Math Problem Statement

(Just answer with a name or short phrase!)

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