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Fixed Income IV Problem Solving Session

Fixed Income IV Problem Solving Session. FIXED INCOME: CFA LEVEL I. Harvard Extension School MGMT E-2900b CFA Exam Level I April 13, 2010. Duration and Convexity Study Session 16: Reading 66 Term Structure of Interest Rates: Alternative Theories Study Session 15: Reading 63.

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Fixed Income IV Problem Solving Session

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  1. Fixed Income IV Problem Solving Session FIXED INCOME: CFA LEVEL I • Harvard Extension School • MGMT E-2900b • CFA Exam Level I • April 13, 2010

  2. Duration and Convexity Study Session 16: Reading 66 Term Structure of Interest Rates: Alternative Theories Study Session 15: Reading 63 Fixed Income IV: FIXED INCOME: CFA LEVEL I

  3. Duration, Convexity & the Term Structure of Interest Rates • Using the full valuation approach and given a 50 bps decrease in required yield, what is the interest rate sensitivity of a portfolio of $17,000 face value 5-year bonds, with 4% semiannual-pay coupons priced to yield 5%. • -2.285% • 2.285% • -2.200% FIXED INCOME: CFA LEVEL I

  4. Duration, Convexity & the Term Structure of Interest Rates • Using the full valuation approach and given a 50 bps decrease in required yield, what is the interest rate sensitivity of a portfolio of $17,000 face value 5-year bonds, with 4% semiannual-pay coupons priced to yield 5%. • -2.285% • 2.285% • -2.200% FIXED INCOME: CFA LEVEL I

  5. Duration, Convexity & the Term Structure of Interest Rates • Explained: Find  PV2/PV1 – 1 • PV1: N=10; I/Y=5/2; PMT=17,000(.04/2) = 340; FV=17,000; CPT PV1 = –16,256.07 • PV2: N=10; I/Y=4.5/2; PMT=17,000(.04/2) = 340; FV=17,000; CPT PV2 = –16,623.19 • PV2/PV1 – 1 = (16,623.19/16,256.07) – 1 = 2.258% FIXED INCOME: CFA LEVEL I

  6. Duration, Convexity & the Term Structure of Interest Rates • Questions 2-3: • Given a 75 bps change in yield, which of the following is the closest to the effective duration of a 7% semiannual-pay bond with 5-years to maturity trading at par: • 4.102. • 4.158. • 0.416. FIXED INCOME: CFA LEVEL I

  7. Duration, Convexity & the Term Structure of Interest Rates • Questions 2-3: • Given a 75 bps change in yield, which of the following is the closest to the effective duration of a 7% semiannual-pay bond with 5-years to maturity trading at par: • 4.102. • 4.158. • 0.416. FIXED INCOME: CFA LEVEL I

  8. Duration, Convexity & the Term Structure of Interest Rates • Questions 2-3: • Explained: • ED = V- – V+ ; • 2V0(∆y) • where: V- = bond value if yield ↓ by ∆y • V+ = bond value if yield ↑ by ∆y • V0 = initial bond price • ∆y = change in yield FIXED INCOME: CFA LEVEL I

  9. Duration, Convexity & the Term Structure of Interest Rates • Questions 2-3: • Explained: • V- = 103.18: N=10; I/Y=6.25/2=3.125; PMT=3.5; FV=100; CPT PV = 103.18 • V+ = 96.94: N=10; I/Y=7.75/2=3.875; PMT=3.5; FV=100; CPT PV = 96.94 • ED = (103.18 – 96.94)/2(100)(.0075) • = 6.24/1.5 = 4.158 FIXED INCOME: CFA LEVEL I

  10. Duration, Convexity & the Term Structure of Interest Rates • Questions 2-3: • Assume the bond is callable today at 102 and the change in yield remains 75 bps. The effective duration would be closest to: • 3.373 • 4.158 • 0.337 FIXED INCOME: CFA LEVEL I

  11. Duration, Convexity & the Term Structure of Interest Rates • Questions 2-3: • Assume the bond is callable today at 102 and the change in yield remains 75 bps. The effective duration would be closest to: • 3.373 • 4.158 • 0.337 FIXED INCOME: CFA LEVEL I

