Suppose an investor would like to buy 200 Treasury notes. The investor wants notes with an annual coupon rate of 7%, a 3-year maturity, and semi-annual coupon payments. Assume each Treasury note has a par value of $1,000.
a) If there were no such Treasury note available, propose a portfolio for this investor (using only Zeroes with maturities ranging from 6 month to 3 years and with par value of $1,000 each) that replicates the cash flows from investing in the Treasury notes above.
b) Assuming the yield curve is flat at 4.0% for bonds with maturities of up to 3 years, calculate the prices of the Zeroes in your portfolio from part (a). Using these prices, compute the no-arbitrage price of a Treasury note.
c) Now suppose there is a 3-year, 7% coupon rate Treasury note available that has a YTM of 4.5%. Would the investor above prefer to buy 200 Treasury notes or the portfolio of Zeroes identified in part (a)?
d) Find a costless and riskless trading strategy that makes an instantaneous profit by buying or selling the Treasury note and the portfolio of zeroes.