Question #76 - Reading 27 Valuation and Analysis of Bonds With Embedded Options

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

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- If the spot-rate curve experiences a parallel downward shift of 50 basis points: A) Portfolio 1 will experience the best price performance. B) all three portfolios will experience the same price performance. C) Portfolio 3 will experience the best price performance. Explanation The sum of a portfolio's key rate durations is the effective duration of the portfolio. Each of the portfolios has an effective duration of five, so a parallel shift in the yield curve will have the same effect on each portfolio, and each will experience the same price performance. (Module 25.6, LOS 25.j)

Question

Is Berg correct about the specified change in yield needed to obtain an accurate estimate of the effective duration and effective convexity of a callable bond using a binomial model?

Answer Choices:

A. No, because the specified change in yield can be larger than, smaller than, or equal to the OAS

B. No, because the specified change in yield must be larger than the option- adjusted spread (OAS)

C. No, because the specified change in yield must be smaller than the OAS. Explanation The steps in the process of calculating the effective duration of a callable bond using a binomial tree are as follows: Step 1: Given assumptions about benchmark interest rates, interest rate volatility, and the call and/or put rule, calculate the OAS for the issue using the binomial model. Step 2: Impose a small parallel shift in the on-the-run yield curve by an amount equal to +Δy. Step 3: Build a new binomial interest rate tree using the new yield curve. Step 4: Add the OAS to each of the 1-year forward rates in the interest rate tree to get a "modified" tree. (We assume that the OAS does not change when interest rates change.) Step 5: Compute BV+Δy using this modified interest rate tree. Step 6: Repeat steps 2 through 5 using a parallel rate shift of −Δy to estimate a value of BV-Δy. There is no restriction on the relationship between the assumed change in the yield (Δy) and the OAS. (Module 27.5, LOS 27.i)

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