Economics Question

Financial Economics

Assignment 1 – Bonds

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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