  12. Duration, Convexity & the Term Structure of Interest Rates • Questions 2-3: • Explained: • V- = 102: N=10; I/Y=6.25/2=3.125; PMT=3.5; FV=100; CPT PV = 103.18 102 (call price) • V+ = 96.94: N=10; I/Y=7.75/2=3.875; PMT=3.5; FV=100; CPT PV = 96.94 • ED = (102 – 96.94)/2(100)(.0075) • = 5.06/1.5 = 3.37 FIXED INCOME: CFA LEVEL I

  13. Duration, Convexity & the Term Structure of Interest Rates • Given a modified duration of 5.21 and a convexity of 52.1 which of the following is closest to the % price change for an increase in yield of 1.21%? • 0.7627% • -6.3041% • -5.5414% FIXED INCOME: CFA LEVEL I

  14. Duration, Convexity & the Term Structure of Interest Rates • Given a modified duration of 5.21 and a convexity of 52.1 which of the following is closest to the % price change for an increase in yield of 1.21%? • 0.7627% • -6.3041% • -5.5414% FIXED INCOME: CFA LEVEL I % ∆ price = -(MD)(∆y) = -(5.21)(.0121) = -0.06304 = -6.3041% Conv. Effect = (convexity)(∆y)2 = 52.1(.0121)2 = 0.007627 = 0.7627% Sum: -6.3041% + 0.7627% = -5.5414%

  15. Duration, Convexity & the Term Structure of Interest Rates • Which of the following is closest to a bond’s duration, given a total % price change of 8% when yields fall 2% and a convexity of 45? • -3.1 • 4.5 • 3.1 FIXED INCOME: CFA LEVEL I

  16. Duration, Convexity & the Term Structure of Interest Rates • Which of the following is closest to a bond’s duration, given a total % price change of 8% when yields fall 2% and a convexity of 45? • -3.1 • 4.5 • 3.1 FIXED INCOME: CFA LEVEL I % ∆ price = duration effect + convexity effect 0.08 = [-(D)(-0.02)] + [45(-0.02)2] 0.08 = 0.02D + 0.018 D = 3.1

  17. Duration, Convexity & the Term Structure of Interest Rates • Consider a 5-year, 6% semiannual-pay bond priced at 99.5. The price value of a basis point for this bond is closest to: • $0.04 • $0.05 • $0.06 FIXED INCOME: CFA LEVEL I

  18. Duration, Convexity & the Term Structure of Interest Rates • Consider a 5-year, 6% semiannual-pay bond priced at 99.5. The price value of a basis point for this bond is closest to: • $0.04 • $0.05 • $0.06 FIXED INCOME: CFA LEVEL I

  19. Duration, Convexity & the Term Structure of Interest Rates • Explained: • Find I/Y: N=10; PV=-99.5; PMT=3; FV=100 • CPT I/Y = 3.0588 x 2 = 6.1176% • Find PV w/ +0.01%: N=10; I/Y=6.1276/2= 3.0638; PMT=3; FV=100 • CPT PV = 99.4575 • PVBP = 99.50 – 99.4575 = $0.0425 ≈ $0.04 FIXED INCOME: CFA LEVEL I

  20. Duration, Convexity & the Term Structure of Interest Rates • Which of the following combinations of convexity and duration measures will provide the most accurate forecast of a price change for a callable bond? • Modified Duration and Modified Convexity. • Effective Duration and Effective Convexity. • Macaulay Duration and Modified Convexity. FIXED INCOME: CFA LEVEL I

  21. Duration, Convexity & the Term Structure of Interest Rates • Which of the following combinations of convexity and duration measures will provide the most accurate forecast of a price change for a callable bond? • Modified Duration and Modified Convexity. • Effective Duration and Effective Convexity. • Macaulay Duration and Modified Convexity. FIXED INCOME: CFA LEVEL I

  22. Duration, Convexity & the Term Structure of Interest Rates • Explained: • Both effective duration and effective convexity takes into account changes in cash flow due to embedded options. FIXED INCOME: CFA LEVEL I

  23. Duration, Convexity & the Term Structure of Interest Rates • A bond whose price changes by a larger magnitude with a 1bp increase in yield versus a 1bp decrease in yield, is what type of bond? • A putable bond • A bond with negative convexity • A zero-coupon bond FIXED INCOME: CFA LEVEL I

