CFA Level I：Fixed Income - Introduction to The Measurement of Interes

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1. A fixed income security’s current price is 101.65. You estimate that the price will rise to 102.98 if interest rates decrease 0.25% and fall to 100.91 if interest rates increase 0.25%. The security’s effective duration is closest to: A. 3.98 B. 4.07 C. 4.87

Ans: B; B is correct because the effective duration =(Bond price when yield falls-Bond price when yield rises) / (2 × Current price × Change in yield in decimal) =(102.98-100.91)/(2 ×101.65×0.0025) =4.07

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2. Amy Lee, a fixed income analyst gathers the following table with the yields and corresponding prices for a hypothetical 10-year option-free bond which initially yields 8%: Yield Price 7.90% $100.8454 8.00% $100.00 8.10% $99.0901 Using a 10 basis point rate shock, the duration of this bond is closes to: A. 8.78 B. 17.56 C. 4.39

Ans: A; Effective duration =(Bond price when yield falls-Bond price when yield rises) / (2 × Current price × Change in yield in decimal) =(100.8454-99.0901)/(2 ×100.00×0.001) =8.78

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3. An 8%, semiannual pay, option-free bond that is trading at par is maturing in 8 years. The effective duration of the bond based on a 50 basis point change in rates is closest to: A. 3.9 B. 4.0 C. 5.8

Ans: C; First calculate the bond’s values at 7.50% and 8.50% yields to maturity. N=16, I/Y=7.50/2=3.75, PMT=4, FV=100 CPT PV=-102.97 N=16, 1/Y=8.50/2=4.25, PMT=4, FV=100 CPT PV=-97.14 The bond values are $102.97 and $97.14 respectively. Therefore duration =(102.97-97.14)/(2 ×100×0.0050) = 5.83

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4. Bond 1 has an effective duration of 3.7. If the bond yield changes by 100 basis points, the price of the bond will change by: A. approximately 0.37%. B. approximately 3.7%. C. exactly 0.37%.

Ans: B; B is correct because the change in price due to a change in yield in only approximate because the calculation of effective duration does not reflect convexity. It is a linear approximation of a non-linear relation.

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5. If three bonds are otherwise identical, the one exhibiting the highest level of positive convexity is most likely the one that is: A. option-free B. callable C. putable

Ans: C; C is correct because when interest rates rise, a putable bond is more likely to be put back to the issuer by the investor, limiting the loss of value and giving the bond more positive convexity than an option-free bond. B is incorrect because a callable bond is likely to be called from the investor when interest rates fall, limiting the gain in value and giving the bond negative convexity.

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6. Lisa Ying manages a fixed income portfolio of three bonds as shown in the following table. The duration of her portfolio is closest to: Bond Maturity Price Par Amount Duration A 15-year $110.3412 $10 million 7.39 B 20-year $101.4835 $5 million 9.21 C 25-year $86.2746 $8 million 12.21 A. 9.24 B. 9.60 C. 28.81

Ans: A; The market values of the bonds (Price×Par Amount) are respectively Bond A: 110.3412/100×10,000,000=$11,034,120 Bond B: 101.4835/100×5,000,000=$5,074,175 Bond C: 86.2746/100×8,000,000=$6,901,968 They sum up to a total portfolio value of $23,010,263. Therefore, the duration of the portfolio = (11,034,120/23,010,263×7.39)+ (5,074,175/23,010,263×9.21)+ (6,901,968/23,010,263×12.21) =9.24

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7. The most relevant description for duration is: A. the first derivative of value with respect to yield. B. a security’s price sensitivity to yield changes. C. the weighted-average time until receipt of the present value of cash flows.

Ans: B; B is correct because bond investors are interested in a security’s price sensitivity to changes in yield, and duration is a good measure of this interest rate risk.

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8. A bond has duration of 5.4 and convexity of -41.30. If interest rates increase by 0.5%, the percentage change in the bond’s price will be closest to: A. -2.85% B. -2.80% C. -2.75%

Ans: B; B is correct because when convexity is known, the percentage change in a bond’s price = (-duration × Δy × 100) + (C × (Δy) 2 × 100) = (-5.4×0.005×100)+(-41.30×0.0052×100) =-2.80

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9. If a bond has a modified duration of 14 and a convexity of 70, the convexity adjustment ( to a duration-based approximation) corresponding to a 50 basis point interest rate decline is closest to: A. -0.175% B. 0.175% C. 0.0075%

Ans: B; Convexity adjustment to percentage change in price(%ΔP) =Convexity measure × (Δy) 2 × 100 =70×(-0.0050) 2×100 =0.175% Therefore B is the correct answer.

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10. David Zhao, a fixed-income analyst, determines that a 6.8% coupon option-free bond, with 7 years to maturity, would fall 2.5% in price if market interest rate rise by 0.5%. If market interest rates fall by 50 basis points, the bond’s price would climb by: A. less than 2.5% B. exactly 2.5% C. more than 2.5%

Ans: C; The bond is option-free and will therefore exhibit positive convexity, which means an equal change in rates will produce a greater percentage gain when rates decrease than the percentage loss produced when rates increase.