CFA Level 1 - Fixed Income Session 16 - Reading 58

CFA Level 1 - Fixed Income Session 16 - Reading 58 (Notes, Practice Questions, Sample Questions) 1. A 6-year annual interest coupon bond was purchased one year ago. The coupon rate is 10% and par value is $1,000. At the timethe bond was bought, the yield to maturity (YTM) was 8%. If thebond is sold after receiving the first interest payment and thebond's yield to maturity had changed to 7%, the annual total rateof return on holding the bond for that year would have been: A)11.95%. B)7.00%.C)8.00%. [Explanation — (A) Price 1 year ago N = 6, PMT = 100, FV =1,000, I = 8, Compute PV = 1,092 Price now N = 5, PMT = 100,FV = 1,000, I = 7, Compute PV = 1,123% Return = (1,123.00 + 100 − 1,092.46)/1,092.46 x 100 =11.95%] 2. An investor purchased a 10-year zero-coupon bond with a yield to maturity of 10% and a par value of $1,000. What would her rateof return be at the end of the year if she sells the bond? Assumethe yield to maturity on the bond is 9% at the time it is sold andannual compounding periods are used. A)19.42%. B)16.00%.

C)15.00%. [Explanation — (A) Purchase price: I = 10; N = 10; PMT = 0; FV= 1,000; CPT → PV = 385.54 Selling price: I = 9; N = 9; PMT = 0; FV = 1,000; CPT → PV = 460.43% Return = (460.43 − 385.54) / 385.54 × 100 = 19.42%] 3. If an investor holds a bond for a period less than the life of the bond, the rate of return the investor can expect to earn is called: A)approximate yield.B)bond equivalent yield. C)expected return, or horizon return. [Explanation — (C) The horizon return is the total return of agiven horizon such as 5 years on a ten year bond] 4. A 30-year, 12% bond that pays interest annually is discounted priced to yield 14%. However, interest payments will be invested at12%. The realized compound yield on this bond must be: A)greater than 14.0%.B)12.0%. C)between 12.0% and 14.0%. [Explanation — (C) Since you are reinvesting the currentincome at 12%, you will have a return of at least 12%. Andsince the bond is priced to yield 14%, you will earn no morethan 14%]

5. An investor purchased a 6-year annual interest coupon bond one year ago. The coupon interest rate was 10% and the par valuewas $1,000. At the time he purchased the bond, the yield tomaturity was 8%. If he sold the bond after receiving the firstinterest payment and the yield to maturity continued to be 8%, hisannual total rate of return on holding the bond for that year wouldhave been: A)8.00%. B)7.82%.C)9.95%. [Explanation — (A) Purchase price N = 6, PMT = 100, FV =1,000, I = 8compute PV = 1,092.46Sale price N = 5, PMT = 100, FV = 1,000, I = 8compute PV = 1,079.85% return = [(1,079.85 - 1,092.46 + 100) / 1,092.46] x 100 = 8%] 6. A bond has a par value of $1,000, a time to maturity of 20 years, a coupon rate of 10% with interest paid annually, a currentprice of $850, and a yield to maturity (YTM) of 12%. If the interestpayments are reinvested at 10%, the realized compounded yieldon this bond is: A)10.0%. B)10.9%. C)12.0%. [Explanation — (B) The realized yield would have to bebetween the reinvested rate of 10% and the yield to maturityof 12%. While no calculation is necessary to answer thisquestion, the realized yield can be calculated as follows. The

