Please help me to answer these four questions. I am also attaching the screenshot of the excel sheet. $($The yields in the excel sheet is annually compounded. You have to convert to continuously compounded yields.$)$ Please try to provide an accurate answer, thank you. According to the term structure model, the $t-$year continuously compounded zero$-$coupon yield

is

$y(t)\frac{?}{b}=ar(y)+$ubrace$(\frac{1}{t}(\frac{1-{}^t}{1-})ubrace{)}_{b(t)}(y(1)\frac{-}{b}ar(y))+$ubrace$(\frac{t-1}{t}ubrace{)}_{a(t)},$

where $y(1)$ is the $1-$year continuously compounded yield $($a$.$k$.$a$.,$ the short rate$).$ There are three

unknown parameters in this model.

$\frac{?}{\text{b}\text{a}\text{r}}(y)$ : Long$-$run mean of the short rate.

$$ : Persistence of the short rate.

$$ : Term premium.

Use the data on annually compounded zero$-$coupon yields on $12/30/2016$ in the spreadsheet

$"$PS$6\_$Data.xlsx$".$

$($a$)[2$ points$]$ The zero$-$coupon yields for maturities $1$ to $30$ years in the spreadsheet are annually

compounded. Convert all of these yields to continuous compounding and report them in

a table.

$($b$)[4$ points$]$ Let hat$(y)(t)$ be the $t-$year continuously compounded yield that you computed in

part $($a$).$ Let $y(t)$ be the $t-$year continuously compounded yield given by the term structure

model $($i$.$e$.,$ equation $(1)).$ Use the Excel solver to find $\frac{?}{\text{b}\text{a}\text{r}}(y),,$ and $$ that minimizes

${\displaystyle \underset{t=1}{\overset{30}{}}}(hat(y)(t)-y(t){)}^2$

That is$,$ find parameters such that the term structure model best fits the data. Report the

parameters.

$($c$)[3$ points$]$ If you were to buy a $10-$year zero$-$coupon bond on $12/30/2016,$ what is the

expected continuously compounded return on your investment over the next year?

$($d$)[3$ points$]$ Is your answer from part $($c$)$ greater than, less than, or equal to the $10-$year

continuously compounded yield on $12/30/2016?$ Explain the reason for why it is so $($in

less than $3$ sentences$).$