CFA Level 1 - Fixed Income Session 16 - Reading 67 - LOS f (Notes, Practice Questions, Sample Questions) 1. The goal of computing e ective duration is to get a: A) preliminary estimate of modiﬁed duration. B) more accurate measure of the bond's price sensitivity whenembedded options exist. C) measure of duration that is e ectively constant for the lifeof the bond Explanation — The point of e ective duration is to considerexpected changes in cash ﬂow from features such asembedded options. When embedded options exist, thee ective duration will give a better measure of the bond’sprice sensitivity to interest rate changes 2. When compared to modiﬁed duration, e ective duration: A) is equal to modiﬁed duration for callable bonds but notputable bonds.B) places less weight on recent changes in the bond's ratings. C) factors in how embedded options will change expectedcash ﬂows Explanation — The point of e ective duration is to considerexpected changes in cash ﬂow from features such asembedded options.
3. Which of the following statements about modiﬁed duration and e ective duration is NOT correct? A) E ective duration should be used for bonds withembedded options.B) The modiﬁed duration measure assumes that yieldchanges do not change the expected cash ﬂows. C) Modiﬁed duration should be used for bonds withembedded options. Explanation — Using modiﬁed duration as a measure of theprice sensitivity of a security with embedded options tochanges in yield would be misleading. With embeddedoptions, yield changes may change the expected cash ﬂows 4. A bond with an 8% semi-annual coupon and 10-year maturity is currently priced at $904.52 to yield 9.5%. If the yielddeclines to 9%, the bond’s price will increase to $934.96, and ifthe yield increases to 10%, the bond’s price will decrease to$875.38. Estimate the percentage price change for a 100 basispoint change in rates. A) 4.35%. B) 6.58%. C) 2.13%. Explanation — The formula for the percentage price changeis: (price when yields fall – price when yields rise) / 2 × (initialprice) × 0.005 = ($934.96 – 875.38) / 2($904.52)(0.005) = $59.58 /$9.05 = 6.58%. Note that this formula is also referred to as thebond’s e ective duration 5. When calculating duration, which of the following bonds would an investor least likely use e ective duration on ratherthan modiﬁed duration? A) Callable bond.
B) Option-free bond. C) Convertible bond. Explanation — The duration computation remains the same.The only di erence between modiﬁed and e ective durationis that e ective duration is used for bonds with embeddedoptions. Modiﬁed duration assumes that all the cash ﬂows onthe bond will not change, while e ective duration considersexpected cash ﬂow changes that may occur with embeddedoptions 6. Which of the following statements about duration is NOT correct A) For a speciﬁc bond, the e ective duration formula resultsin a value of 8.80%. For a 50 basis point change in yield, theapproximate change in price of the bond would be 4.40%.B) The numerator of the e ective duration formula assumesthat market rates increase and decrease by the same numberof basis points. C) E ective duration is the exact change in price due to a 100basis point change in rates Explanation — E ective duration is an approximationbecause the duration calculation ignores the curvature inthe price/yield graph 7. Which of the following statements about duration is most accurate? A) E ective duration accounts for changes in a bond’s cashﬂows resulting from interest rate changes. B) Modiﬁed duration is the most appropriate measure ofinterest rate sensitivity for bonds with embedded options.C) E ective duration is calculated from past price changes inresponse to changes in yield.
Explanation — Neither Macaulay nor modiﬁed duration is anappropriate measure of interest rate risk for bonds withembedded options. Macaulay duration does not take thecurrent YTM into account as modiﬁed duration does.E ective duration, however, explicitly takes into accountchanges in a bond’s cash ﬂows due to interest rate changesand is calculated from expected price changes in responseto a given increase or decrease in yield 8. E ective duration is more appropriate than modiﬁed duration as a measure of a bond's price sensitivity to yieldchanges when: A) the bond has a low coupon rate and a long maturity. B) the bond contains embedded options. C) yield curve changes are not parallel Explanation — E ective duration takes into considerationembedded options in the bond. Modiﬁed duration does notconsider the e ect of embedded options. For option-freebonds, modiﬁed duration will be similar to e ective duration.Both duration measures are based on the value impact of aparallel shift in a ﬂat yield curve 9. Why should e ective duration, rather than modiﬁed duration, be used when bonds contain embedded options? A) Modiﬁed duration considers expected changes in cashﬂows. B) E ective duration considers expected changes in cashﬂows. C) Either could be used if the bond has embedded options. Explanation — Modiﬁed duration assumes that the cash ﬂowson the bond will not change (i.e., that we are dealing withnon-callable bonds). This greatly di ers from e ective
duration, which considers expected changes in cash ﬂowsthat may occur for bonds with embedded options