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Fixed Income III - Problem Solving Session

Fixed Income III - Problem Solving Session. FIXED INCOME: CFA LEVEL I. Harvard Extension School MGMT E-2900b CFA Exam Level I April 6, 2010. Valuation of Debt Securities Yield Measures, Spot Rates & Forward Rates. Fixed Income III:. FIXED INCOME: CFA LEVEL I. Study Session 16

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Fixed Income III - Problem Solving Session

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  1. Fixed Income III - Problem Solving Session FIXED INCOME: CFA LEVEL I • Harvard Extension School • MGMT E-2900b • CFA Exam Level I • April 6, 2010

  2. Valuation of Debt Securities Yield Measures, Spot Rates & Forward Rates Fixed Income III: FIXED INCOME: CFA LEVEL I • Study Session 16 • Reading 64 & 65

  3. Valuation, Yield Measures, Spots & Forwards • Questions 1-3: • Consider a 5-year, 8% semiannual bond with a €1,000 face value. Current market rates 5.5%. • How much is each coupon payment? • €27.50 • €80.00 • €40.00 FIXED INCOME: CFA LEVEL I

  4. Valuation, Yield Measures, Spots & Forwards • Questions 1-3: • Consider a 5-year, 8% semiannual bond with a €1,000 face value. Current market rates 5.5%. • How much is each coupon payment? • €27.50 • €80.00 • €40.00 FIXED INCOME: CFA LEVEL I €1,000 x (0.08/2) = €40 N=10, PV= -1,000, FV=1,000, I/Y=4 CPT PMT = €40

  5. Valuation, Yield Measures, Spots & Forwards • Questions 1-3 (cont.): • What would the bond trade for if it were priced with YTM equal to current rates? • €1,107 • €1,108 • €899 FIXED INCOME: CFA LEVEL I

  6. Valuation, Yield Measures, Spots & Forwards • Questions 1-3 (cont.): • What would the bond trade for if it were priced with YTM equal to current rates? • €1,107 • €1,108 • €899 FIXED INCOME: CFA LEVEL I N=10, I/Y=(5.5/2)=2.75, PMT=40, FV=1000 CPT PV = 1,108

  7. Valuation, Yield Measures, Spots & Forwards • Questions 1-3 (cont.): • Current market rates have moved. If the bond was quoted at €950, what would this infer about the new market rate and what would it be? • Market rates are lower than the bond’s rate, 7.15% • Market rates are higher than the bond’s rate, 9.27% • Market rates are equal to the bond’s rate, 8% FIXED INCOME: CFA LEVEL I

  8. Valuation, Yield Measures, Spots & Forwards • Questions 1-3 (cont.): • Current market rates have moved. If the bond was quoted at €950, what would this infer about the new market rate and what would it be? • Market rates are lower than the bond’s rate, 7.15% • Market rates are higher than the bond’s rate, 9.27% • Market rates are equal to the bond’s rate, 8% FIXED INCOME: CFA LEVEL I

  9. Valuation, Yield Measures, Spots & Forwards • Questions 1-3 (cont.): • Explained: Same as solving for YTM • €950 = ∑10t=1 40/(1+YTM/2)t +…+ 1040/(1+YTM/2)10 • or: N=10; PV=-950; PMT=40; FV=1,000 • CPT I/Y = 4.636 x 2 = 9.27% FIXED INCOME: CFA LEVEL I

  10. Valuation, Yield Measures, Spots & Forwards • Bond A is 10-year, 10% semiannual-pay bond that is priced to yield 8% as an annual rate. Bond B is a 15-year, 8% semiannual-pay bond priced with a yield to maturity of 10%. If face value for each bond is $1,000, the prices of these two bonds would be? • Bond ABond B • $1,136 $ 846 • $ 875 $1,173 • $1,134 $ 848 FIXED INCOME: CFA LEVEL I

  11. Valuation, Yield Measures, Spots & Forwards • Bond A is 10-year, 10% semiannual-pay bond that is priced to yield 8% as an annual rate. Bond B is a 15-year, 8% semiannual-pay bond priced with a yield to maturity of 10%. If face value for each bond is $1,000, the prices of these two bonds would be? • Bond ABond B • $1,136 $ 846 • $ 875 $1,173 • $1,134 $ 848 FIXED INCOME: CFA LEVEL I

  12. Valuation, Yield Measures, Spots & Forwards • Explained: • Bond A: • N=20; I/Y=8/2=4; PMT=50; FV=1000 • CPT PV = 1,136 • Bond B: • N=30; I/Y=10/2=5; PMT=40; FV=1000 • CPT PV = 846 FIXED INCOME: CFA LEVEL I

