Math Problem Statement
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a. Betty owns a 6% per annum (coupon rate) coupon bond and Bob owns a 7% per annum (coupon rate) coupon bond. All other things being equal whose bond has the greater Macaulay duration? _______
b. Bela owns a 7-year (term) bond and Boris owns an 6 -year (term) bond. All other things being equal whose bond has the lesser Macaulay duration? _________
c. Art owns a bond whose Macaulay duration is 10 years and Bertha owns a bond whose Macaulay duration is 12 years. Both bonds have the same yield to maturity. For a given change in the magnitude (absolute value) of interest rates whose bond’s magnitude (absolute value) of percentage price change would be greater? __________
d. Consider the graph of price versus yield for a bond. As price decreases does the magnitude of dollar duration increase or decrease? _______
e. Alex owns a bond whose Macaulay duration is 3 years and Elinor owns a bond whose Macaulay duration is 10 years. As interest rates decrease whose bond should do better? ___________
Solution
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Math Problem Analysis
Mathematical Concepts
Macaulay Duration
Bond Pricing
Interest Rate Sensitivity
Yield to Maturity
Formulas
Macaulay Duration formula: D = (Σ t * C / (1 + y)^t + T * F / (1 + y)^T) / Price
Bond Price formula: Price = Σ C / (1 + y)^t + F / (1 + y)^T
Theorems
Duration Theorem
Convexity of Bonds
Suitable Grade Level
Undergraduate - Finance/Economics
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