value of the reinvested coupons at the maturity date is: N = 20;I/Y = 10; PMT = 100; PV = 0; CPT FV = 5,727.50. Adding theprincipal repayment, total cash at maturity is $6,727.50.Realized yield: N = 20; PMT = 0; PV = -850; FV = 6727.5; CPTI/Y = 10.8975] 7. The zero volatility spread (Z-spread) is the spread that: A)is added to the yield to maturity of a similar maturity Treasurybond to equal the yield to maturity of the risky bond. B)is added to each spot rate on the Treasury yield curve thatwill cause the present value of the bond's cash flows to equalits market price. C)results when the cost of the call option in percent is subtractedfrom the option adjusted spread. [Explanation — (B) The zero volatility spread (Z-spread) is theinterest rate that is added to each zero-coupon bond spot ratethat will cause the present value of the risky bond's cash flowsto equal its market value. The nominal spread is the spreadthat is added to the YTM of a similar maturity Treasury bondthat will then equal the YTM of the risky bond. The zerovolatility spread (Z-spread) is the spread that results when thecost of the call option in percent is added to the optionadjusted spread] 8. The following information is available for two bonds: ● Bond X is callable and has an option-adjusted spread (OAS) of 55bp. Similar bonds have a Z-spread of 68bp and a nominal spread of 60bp.

● Bond Y is putable and has an OAS of 100bp. Similar bonds have a Z-spread of 78bp and a nominal spread of 66bp. The embedded option cost for Bond: A)X is 5bp. B)X is 13bp. C)X is 8bp. [Explanation — (B) Option cost (Bond X) = Z-spread – OAS =68bp – 55bp = 13bpOption cost (Bond Y) = Z-spread – OAS = 78bp – 100bp = -22bp] 9. Which of the following statements on spreads is NOT correct? A)The Z-spread may be used for bonds that contain calloptions. B)The Z-spread will equal the nominal spread if the term structureof interest rates is flat.C)The option-adjusted spread (OAS) is the di erence between theZ-spread and the option cost [Explanation — (A) The Z-spread is used for risky bonds thatdo NOT contain call options in an attempt to improve on theshortcomings of the nominal spread. The other statements arecorrect] 10. An analyst has gathered the following information:

● Bond A is an 11% annual coupon bond currently trading at 106.385 and matures in 3 years. The yield-to-maturity (YTM) for Bond A is 8.50%. ● The YTM for a Treasury bond that matures in 3-years is 7.65%. ● 1, 2, and 3-year spot rates are 5.0%, 6.5% and 8.25%, respectively. Which of the following statements regarding spreads on bond A isCORRECT? A)The nominal spread is approximately 25 basis points.B)The Z-spread is approximately 85 basis points. C)The nominal spread is approximately 85 basis points. [Explanation — (C) The nominal spread is 8.50% − 7.65% =0.85%. Note that the Z-spread, calculated by trial and error, isapproximately 48 basis points] 11. Assume that an option-free 5% coupon bond with annual coupon payments has two years to maturity. A callable bond thatis the same in every respect as the option-free bond is priced at91.76. With the term structure flat at 6% what is the value of theembedded call option? A)-8.24.B)4.58. C)6.41.

[Explanation — (C) The option value is the di erence betweenthe option-free bond price and the corresponding callablebond price.The value of the option free bond is computed as follows: PMT= 5; N = 2; FV = 100; I = 6; CPT → PV = -98.17(ignore sign). The option value = 98.17 – 91.76 = 6.41] 12. Assume an option-free 5% coupon bond with annual coupon payments has two years remaining to maturity. A putable bondthat is the same in every respect as the option-free bond is pricedat 101.76. With the term structure flat at 6% what is the value ofthe embedded put option? A)1.76. B)3.59. C)-3.59. [Explanation — (B) The value of the embedded put option ofthe putable bond is the di erence between the price of theputable bond and the price of the option-free bond.The value of the option-free bond is computed as follows: PMT= 5; N = 2; FV = 100; I = 6; CPT → PV = -98.17(ignore sign). The option value = 101.79 − 98.17 = 3.59] 13. The six-year spot rate is 7% and the five-year spot rate is 6%. The implied one-year forward rate five years from now is closestto: A)6.5%. B)12.0%. C)5.0%.

