CFA Level 1 - Fixed Income Session 16 - Reading 59

CFA Level 1 - Fixed Income Session 16 - Reading 59 (Notes, Practice Questions, Sample Questions) 1. Which of the following approaches in measuring interest rate risk is most accurate when properly performed? A)Duration approach. B)Duration/convexity approach. C)Full Valuation approach. Explanation — C: The most accurate approach method for measuring interest rate risk is the so-called full valuation approach. Essentially this boils down to the following four steps: (1) begin with the current market yield and price, (2) estimate hypothetical changes in required yields, (3) recompute bond prices using the new required yields, and (4) compare the resulting price changes. Duration and convexity are summary measures and sacrifice some accuracy 2. Holding other factors constant, the interest rate risk of a coupon bond is higher when the bond's: A)current yield is higher. B)coupon rate is higher. C)yield to maturity is lower. Explanation — C: There are three features that determine the magnitude of the bond price volatility: 1.The lower the coupon, the greater the bond price volatility. 2.The longer the term to maturity, the greater the price volatility. 3.The lower the initial yield, the greater the price volatility. In this case the only determinant that will cause a higher interest rate risk is having a low yield to maturity (initial yield). A higher coupon yield and a higher current yield will cause for lower interest rate risk 3. If interest rates fall, the: A)value of call option embedded in the callable bond falls. B)callable bond's price rises faster than that of a noncallable but otherwise identical bond. C)callable bond's price rises more slowly than that of a noncallable but otherwise identical bond. Explanation — C: When a callable bond's yield falls to a certain point, when the yields fall the price will increase at a decreasing rate. Compare this to a noncallable bond where, as the yield falls the price rises at an increasing rate 4. In comparing the price volatility of putable bonds to that of option-free bonds, a putable bond will have: A)less price volatility at low yields. B)less price volatility at higher yields. C)more price volatility at higher yields Explanation — B: The only true statement is that putable bonds will have less price volatility at higher yields. At higher yields the put becomes more valuable and reduces the decline in price of the putable bond relative to the option-free bond. On the other hand, when yields are low, the put option has little or no value and the putable bond will behave much like an option-free bond. Therefore at low yields a putable bond will not have more price volatility nor will it have less price volatility than a similar option-free bond 5. A $1,000 face, 10-year, 8.00% semi-annual coupon, option-free bond is issued at par (market rates are thus 8.00%). Given that the bond price decreased 10.03% when market rates increased 150 basis points (bp), which of the following statements is CORRECT? If market yields: A)decrease by 150bp, the bond's price will decrease by more than 10.03%. B)decrease by 150bp, the bond's price will increase by more than 10.03%. C)decrease by 150bp, the bond's price will increase by 10.03% Explanation — B: All other choices are false because of positive convexity - bond prices rise faster than they fall. Positive convexity applies to both dollar and percentage price changes. For any given absolute change in yield, the increase in price will be more than the decrease in price for a fixed-coupon, noncallable bond. As yields increase, bond prices fall, and the price curve gets flatter, and changes in yield have a smaller effect on bond prices. As yields decrease, bond prices rise, and the price curve gets steeper, and changes in yield have a larger effect on bond prices. Here, for an absolute 150bp change, the price increase would be more than the price decrease. For a 100bp increase, the price decrease would be less than that for a 150bp increase 6. Which of the following bonds is likely to exhibit the greatest volatility due to interest rate changes? A bond with a: A)low coupon and a long maturity. B)high coupon and a long maturity. C)low coupon and a short maturity Explanation — A: There are three features that determine the magnitude of the bond price volatility: (1) The lower the coupon, the greater the bond price volatility. (2) The longer the term to maturity, the greater the price