Revision as of 01:07, 20 November 2023 by Admin (Created page with "A bond has a modified duration of 8 and a price of 112,955 calculated using an annual effective interest rate of 6.4%. <math>E_{MAC}</math> is the estimated price of this bond at an interest rate of 7.0% using the first-order Macaulay approximation. <math>E_{MOD}</math> is the estimated price of this bond at an interest rate of 7.0% using the first-order modified approximation. Calculate <math>E_{MAC}-E_{MOD}</math>. <ul class="mw-excansopts"><li>91</li><li>102</li><li...")
Nov 20'23
Exercise
A bond has a modified duration of 8 and a price of 112,955 calculated using an annual effective interest rate of 6.4%. [math]E_{MAC}[/math] is the estimated price of this bond at an interest rate of 7.0% using the first-order Macaulay approximation. [math]E_{MOD}[/math] is the estimated price of this bond at an interest rate of 7.0% using the first-order modified approximation.
Calculate [math]E_{MAC}-E_{MOD}[/math].
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Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Nov 20'23
Solution: C
The Macaulay duration of the portfolio is
[[math]]\frac{35, 000(7.28) + 65, 000(12.74)}{35, 000 + 65, 000} = 10.829.[[/math]]
Then
[[math]]
105,000=100,000{\left({\frac{1.0432}{1+i}}\right)}^{1.0432}\Rightarrow{\frac{1.0432}{1+i}}=\left({\frac{105,000}{100,000}}\right)^{1.029}=1.004516\Rightarrow i=0.0385.
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.