Business: You are interested in valuing a 2-year semi-annual corporate coupon bond using spot rates but there are no liquid strips available. However, you do find the following 4 comparable semi-annual bonds (below) maturing over the next 2 years. Using the bootstrap approach, calculate the 12-month spot rate. Time remaining to maturity Coupon Bond price 6 months 0.000% 99.000 1 year 1.250% 98.000 18 months 1.500% 97.000 2 years 1.250% 96.000 a. 1.668% b. 3.335% c. 4.167% d. 4.189% e. 4.204%

Students in mrs. carr’s class are asked to make a prediction after reading this passage from white fang.but the bane of his life was lip-lip. larger, older, and stronger, lip-lip had selected white fang for his special object of persecution. white fang fought willingly enough, but he was outclassed. his enemy was too big. lip-lip became a nightmare to him. whenever he ventured away from his mother, the bully was sure to appear.which student prediction is most reasonable?...

You are interested in valuing a 2-year semi-annual

Ответ:

alyea231

07.04.2021

Business

Following are the solution to this question:

Explanation:

Assume that r_1 will be a 12-month for the spot rate:

$\to 1.25 \% \times \frac{100}{2} \times 0.99 + \frac{(1.25\% \times \frac{100}{2}+100)}{(1+\frac{r_1}{2})^2}=98\\\\\to \frac{1.25}{100} \times \frac{100}{2} \times 0.99 + \frac{(\frac{1.25}{100} \times \frac{100}{2}+100)}{(1+\frac{r_1}{2})^2}=98\\\\\to \frac{1.25}{2} \times 0.99 + \frac{(\frac{1.25}{2} +100)}{(1+\frac{r_1}{2})^2}=98\\\\\to 0.61875 + \frac{( 0.625 +100)}{(\frac{2+r_1}{2})^2}=98\\\\\to 0.61875 + \frac{( 100.625)}{(\frac{2+r_1}{2})^2}=98\\\\\to 0.61875 + \frac{402.5}{(2+r_1)^2}=98\\\\$

$\to 0.61875 + \frac{402.5}{(2+r_1)^2}=98\\\\\to 0.61875 -98 = \frac{402.5}{(2+r_1)^2}\\\\\to -97.38125= \frac{402.5}{(2+r_1)^2}\\\\\to (2+r_1)^2= \frac{402.5}{ -97.38125}\\\\\to (2+r_1)^2= -4.13\\\\ \to r_1=3.304\%$

Assume that r_2 will be a 18-month for the spot rate:

$\to 1.5\% \times \frac{100}{2} \times 0.99+1.5\% \times \frac{100}{2} \times \frac{1}{(1+ \frac{3.300\%}{2})^2}+\frac{(1.5\% \times \frac{100}{2}+100)}{(1+\frac{r_2}{2})^3}=97\\\\\to \frac{1.5}{100} \times \frac{100}{2} \times 0.99+\frac{1.5}{100} \times \frac{100}{2} \times \frac{1}{(1+ \frac{\frac{3.300}{100}}{2})^2}+\frac{(\frac{1.5}{100} \times \frac{100}{2}+100)}{(1+\frac{r_2}{2})^3}=97\\\\$

$\to \frac{1.5}{2} \times 0.99+\frac{1.5}{2}\times \frac{1}{(1+ \frac{\frac{3.300}{100}}{2})^2}+\frac{(\frac{1.5}{2} +100)}{(1+\frac{r_2}{2})^3}=97\\\\\to 0.7425+0.75 \times \frac{1}{(1+ \frac{\frac{3.300}{100}}{2})^2}+\frac{(0.75 +100)}{(1+\frac{r_2}{2})^3}=97\\\\\to 1.4925 \times \frac{1}{(1+0.0165)^2}+\frac{(100.75 )}{(1+\frac{r_2}{2})^3}=97\\\\\to 1.4925 \times \frac{1}{(1.033)}+\frac{(100.75 )}{(1+\frac{r_2}{2})^3}=97\\\\$

$\to 1.4925 \times 0.96+\frac{(100.75 )}{(1+\frac{r_2}{2})^3}=97\\\\\to 1.4328+\frac{(100.75 )}{(1+\frac{r_2}{2})^3}=97\\\\\to 1.4328-97= \frac{(100.75 )}{(1+\frac{r_2}{2})^3}\\\\\to -95.5672= \frac{(100.75 )}{(1+\frac{r_2}{2})^3}\\\\\to (1+\frac{r_2}{2})^3= -1.054\\\\\to r_2=3.577\%$

Assume that r_3 will be a 18-month for the spot rate:

$\to 1.25\% \times \frac{100}{2} \times 0.99+1.25\% \times \frac{100}{2} \times \frac{1}{(1+\frac{3.300\%}{2})^2}+1.25\%\times\frac{100}{2} \times \frac{1}{(1+\frac{3.577\%}{2})^3}+(1.25\% \times \frac{\frac{100}{2}+100}{(1+\frac{r_3}{2})^4})=96\\\\$

to solve this we get $r_3=3.335\%$

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