volatility. (3) The lower the initial yield, the greater the price volatility. So the bond with a low coupon and long maturity will have the greatest price volatility 7. Which of the following is the most significant limitation of the portfolio duration measure? The assumption of: A)a nonparallel shift in the yield curve. B)a linear approximation of the actual price-yield function. C)a parallel shift in the yield curve. Explanation — C: The most significant limitation of portfolio duration is the assumption that the yield for all maturities changes by the same amount (a parallel shift in the yield curve) 8. How does the convexity of a bond influence the yield on the bond? All else the same, for a bond with high convexity investors will require: A)a higher or lower yield depending on the bond's duration. B)a higher yield. C)a lower yield Explanation — C: Convexity is to the advantage of the bond holder because a high-convexity bond's price will decrease less when rates increase and will increase more when rates decrease than a low-convexity bond's price 9. Assume that a straight bond has a duration of 1.89 and a convexity of 15.99. If interest rates decline by 1% what is the total estimated percentage price change of the bond? A)1.56%. B)2.05%. C)1.89%. Explanation — B: The total percentage price change estimate is computed as follows: Total estimated price change = -1.89 × (-0.01) × 100 + 15.99 × (-0.01)2 × 100 = 2.05% 10. Which of the following statements about the market yield environment is most accurate? A)As yields increase, bond prices rise, the price curve flattens, and further increases in yield have a smaller effect on bond prices. B)For a given change in interest rates, bond price sensitivity is lowest when market yields are already high. C)Positive convexity applies to the percentage price change, not the absolute dollar price change Explanation — B: The price volatility of noncallable (option-free) bonds is inversely related to the level of market yields. In other words, when the yield level is high, bond price volatility is low and vice versa. The statement beginning with, As yields increase. . . should continue . . .bond prices fall. Positive convexity (bond prices increase faster than they decrease for a given change in yield) applies to both absolute dollar changes and percentage changes 11. Consider a bond with a duration of 5.61 and a convexity of 21.92. Which of the following is closest to the estimated percentage price change in the bond for a 75 basis point decrease in interest rates? A)4.33%. B)4.21%. C)4.12% Explanation — A: The estimated percentage price change is equal to the duration effect plus the convexity effect. The formula is: [–duration × (Δy)] + [convexity × (Δy)2]. Therefore, the estimated percentage price change is: [–(5.61)(–0.0075)] + [(21.92)(-0.0075)2] = 0.042075 + 0.001233 = 0.043308 = 4.33% 12. A bond has a convexity of 25.72. What is the approximate percentage price change of the bond due to convexity if rates rise by 150 basis points? A)0.71%. B)0.26%. C)0.58% Explanation — C: The convexity effect, or the percentage price change due to convexity, formula is: convexity × (Δy)2. The percentage price change due to convexity is then: (25.72)(0.015)2 = 0.0058 13. A bond has a modified duration of 6 and a convexity of 62.5. What happens to the bond's price if interest rates rise 25 basis points? It goes: A)down 15.00%. B)up 1.46%. C)down 1.46%. Explanation — C: ∆P = [(-MD × ∆y) + (convexity) × (∆y)2] × 100 ∆P = [(-6 × 0.0025) + (62.5) × (0.0025)2] × 100 = -1.461% 14. A bond has a modified duration of 7 and convexity of 50. If interest rates decrease by 1%, the price of the bond will most likely: A)increase by 6.5%. B)increase by 7.5%. C)decrease by 7.5% Explanation — B: Percentage Price Change = –(duration) (∆i) + convexity (∆i)2 therefore Percentage Price Change = –(7) (–0.01) + (50) (–0.01)2=7.5% 15. A bond has a modified duration of 6 and a convexity of 62.5. What happens to the bond's price if interest rates rise 25 basis points? It goes: A)up 4.00%. B)down 1.46%. C)down 15.00% Explanation — B: ΔP/P = (-)(MD)(Δi) +(C) (Δi)2 = (-)(6)(0.0025) + (62.5) (0.0025)2 = -0.015 + 0.00039 = - 0.01461 16. A bond’s duration is 4.5 and its convexity is 43.6. If interest rates rise 100 basis points, the bond’s percentage price change is closest to: A)-4.50%. B)-4.94%. C)-4.06%. Explanation — C: Recall that the percentage change in prices = Duration effect + Convexity effect = [-duration × (change