Revision as of 11:42, 20 November 2023 by Admin (Created page with "'''Solution: B''' Duration equals <math display = "block"> \frac{\sum_{t=1}^{\infty}tv^tR_t}{\sum_{t=1}^{\infty}v^tR_t} = \frac{\sum_{t=1}^{\infty}tv^t1.02^t}{\sum_{t=1}^{\infty}v^t 1.02^t} = \frac{(Ia)_{\overline{\infty}|j}}{a_{\overline{\infty}|j}} = \frac{\ddot a_{\overline{\infty}|j}/j}{1/j} = \frac{1}{d}. </math> The interest rate j is such that (1+j)<sup>-1</sup> = 1.02v =1.02 /1.05 => j = 0.03 /1.02. Then the duration is <math display = "block"> 1/\,d=(1+j)/\...")
Exercise
Nov 20'23
Answer
Solution: B
Duration equals
[[math]]
\frac{\sum_{t=1}^{\infty}tv^tR_t}{\sum_{t=1}^{\infty}v^tR_t} = \frac{\sum_{t=1}^{\infty}tv^t1.02^t}{\sum_{t=1}^{\infty}v^t 1.02^t} = \frac{(Ia)_{\overline{\infty}|j}}{a_{\overline{\infty}|j}} = \frac{\ddot a_{\overline{\infty}|j}/j}{1/j} = \frac{1}{d}.
[[/math]]
The interest rate j is such that (1+j)-1 = 1.02v =1.02 /1.05 => j = 0.03 /1.02. Then the duration is
[[math]]
1/\,d=(1+j)/\,j=(1.05/\,1.02)/\,(0.03/\,1.02)=1.05/\,0.03=35.
[[/math]]
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