  13. Valuation, Yield Measures, Spots & Forwards • A 1-year, 5% Treasury bill is trading at $950. Treasury spot rates (expressed as semiannual-pay yields to maturity) are: 6-months = 5%, 1-year = 6%. The arbitrage trade and profit are: • Sell the bond, buy the pieces, earn $40.55 • Buy the bond, sell the pieces, earn $50.00 • Buy the bond, sell the pieces, earn $40.55 FIXED INCOME: CFA LEVEL I

  14. Valuation, Yield Measures, Spots & Forwards • A 1-year, 5% Treasury bill is trading at $950. Treasury spot rates (expressed as semiannual-pay yields to maturity) are: 6-months = 5%, 1-year = 6%. The arbitrage trade and profit are: • Sell the bond, buy the pieces, earn $40.55 • Buy the bond, sell the pieces, earn $50.00 • Buy the bond, sell the pieces, earn $40.55 FIXED INCOME: CFA LEVEL I

  15. Valuation, Yield Measures, Spots & Forwards • Explained: • arbitrage free value: • = 25 + 1025 = • 1.025 1.032 • 24.39 + 966.16 = 990.55 • bond price < discounted price • buy the bond, sell the pieces for an arbitrage profit of $40.55. FIXED INCOME: CFA LEVEL I

  16. Valuation, Yield Measures, Spots & Forwards • A $1,000, 10-year, 6% semiannual coupon bond is priced to yield 4.5%. How much will the bond value decrease in 4 years if the yield remains the same? • 3.694% • -3.717% • -3.694% FIXED INCOME: CFA LEVEL I

  17. Valuation, Yield Measures, Spots & Forwards • A $1,000, 10-year, 6% semiannual coupon bond is priced to yield 4.5%. How much will the bond value decrease in 4 years if the yield remains the same? • 3.694% • -3.717% • -3.694% FIXED INCOME: CFA LEVEL I

  18. Valuation, Yield Measures, Spots & Forwards • Explained: • Calculate PV: N=20; I/Y=4.5/2; PMT=30; FV=1,000 CPT PV = 1,119.73 • Calculate PV in 4 years: N=12; I/Y=4.5/2; PMT=30; FV=1,000 CPT PV = 1,078.11 • % ∆ = (1,078.11/1,119.73)-1 = -3.717% FIXED INCOME: CFA LEVEL I

  19. Valuation, Yield Measures, Spots & Forwards • A 10-year, 5% option-free bond is issued at the require yield to maturity. A year later the required rate increases. At what price is the bond issued, and what happens to the bond’s price as a result of the rise in yield? • Issued at par, bond price falls • Issued below par, bond price falls • Issued at par, bond price increases FIXED INCOME: CFA LEVEL I

  20. Valuation, Yield Measures, Spots & Forwards • A 10-year, 5% option-free bond is issued at the require yield to maturity. A year later the required rate increases. At what price is the bond issued, and what happens to the bond’s price as a result of the rise in yield? • Issued at par, bond price falls • Issued below par, bond price falls • Issued at par, bond price increases FIXED INCOME: CFA LEVEL I

  21. Valuation, Yield Measures, Spots & Forwards • Explained: • If the stated coupon rate is equal to the required rate (YTM), then the bond is priced at par. • There is an inverse relationship between price and yield. Thus, if the required yield increases (decreases), the bond’s price will fall (rise). FIXED INCOME: CFA LEVEL I

  22. Valuation, Yield Measures, Spots & Forwards • Questions 8-11: • Observe a $1,000 par, 3%, 5-year semiannual-pay bond trading at $1,015 that is callable after one year at 103 (as a % of par) and putable at 101 in two years. • What is the current yield of the bond? • 3.000% • 2.677% • 2.956% FIXED INCOME: CFA LEVEL I

  23. Valuation, Yield Measures, Spots & Forwards • Questions 8-11: • Observe a $1,000 par, 3%, 5-year semiannual-pay bond trading at $1,015 that is callable after one year at 103 (as a % of par) and putable at 101 in two years. • What is the current yield of the bond? • 3.000% • 2.677% • 2.956% FIXED INCOME: CFA LEVEL I Current Yield = CPN/PV = 30/1,015 = 2.956%

  24. Valuation, Yield Measures, Spots & Forwards • Questions 8-11: • Observe a $1,000 par, 3%, 5-year semiannual-pay bond trading at $1,015 that is callable after one year at 103 (as a % of par) and putable at 101 in two years. • What is the bond’s yield to maturity? • 1.339% • 2.677% • 3.000% FIXED INCOME: CFA LEVEL I

  25. Valuation, Yield Measures, Spots & Forwards • Questions 8-11: • Observe a $1,000 par, 3%, 5-year semiannual-pay bond trading at $1,015 that is callable after one year at 103 (as a % of par) and putable at 101 in two years. • What is the bond’s yield to maturity? • 1.339% • 2.677% • 3.000% FIXED INCOME: CFA LEVEL I YTM: N=10; PV=-1,015; PMT=15; FV=1,000 CPT I/Y = 1.3387 x 2 =2.677%