  24. Duration, Convexity & the Term Structure of Interest Rates • A bond whose price changes by a larger magnitude with a 1bp increase in yield versus a 1bp decrease in yield, is what type of bond? • A putable bond • A bond with negative convexity • A zero-coupon bond FIXED INCOME: CFA LEVEL I

  25. Duration, Convexity & the Term Structure of Interest Rates • Price-Yield Curve for a Callable Bond FIXED INCOME: CFA LEVEL I Ps1 Ps2 Pc1 Pc2 Y1 Y2

  26. Duration, Convexity & the Term Structure of Interest Rates • The Fed’s most commonly used method to manage interest rates is: • bank reserve requirements • the discount rate • open market operations FIXED INCOME: CFA LEVEL I

  27. Duration, Convexity & the Term Structure of Interest Rates • The Fed’s most commonly used method to manage interest rates is: • bank reserve requirements • the discount rate • open market operations FIXED INCOME: CFA LEVEL I

  28. Duration, Convexity & the Term Structure of Interest Rates • Explained: • Open Market Operations: buying and selling of Treasury securities by the Fed in the open market. • Sell MS↓ interest rates ↑ • Buy MS↑ interest rates ↓ • Discount Rate: rate at which banks can borrow from the Fed; low rate encourages lending. • Bank Reserve Requirements: % of deposits that banks must retain; lower % encourage more loans. • Persuading banks to tighten/loosen credit policies: encouraging lending interest rates ↓ FIXED INCOME: CFA LEVEL I

  29. Duration, Convexity & the Term Structure of Interest Rates • According to pure expectations theory, a normal yield curve indicates that investors expect: • short-term rates will increase in the future • higher return for illiquidity • inflation to remain flat FIXED INCOME: CFA LEVEL I

  30. Duration, Convexity & the Term Structure of Interest Rates • According to pure expectations theory, a normal yield curve indicates that investors expect: • short-term rates will increase in the future • higher return for illiquidity • inflation to remain flat FIXED INCOME: CFA LEVEL I

  31. Duration, Convexity & the Term Structure of Interest Rates • Pure Expectations Theory: • Average of short-term rates that are expected in the future. If short-term rates are expected to rise in the future, then rates on longer maturities will be higher in the future. FIXED INCOME: CFA LEVEL I

  32. Duration, Convexity & the Term Structure of Interest Rates • According to liquidity preference theory, which of the following would investors not expect? • An illiquidity premium • Little risk differential between short-term and long-term securities • A flat yield curve FIXED INCOME: CFA LEVEL I

  33. Duration, Convexity & the Term Structure of Interest Rates • According to liquidity preference theory, which of the following would investors not expect? • An illiquidity premium • Little risk differential between short-term and long-term securities • A flat yield curve FIXED INCOME: CFA LEVEL I

  34. Duration, Convexity & the Term Structure of Interest Rates • Liquidity Preference Theory: • In addition to expectations about the future of short term rates (pure expectations), investors demand a risk premium for holding longer dates securities. FIXED INCOME: CFA LEVEL I

  35. Duration, Convexity & the Term Structure of Interest Rates • According to market segmentation theory, the structure of interest rates is most likely determined by: • An increase in demand for short-term bonds • The relationship between short-term and long-term securities • The demand for various maturities by investors FIXED INCOME: CFA LEVEL I

  36. Duration, Convexity & the Term Structure of Interest Rates • According to market segmentation theory, the structure of interest rates is most likely determined by: • An increase in demand for short-term bonds • The relationship between short-term and long-term securities • The demand for various maturities by investors FIXED INCOME: CFA LEVEL I

  37. Duration, Convexity & the Term Structure of Interest Rates • Market Segmentation Theory: • The supply (desire to borrow) and demand (desire to lend) for bonds determines the equilibrium rate for various maturity ranges. • Based on the idea that investors have a preference for different maturities. FIXED INCOME: CFA LEVEL I

  38. Duration, Convexity & the Term Structure of Interest Rates • Consider a corporate bond structure with three-year bonds yielding 6%, four-year bonds yielding 7%, and five-year bond yielding 8%. What is the absolute and relative yield spread on the five-year corporate issue if a similar dated Treasury is yielding 6%. • 0, 0% • 100bps, 14.28% • 200bps, 33.33% FIXED INCOME: CFA LEVEL I

