Ec123 Spring 2023 Homework 1
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Ec123
Spring 2023
Homework 1
Due 4/28/2023 by 11pm. See the announcements for instructions on how to upload this homework as a PDF.
1. Suppose that over one year the number of Dollars per one Euro changes from 1.00 to 1.20. That is, the Euro appreciates.
a. Obtain the Annual appreciation rate of the Euro.
b. Obtain the Annualized compound-monthly appreciation rate of the Euro
c. Obtain the Annualized continuously compounded appreciation rate of the Euro
d. Suppose there are exactly 52 weeks in the year. Obtain the Annualized compound-weekly appreciation rate of the Euro.
2. Compute the present value of a $1,000 zero-coupon bond with 5 years to maturity if the
required annual interest rate is 6%.
3. Consider a 10-year bond with a face value of $1,000 that pays a 2.5% annual coupon
(i.e., $25 coupon per year). This bond trades for $950 in the secondary market. Compute the yield to maturity of this bond.
4. Consider a 5-year bond with a face value of $1,000 selling at par (i.e., at $1,000) that
pays a 5% annual coupon.
(a) Compute the duration of this bond
(b) Suppose the market required yield to maturity increases by 50 basis points. What is
the percentage change in the bond price?
5. You expect interest rates to go down next year. Which bond will generate the largest
price increase?
a. A 5-year Treasury paying 4% annualized coupon
b. A 5-year Junk Bond paying 7% annual coupon
6. Read the following story from The Wall Street Journal (4/7/23).
Office Vacancies Send Real-Estate Investors to the Exits
What are CMBS with a triple-B rating? What has happened to the average price of these bonds and to their yield? What does it imply for the macroeconomy and economic growth?
7. Obtain daily data for the number of dollars per Euro (S) for the period Oct 1, 2022 to April 14, 2023.
(a) Compute the mean weekly percent change of S and its standard deviation
(b) Compute the expected value S will take on 4/22/2023 and its 95% confidence interval.
(c) Was the realized value of S on 4/21/2023 within its 95% confidence interval?
(d) Propose a simple momentum forecasting strategy to determine whether the Euro will appreciate or depreciate between 4/21/2023 and 5/1/2023. What is your forecast?
2023-04-19