  26. Valuation, Yield Measures, Spots & Forwards • Questions 8-11: • Observe a $1,000 par, 3%, 5-year semiannual-pay bond trading at $1,015 that is callable after one year at 103 (as a % of par) and putable at 101 in two years. • What is the bond’s yield to call? • 4.417% • 2.209% • 2.466% FIXED INCOME: CFA LEVEL I

  27. Valuation, Yield Measures, Spots & Forwards • Questions 8-11: • Observe a $1,000 par, 3%, 5-year semiannual-pay bond trading at $1,015 that is callable after one year at 103 (as a % of par) and putable at 101 in two years. • What is the bond’s yield to call? • 4.417% • 2.209% • 2.466% FIXED INCOME: CFA LEVEL I YTM: N=2; PV=-1,015; PMT=15; FV=1,030 CPT I/Y = 2.209 x 2 = 4.417%

  28. Valuation, Yield Measures, Spots & Forwards • Questions 8-11: • Observe a $1,000 par, 3%, 5-year semiannual-pay bond trading at $1,015 that is callable after one year at 103 (as a % of par) and putable at 101 in two years. • What is the bond’s yield to put? • 4.417% • 1.357% • 2.714% FIXED INCOME: CFA LEVEL I

  29. Valuation, Yield Measures, Spots & Forwards • Questions 8-11: • Observe a $1,000 par, 3%, 5-year semiannual-pay bond trading at $1,015 that is callable after one year at 103 (as a % of par) and putable at 101 in two years. • What is the bond’s yield to put? • 4.417% • 1.357% • 2.714% FIXED INCOME: CFA LEVEL I YTM: N=4; PV=-1,015; PMT=15; FV=1,010 CPT I/Y = 1.357 x 2 = 2.714%

  30. Valuation, Yield Measures, Spots & Forwards • What is the bond equivalent yield for a bond with annual coupons that is priced to yield 7%? • 7.000% • 6.881% • 3.441% FIXED INCOME: CFA LEVEL I

  31. Valuation, Yield Measures, Spots & Forwards • What is the bond equivalent yield for a bond with annual coupons that is priced to yield 7%? • 7.000% • 6.881% • 3.441% FIXED INCOME: CFA LEVEL I BEY = [(1+EAY)(1/2)-1] x 2 BEY = [(1.07 )(1/2)-1] x 2 = 6.881%

  32. Valuation, Yield Measures, Spots & Forwards • What is the bond equivalent yield for a CDO paying 40bps per month? • 2.424% • 4.800% • 4.848% FIXED INCOME: CFA LEVEL I

  33. Valuation, Yield Measures, Spots & Forwards • What is the bond equivalent yield for a CDO paying 40bps per month? • 2.424% • 4.800% • 4.848% FIXED INCOME: CFA LEVEL I BEY = [(1+CFY)6-1] x 2 BEY = [(1.004 )6-1] x 2 = 4.848%

  34. Valuation, Yield Measures, Spots & Forwards • Questions 13-16: • Consider a 10-year, $1,000 semiannual par value bond with prevailing market rates of 4%. • If the bond were a zero-coupon bond issued at $672.97, what is its YTM? • 4.000% • 2.000% • 4.200% FIXED INCOME: CFA LEVEL I

  35. Valuation, Yield Measures, Spots & Forwards • Questions 13-16: • Consider a 10-year, $1,000 semiannual par value bond with prevailing market rates of 4%. • If they bond were a zero-coupon bond issued at $672.97, what is its YTM? • 4.000% • 2.000% • 4.200% FIXED INCOME: CFA LEVEL I YTM: N=20; PV=-672.97; PMT=0; FV=1,000 CPT I/Y = 2.000 x 2 = 4%

  36. Valuation, Yield Measures, Spots & Forwards • Questions 13-16: • Consider a 10-year, $1,000 semiannual par value bond with prevailing market rates of 4%. • At what price would the bond sell for if it were issued with a 6% coupon rate, and which of the three sources of return is it most susceptible? • $851.23, principal loss • $1,163.51, reinvestment of coupons • $1,000.00, interest payments FIXED INCOME: CFA LEVEL I

  37. Valuation, Yield Measures, Spots & Forwards • Questions 13-16: • Consider a 10-year, $1,000 semiannual par value bond with prevailing market rates of 4%. • At what price would the bond sell for if it were issued with a 6% coupon rate, and which of the three sources of return is it most susceptible? • $851.23, principal loss • $1,163.51, reinvestment of coupons • $1,000.00, interest payments FIXED INCOME: CFA LEVEL I N=20; I/Y=4/2; PMT=30; FV=1,000 CPT PV = $1,163.51

