Revision as of 00:27, 5 December 2023 by Admin (Created page with "'''Solution: B''' <math display = "block"> \begin{gathered}95.92=\frac{100}{1+r_1} \\ 92.01=\frac{100}{\left(1+r_2\right)^2} \\ 87.00=\frac{100}{\left(1+r_3\right)^3} \\ r_1=\frac{100}{95.92}-1=4.25 \% \\ r_2=\left(\frac{100}{92.01}\right)^{1 / 2}-1=4.25 \% \\ r_3=\left(\frac{100}{87.00}\right)^{1 / 3}-1=4.75 \%\end{gathered} </math> The yield to maturity is simply 4.25% since the one year and two year spot rates are roughly equivalent, more specifically when we calc...")
Exercise
Dec 05'23
Answer
Solution: B
[[math]]
\begin{gathered}95.92=\frac{100}{1+r_1} \\ 92.01=\frac{100}{\left(1+r_2\right)^2} \\ 87.00=\frac{100}{\left(1+r_3\right)^3} \\ r_1=\frac{100}{95.92}-1=4.25 \% \\ r_2=\left(\frac{100}{92.01}\right)^{1 / 2}-1=4.25 \% \\ r_3=\left(\frac{100}{87.00}\right)^{1 / 3}-1=4.75 \%\end{gathered}
[[/math]]
The yield to maturity is simply 4.25% since the one year and two year spot rates are roughly equivalent, more specifically when we calculate the present value of a coupon bond with a coupon rate of 4.25% this bond has a current price at par.
[[math]]
\begin{aligned} P V & =\frac{4.25}{1+r_1}+\frac{104.25}{\left(1+r_2\right)^2} \\ & =\frac{4.25}{1.0425}+\frac{104.25}{(1.0425)^2}=100\end{aligned}
[[/math]]
References
Lo, Andrew W.; Wang, Jiang. "MIT Sloan Finance Problems and Solutions Collection Finance Theory I" (PDF). alo.mit.edu. Retrieved November 30, 2023.