1. You are an investment manager for Lemon County. You are given the following information about the yields of U.S. Treasury strips (which are zero-coupon, or pure discount, bonds which pay $100 at maturity):
YTM1 = 3%, YTM2 = 4%, YTM3 = 6.1%, YTM4 = 6.0%,
Where YTMj is the yield-to-maturity on a j-year strip. Assume that all cash flows are riskless and we can borrow and lend at the stated rates. You buy 50,000 30-year strips and partially finance these by issuing 5,000 2-year strips (i.e., you are borrowing money by promising to pay $500,000 in two years).
(a) How much of Lemon County’s money are you investing (i.e., what is the net investment)?
(b) Suppose that one second 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., YTM1 = 4%, YTM2 = 5%, YTM3 = 7.1%, YTM4 = 7.0%). By how much (in dollars and in percentage terms) does the value of the county’s investment change due to the unexpected announcement?
(c) After the announcement, what are the forward rates of interest f2 and f 30?