Problem $4.$ Interest Rate Risk. You are given the following information about

the yields of Treasury STRIPS $($zero$-$coupon bonds that pay $$100$ at maturity$)$:

y$1=3\%,$ y$2=4\%,$ y$29=6\mathrm{.}1\%,$ and y$30=6\mathrm{.}0\%,$ where yt

is the yield$-$to$-$maturity on

a t$-$year STRIP. Assume that all cash flows are riskless and we can borrow and lend

at the stated rates. You buy $50,00030-$year STRIPS and partially finance these by

issuing $5,0002-$year STRIPS $($i$.$e$.,$ you are borrowing money by promising to pay

$$500,000=5,000\backslash$times $$100$ in two years$).$

$2$

$($a$)$ How much money are you investing $($i$.$e$.,$ what is the net investment, given by

the cost of the $50,00030-$year STRIPS minus the proceeds from issuing $5,000$

$2-$year STRIPS$)?$

$($b$)$ Suppose that right after you make the above investments, the Federal Reserve

Board announces that it is taking steps to raise interest rates. Assume that the

yields on all of the strips immediately increase by one percentage point $($i$.$e$.,$

y$1=4\%,$ y$2=5\%,$ y$29=7\mathrm{.}1\%,$ and y$30=7\mathrm{.}0\%).$ By how much $($in dollars and

in percentage terms$)$ does the value of your net investment change due to the

unexpected announcement?

$($c$)$ Now suppose that right after your initial investments, the Fed makes a confusing

announcement, investors start talking about a recession, and Treasury yields

invert: y$1=4\mathrm{.}8\%,$ y$2=4\mathrm{.}2\%,$ y$29=3\mathrm{.}8\%,$ and y$30=3\mathrm{.}8\%.$ By how much $($in

dollars and in percentage terms$)$ does the value of your net investment change?