Question #15 - Reading 27 Valuation and Analysis of Bonds With Embedded Options

Reading: Reading 27 Valuation and Analysis of Bonds With Embedded Options - Anwers

PDF File: Reading 27 Valuation and Analysis of Bonds With Embedded Options - Anwers.pdf

Page: 8

Status: Unattempted

Shared Context

- Which value for the backwardly induced price of the corporate callable bond using the binomial tree in Exhibit 1 is most accurate? A) $105.69. B) $104.89. C) $105.20. Explanation First compute the missing rate using the relationship: upper rate = lower rate e2 × volatility = 2.85%e2×0.2 = 4.25% Then use backward induction: Value at T2 Upper: 106 / 1.0634 = 99.68. Value at T2 Middle: 106 / 1.0425 = 101.67. Replace with the call price of $101. Value at T2 Lower: 106 / 1.0285 = 103.06. Replace with the call price of $101. Value at T1 Upper: ((99.68 + 101) / 2 + 6) / 1.0545 = 100.84. Bond is not callable at T1. Value at T1 Lower: ((101 + 101) / 2 + 6) / 1.0365 = 103.23. Bond is not callable at T1. Value at T0 ((100.84 + 103.23) / 2 + 6) / 1.03 = $104.89. (Module 27.2, LOS 27.f)

Question

How many of Inka's comments about duration are accurate?

Answer Choices:

A. One

B. Three

C. Two. Explanation Comment 1 is true. Effective duration calculates sensitivity to a 100 basis point change in yield to maturity by taking the arithmetic mean impact of parallel upwards and downwards shift in a bonds yield on price. Even for option free bonds, this linear estimation approach causes estimation error due to the convex nature of bonds. An embedded option causes greater estimation error. A callable bond will react very differently to upwards and downwards shifts in yield due to the option moving towards or away from the money. A solution to this is to analyze sensitivity to upwards and downwards shifts in yield separately by using one-sided durations. Comment 2 is false. Effective duration of a callable bond will be less than (or equal to) an otherwise identical straight bond. Comment 3 is false. Key rate duration measures the sensitivity of a bond's price to a change in a single par rate, holding all other par rates constant. For an option free bond, the highest key rate duration is the maturity-matched key rate. For callable bonds with low coupons, the greatest key rate duration will be the maturity-matched key rate (due to the low probability of the bond being called). As the coupon rate is increased, the probability of the bond being called increases and as a result the key rate duration relating to the call date will increase while the maturity-matched key rate duration will decrease. (Module 27.6, LOS 27.k)

Actions

Practice Flashcards