Use the following information to answer the next three questions.

Suppose that the prevailing Treasury spot rate curve is the one shown in the following table.

1. What is the (arbitrage-free) value of a 4.5% 5-year Treasury issue?
2. Suppose that the 4.5% 5-year Treasury issue is priced in the market based on the on-the-run 5-year Treasury yield. Assume further that yield is 4.8%, so that each cash flow is discounted at 4.8% divided by 2. What is the price of the 4.5% 5-year Treasury issue based on a 4.8% discount rate?
3. Given the arbitrage-free value found in part a and the price in part b, what action would a dealer take to earn an would the arbitrage profit? (Hint: the arbitrage profit is $1.77).
4. On January 15, 2010, the U.S. Treasury issued a 10-year inflation-indexed note with a coupon of 3% with semi-annual payments. Suppose an investor purchased $10,000 par value of this bond and on the issuance date, the consumer price index (CPI) was 200. By January 15, 2015, the CPI had increased to 250 (an increase of 25% over 5 years). Compute the coupon payment in dollars made to the investor on January 15, 2015. 5. In previous question, assume that by January 15, 2020 the consumer price index (CPI) drops to 175 (a 30% drop with respect to January 15, 2015). Again compute the coupon payment in dollars made to the investor on January 15, 2020. 6. In previous question, what is the principal paid back to investor on maturity date, 15 January, 2020? 7. An investor has purchased a $100 million inverse floating-rate security with a 5-year maturity. The coupon formula for the inverse floater is 10 minus the 3-month LIBOR or (10% - LIBOR) with a zero floor. The interest payments are made quarterly. The inverse floater is not callable. At the time of purchase, 3-month LIBOR is 4%. The investor financed the purchase by issuing a 5-year note at par with a fixed coupon rate of 5%. Which of the following interest rate swaps helps this investor to offset the mismatch between his assets and liabilities risks? Explain using a diagram. 8. Assuming that the swap rate in previous question is 3.5%, after entering the swap contract, what is the annual income spread that can the investor lock in? Enter your answer in percentage format, say 2% (without the "%" sign).

\begin{tabular}{|c|c|c|c|c|} \hlinePeriod & Year & Cash & SpotRate & Discount \\ \hline 1 & 0.5 & & 0.03 & \\ \hline 2 & 1 & & 0.033 & \\ \hline 3 & 1.5 & & 0.035053 & \\ \hline 4 & 2 & & 0.039164 & \\ \hline 5 & 2.5 & & 0.044376 & \\ \hline 6 & 3 & & 0.04752 & \\ \hline 7 & 3.5 & & 0.049622 & \\ \hline 8 & 4 & & 0.05065 & \\ \hline 9 & 4.5 & & 0.051701 & \\ \hline 10 & 5 & & 0.052772 & \\ \hline \end{tabular}