The following table summarizes prices of several discount bonds paying $$1$ at maturity:

$\backslash$table$[[$Maturity$,$Price$],[1$ Year,$0\mathrm{.}9921],[2$ Year,$0\mathrm{.}9688],[3$ Year,$0\mathrm{.}9396]]$

Please answer the folowing sub$-$questions using information from this table.

$1-$year spot rate:

$\%$

$x$

$2-$year spot rate:

$$

$3-$year spot rate:

$$

$\%$

$1-$year forward rate in year $1($the forward rate that applies to the period from year $1$ to year $2)$:

$\%$

Note: Your answer to the last subquestion is correct conditionally on your numerical answers to the first three subquestions. If you change the previous answers, you should recalculate the item as well.

Now suppose the $1-$year spot rate is $r_1=1\mathrm{.}5\%,$ the $2-$year spot rate is $r_2=2\%,$ and the $1-$year forward rate in year $1$ is $f_1=4\mathrm{.}1\%.$ The prices of bonds are different from the subquestions above.

Assume at time $0$ we invest $$x$ in $1-$year bond, short $$x$ in $2-$year bond, and invest $$y$ at time $1$ at the fixed forward rate. If this is an arbitrage strategy generating $$100$ at time $t=1$ and nothing otherwise, then:

$x=$

$$

$y=$

Note that since we effectively invest $y$ at time $1,y$ is a negative number.

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