Report the yields for the one, two, and three-year Treasury notes. Is the yield curve upward or downward sloping?
1. (30) Go to the U.S. Treasury website here and look up the daily yield curve rates.
(a) (10) Report the yields for the one, two, and three-year Treasury notes. Is the yield curve upward or downward sloping? According to the expectations theory, what does this say about investors’ beliefs regarding short term interest rates?
(b) (10) Although we cannot know what future bond yields will be, we can look back in time and check whether investors’ past beliefs were conrmed. Report the historical yields for the same Treasury notes from dates one, two, and three years ago. Do the expectations indicated by the historical yield curves line up with the actual movement of interest rates?
(c) (10) For each of the previous years, use the one and two-year spot rates to calculate the one-year forward rate one year from that date and check how it compares to the actual one-year spot rate from the following year.
2. (30) In September 2017, RussellWestbrook signed the richest contract in NBA history, a so-called super-max” deal starting from the 2018-19 season and running for ve years that would entitle him to a salary equal to 35% of the projected salary cap of $100 million that year, with 8% annual raises thereafter. For the sake of simplicity, assume that he receives the entirety of his annual salary as a lump sum at the beginning of each season, and that these payments grow at a constant rate, rather than increasing linearly as they do in actual NBA contracts.
(a) (10) Write Westbrook’s salary schedule, and compute the nominal value of the contract, as you would have seen it reported in the news.
(b) (10) Assuming an interest rate of 3%, calculate the present value, on the date of signing, of each annual payment and of the contract as a whole.
(c) (10) Calculate the present value of the contract using the growing annuity formula. What restriction of the perpetuity formula does not apply to the annuity formula?
3. (20) Suppose that we have one, two, three, and four-year bonds, each with face value normalized to $1000 and an annual coupon with a rate of 10%, priced as follows.
Bond 1-Year 2-Year 3-Year 4-Year
C1 1100 100 100 100
C2 1100 100 100
C3 1100 100
C4 1100
Price 1008.33 1000.76 976.21 933.93
Using the law of one price, calculate the one, two, three, and four-year spot rates.
4. (20) Consider introducing compound interest to the pricing formulas for perpetuities and annuities. Suppose each annual payment C is paid in n installments, spread equally over each year, and let r denote the nominal annual interest rate.
(a) (10) Show that the present value of a perpetuity does not depend on the number of compounding periods.
(b) (10) Show that the present value of an annuity is increasing in the number of compounding periods. What if the payments are made continuously throughout the year?
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