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.
a. If there were no such Treasury note available, propose a portfolio for this investor (using only Zeroes with maturities up to 3 years) 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.
e. If this costless strategy required that you put up 50% collateral for the short sales, would you be willing to use all of your available capital for collateral in this strategy?