[Explanation — (B) 1r5= [(1 + R6)6 / (1 + R5)5] - 1 =[(1.07)6/(1.06)5] – 1 = [1.5 / 1.338] - 1 = 0.12] 14. Suppose the 3-year spot rate is 12.1% and the 2-year spot rate is 11.3%. Which of the following statements concerning forwardand spot rates is most accurate? The 1-year: A)forward rate two years from today is 13.2%.B)forward rate one year from today is 13.7%. C)forward rate two years from today is 13.7% [Explanation — (C) The equation for the three-year spot rate,Z3, is (1 + Z1)(1 + 1f1)(1 + 1f2) = (1 + Z3)3. Also, (1 + Z1)(1 + 1f1)= (1 + Z2)2. So, (1 + 1f2) = (1 + Z3)3 / (1 + Z2)2, computed as: (1+ 0.121)3 / (1 + 0.113)2 = 1.137. Thus, 1f2 = 0.137, or 13.7%] 15. Given the following spot and forward rates, how much should an investor pay for each $100 of a 3-year, annual zero-couponbond? ● One-year spot rate is 3.75% ● The 1-year forward rate 1 year from today is 9.50% ● The 1-year forward rate 2 years from today is 15.80% The investor should pay approximately: A)$76. B)$44.C)$83. [Explanation — (A) The yield to maturity on an N-year zerocoupon bond is equivalent to the N-year spot rate. Thus, to

determine the present value of the zero-coupon bond, we needto calculate the 3-year spot rate.Using the formula: (1 + Z3)3 = (1 + 1f0)(1 + 1f1)(1 + 1f2)where Z = spot rate and nfm = the n year rate m periods fromtoday, (1f0 = the 1 year spot rate now).(1 + Z3)3 = (1.0375) × (1.095) × (1.158)Z3 = 1.3155601/3 − 1 = 0.095730, or 9.57%Then, the value of the zero coupon bond = 100 / (1.09573)3 =76.01, or approximately $76,or, using a financial calculator, N = 3; I/Y = 9.57; FV = 1,000;PMT = 0; CPT → PV = 76.20 or approximately $76] 16. Given the one-year spot rate S1 = 0.06 and the implied 1-year forward rates one, two, and three years from now of: 1f1 = 0.062;1f2 = 0.063; 1f3 = 0.065, what is the theoretical 4-year spot rate? A)6.75%.B)6.00%. C)6.25%. [Explanation — (C) S4 = [ (1.06) (1.062) (1.063) (1.065) ].25 − 1 =6.25%.] 17. The one-year spot rate is 6% and the one-year forward rates starting in one, two and three years respectively are 6.5%, 6.8%and 7%. What is the four-year spot rate? A)6.51%.B)6.58%. C)6.57%.

[Explanation — (C) The four-year spot rate is computed asfollows:Four-year spot rate = [(1 + 0.06)(1 + 0.065)(1 + 0.068)(1 + 0.07)]1/4 – 1 = 6.57%] 18. Given the implied forward rates of: R1 = 0.04; 1r1 = 0.04300; 1r2 = 0.05098; 1r3 = 0.051005, what is the theoretical 4-period spotrate? A)6.67%.B)2.33%. C)4.62%. [Explanation — (C) [(1.04)(1.043)(1.05098)(1.051005)].25−1] 19. If the current two-year spot rate is 6% while the one-year forward rate for one year is 5%, what is the current spot rate forone year? A)5.5%.B)5.0%. C)7.0% [Explanation — (C) (1 + f)(1 + r1) = (1 + r2)2(1 + 0.05)(1 + r1) = (1 + 0.06)2(1 + r1) = (1.06)2 / (1 + 0.05)1 + r1 = 1.1236 / 1.051 + r1 = 1.0701r1 = 0.07 or 7%]

20. Which of the following statements regarding forward rates is NOT correct? A)Forward rates do not account for the market's tolerance forrisk. B)By the aggregation of forward rates, spot rates can beestimated.C)Forward rates may be estimated from spot rates. [Explanation — (A) Spot interest rates are the result of marketparticipant’s tolerance for risk and their collective viewregarding the future path of interest rates. If we assume thatthese results are purely a function of expectations, we can usespot rates to estimate the market’s consensus on forwardinterest rates] 21. The one-year spot rate is 5% and the two-year spot rate is 6.5%. What is the one-year forward rate starting one year fromnow? A)5.00%. B)8.02%. C)7.87% [Explanation — (B) The forward rate is computed as follows:One-year forward rate = 1.0652 / 1.05 – 1 = 8.02%]