+0.0234)1+5(1+0. 0495+0.0234)2+105(1+0.0565+0.0234)3=51.0720+51.15111+1051.25936=4.66+4.34+ 83.38=92.38 n option-adjusted spread (OAS) on a callable bond is the Z-spread: over the benchmark spot curve. minus the standard swap rate in that currency of the same tenor. minus the value of the embedded call option expressed in basis points per year. C is correct. The option value in basis points per year is subtracted from the Z-spread to calculate the option-adjusted spread (OAS). The Z-spread is the constant yield spread over the benchmark spot curve. The I-spread is the yield spread of a specific bond over the standard swap rate in that currency of the same tenor.