Suppose an investor would like to buy 200 Treasury notes. The investor wants not
ID: 2641215 • Letter: S
Question
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.
Explanation / Answer
Money available for investment = 200 * 1000 = 200,000
a) Price of zero = 1000 / (1+.035)^6
= 813.50
Zeros to be purchased to replicate the portfolio = 200000 / 813.50
= 245.85
b) Price of zero = 1000 / (1+.02)^6
= 887.97
No arbitrage price of treasury note:
=-PV(0.02,6,35,1000)
= 1084.02
c) If zero are available at price as calcualted in part (a) then zeros will be preferred as it will have higher yield of 7%.
d) Zeros have better yield therefore should be purchased or take a long position and treasury note has lower yield therefore should be sold or short position.
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