  38. Valuation, Yield Measures, Spots & Forwards • Questions 13-16: • Consider a 10-year, $1,000 semiannual par value bond with prevailing market rates of 4%. • At what price would the bond sell for if it were issued with a 6% coupon rate and prevailing rates increased to 6%? • $851.23 • $1,163.51 • $1,000.00 FIXED INCOME: CFA LEVEL I

  39. Valuation, Yield Measures, Spots & Forwards • Questions 13-16: • Consider a 10-year, $1,000 semiannual par value bond with prevailing market rates of 4%. • At what price would the bond sell for if it were issued with a 6% coupon rate, and prevailing rates increased to 6%? • $851.23 • $1,163.51 • $1,000.00 FIXED INCOME: CFA LEVEL I N=20; I/Y=6/2; PMT=30; FV=1,000 CPT PV = $1,000

  40. Valuation, Yield Measures, Spots & Forwards • Questions 13-16: • Consider a 10-year, $1,000 semiannual par value bond with prevailing market rates of 4%. • Was the reinvestment risk from the bond in #14, higher, lower, or the same as the bond in #15? • Higher • Lower • Same FIXED INCOME: CFA LEVEL I

  41. Valuation, Yield Measures, Spots & Forwards • Questions 13-16: • Consider a 10-year, $1,000 semiannual par value bond with prevailing market rates of 4%. • Was the reinvestment risk from the bond in #14, higher, lower, or the same as the bond in #15? • Higher • Lower • Same FIXED INCOME: CFA LEVEL I

  42. Valuation, Yield Measures, Spots & Forwards • Explained: • Reinvestment risk will increase with: • Higher Coupons • Longer Maturities • Because both bonds paid the same coupon and had the same maturity, reinvestment risk was the same. • However, their reinvestment outcome varied due to differing reinvestment rates. FIXED INCOME: CFA LEVEL I

  43. Valuation, Yield Measures, Spots & Forwards • The 2-year spot rate is 6% and the 3-year spot rate is 7%. What is the 1-year forward rate two years from today? • 0.943% • 7.000% • 9.028% FIXED INCOME: CFA LEVEL I

  44. Valuation, Yield Measures, Spots & Forwards • The 2-year spot rate is 6% and the 3-year spot rate is 7%. What is the 1-year forward rate two years from today? • 0.943% • 7.000% • 9.028% (1+S3)3 = (1+S2)2 x (1+1f2) (1.07)3 = (1.06)2 x (1+1f2) (1.07)3 – 1 = 1f2 = 9.028% (1.06)2 FIXED INCOME: CFA LEVEL I

  45. Valuation, Yield Measures, Spots & Forwards • Consider a callable bond. If the Z-spread is 300 bps, the option-adjusted spread (OAS) will be: • equal to 300 bps • less than 300 bps • greater than 300 bps FIXED INCOME: CFA LEVEL I

  46. Valuation, Yield Measures, Spots & Forwards • Consider a callable bond. If the Z-spread is 300 bps, the option-adjusted spread (OAS) will be: • equal to 300 bps • less than 300 bps • greater than 300 bps FIXED INCOME: CFA LEVEL I

  47. Valuation, Yield Measures, Spots & Forwards • Explained: • Option cost > 0; The investor receives compensation for writing the option to the issuer OAS < Z-spread. That is, the investor requires more yield on the callable bond than for an option-free bond. The opposite is true for putable bonds. • The OAS is the comparable spread for non-option bond characteristics like credit risk, interest rate risk, and liquidity risk. FIXED INCOME: CFA LEVEL I

  48. Valuation, Yield Measures, Spots & Forwards • A coupon bond’s nominal spread, Z-spread, and OAS spread would be equal if: • the bond has no embedded option • the bond is option free, the yield curve is flat, and the coupons are relatively high • the bond is not putable and the yield curve is steep FIXED INCOME: CFA LEVEL I

  49. Valuation, Yield Measures, Spots & Forwards • A coupon bond’s nominal spread, Z-spread, and OAS spread would be equal if: • the bond has no embedded option • the bond is option free, the yield curve is flat, and the coupons are relatively high • the bond is not putable and the yield curve is steep FIXED INCOME: CFA LEVEL I

  50. Valuation, Yield Measures, Spots & Forwards • Explained: • Zero-volatility spread is the equal amount that must be added to each rate on the Treasury spot curve in order the make the present value of the risky bond’s cash flow equal to its price. • Thus, a flat yield curve will make nominal and zero-volatility spreads equal. • The higher the coupon payment, the earlier principle is received and discounted with each periodic Z-spread. FIXED INCOME: CFA LEVEL I

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