  39. Duration, Convexity & the Term Structure of Interest Rates • Consider a corporate bond structure with three-year bonds yielding 6%, four-year bonds yielding 7%, and five-year bond yielding 8%. What is the absolute and relative yield spread on the five-year corporate issue if a similar dated Treasury is yielding 6%. • 0, 0% • 100bps, 14.28% • 200bps, 33.33% FIXED INCOME: CFA LEVEL I Absolute yld spread = corp – trsy = 8% - 6% = 200 bps Relative yld spread = absolute/trsy = .02/.06 = 33.33%

  40. Duration, Convexity & the Term Structure of Interest Rates • Consider two bonds similar in all respects except duration who exhibit a yield ratio of 1.0825. The relative yield is closest to: • 8.25% • 108.25 • 0.825 FIXED INCOME: CFA LEVEL I

  41. Duration, Convexity & the Term Structure of Interest Rates • Consider two bonds similar in all respects except duration who exhibit a yield ratio of 1.0825. The relative yield is closest to: • 8.25% • 108.25 • 0.825 FIXED INCOME: CFA LEVEL I

  42. Duration, Convexity & the Term Structure of Interest Rates • Explained: • Relative Yld Spread = • absolute yld spread / lower yld = • higher yld/lower yld - 1 • Yield Ratio = higher yld/lower yld • relative yld spread = yield ratio – 1 • relative yld spread = 1.0825 – 1 • 8.25% FIXED INCOME: CFA LEVEL I

  43. Duration, Convexity & the Term Structure of Interest Rates • An economist is projecting a tightening in the yield spread between corporate bonds and U.S. Treasury. The economist most likely expects: • the economy to expand. • the economy to contract. • the economy to remain the same. FIXED INCOME: CFA LEVEL I

  44. Duration, Convexity & the Term Structure of Interest Rates • An economist is projecting a tightening in the yield spread between corporate bonds and U.S. Treasury. The economist most likely expects: • the economy to expand. • the economy to contract. • the economy to remain the same. FIXED INCOME: CFA LEVEL I

  45. Duration, Convexity & the Term Structure of Interest Rates • Explained: • Credit spreads shrink during an expanding economy as corporations are expected to have increasing cash flows to service outstanding debt. • Conversely, credit spreads widen during a slowing economy as corporations are expected to experience shrinking cash flows and become more susceptible to default. FIXED INCOME: CFA LEVEL I

  46. Duration, Convexity & the Term Structure of Interest Rates • Investors will demand a higher yield for which of the following bond types: • a putable bond. • a convertible bond. • a callable bond. FIXED INCOME: CFA LEVEL I

  47. Duration, Convexity & the Term Structure of Interest Rates • Investors will demand a higher yield for which of the following bond types: • a putable bond. • a convertible bond. • a callable bond. FIXED INCOME: CFA LEVEL I A call feature is beneficial to the issuer and will be exercised when it’s advantageous for the issuer to do so. As such, an investor would prefer a straight bond to a callable bond and will demand additional compensation in the form of higher yields for a callable bond.

  48. Duration, Convexity & the Term Structure of Interest Rates • Consider two equivalent bonds that are the same except for tax status. What is the marginal tax rate that would make an investors indifferent between a 4.5% tax-exempt bond and a 6.5% taxable bond? • 30.77% • 44.44% • 69.23% FIXED INCOME: CFA LEVEL I

  49. Duration, Convexity & the Term Structure of Interest Rates • Consider two equivalent bonds that are the same except for tax status. What is the marginal tax rate that would make an investors indifferent between a 4.5% tax-exempt bond and a 6.5% taxable bond? • 30.77% • 44.44% • 69.23% FIXED INCOME: CFA LEVEL I

  50. Duration, Convexity & the Term Structure of Interest Rates • Explained: • Taxable-equivalent yield = (tax-free yield)/(1 – marginal tax rate) • 6.5% = 4.5%/(1 – MTR) • MTR = - (4.5%/6.5% - 1) = 30.77% FIXED INCOME: CFA LEVEL I

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