in yields)] + [convexity × (change in yields)2] = (-4.5)(0.01) + (43.6)(0.01)2 = -4.06%. Remember that you must use the decimal representation of the change in interest rates when computing the duration and convexity adjustments 17. If a bond has a convexity of 120 and a modified duration of 10, what is the convexity adjustment associated with a 25 basis point interest rate decline? A)-2.875%. B)+0.075%. C)-2.125%. Explanation — B: Convexity adjustment: +(C) (Δi)2 Con adj = +(120)(-0.0025)(-0.0025) = +0.000750 or 0.075% 18. One major difference between standard convexity and effective convexity is: A)effective convexity is Macaulay's duration divided by [1 + yield/2]. B)effective convexity reflects any change in estimated cash flows due to embedded bond options. C)standard convexity reflects any change in estimated cash flows due to embedded options Explanation — B: The calculation of effective convexity requires an adjustment in the estimated bond values to reflect any change in estimated cash flows due to the presence of embedded options. Note that this is the same process used to calculate effective duration 19. William Morgan, CFA, manages a fixed-income portfolio that contains several bonds with embedded options. Morgan would like to evaluate the sensitivity of his portfolio to large interest rate changes and will therefore use a convexity measure in addition to duration. The convexity measure that will best estimate the price sensitivity of Morgan’s portfolio is: A)modified convexity. B)either effective or modified convexity. C)effective convexity. Explanation — C: Effective convexity is the appropriate measure because it takes into account changes in cash flows due to embedded options, while modified convexity does not 20. The distinction between modified convexity and effective convexity is that: A)effective convexity accounts for changes in cash flows due to embedded options, while modified convexity does not. B)different dealers may calculate modified convexity differently, but there is only one formula for effective convexity. C)modified convexity becomes less accurate as the change in yield increases, but effective convexity corrects for this Explanation — A: Effective convexity is the appropriate measure to use for bonds with embedded options because it takes into account the effect of the embedded options on the bond’s cash flows 21. Which of the following statements is most accurate concerning the differences between modified convexity and effective convexity? A)Modified convexity takes into account changes in cash flows due to embedded options, while effective convexity does not. B)For an option-free bond, modified convexity is slightly greater than effective convexity. C)Effective convexity is most appropriate for bonds with embedded options. Explanation — C: Effective convexity is most appropriate for bonds with embedded options because it takes into account changes in cash flows due to changes in yield, while modified convexity does not. For an option-free bond, modified convexity and effective convexity should be very nearly equal 22. The price value of a basis point (PVBP) for a 7-year, 10% semiannual pay bond with a par value of $1,000 and yield of 6% is closest to: A)$0.92. B)$0.28. C)$0.64 Explanation — C: PVBP = initial price – price if yield changed by 1 bps. Initial price: Price with change: FV = 1000 FV = 1000 PMT = 50 PMT = 50 N = 14 N = 14 I/Y = 3% I/Y = 3.005 CPT PV = 1225.92 CPT PV = 1225.28 PVBP = 1,225.92 – 1,225.28 = 0.64 PVBP is always the absolute value 23. The price value of a basis point (PVBP) of a bond is $0.75. If the yield on the bond goes up by 1 bps, the price of the bond will: A)increase by $0.75. B)decline by $0.75. C)increase or decrease by $0.75 Explanation — B: Inverse relationships exist between price and yields on bonds. The larger the PVBP, the more volatile the bond’s price 24. In addition to effective duration, analysts often use measures such as Value–at–Risk (VaR) to estimate the price sensitivity of bonds to changes in interest rates because these measures also incorporate the effects of: A)time to maturity. B)embedded options. C)yield volatility Explanation — C: The volatility of a bond’s yield should be considered along with the bond’s effective duration when estimating its price sensitivity to interest rates. Measures of price risk such as VaR account for yield volatility. Effective duration includes the effects of time to maturity and embedded options