Sessions 6 and 7 Question 1: Suppose that you have the following interest rates: Time period (Years) Spot rate 1 8.00 2 8.75 3 9.33 4 9.79 5 10.13 Forward rate Expected future single year spot rate Plot the yield curve based on these rates. Compute the forward rate and the expected future single period spot rate.
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- Q2: Suppose the current 1-year spot rate is 3% and the forward rate from time 1 to time 2 consistent with the current term structure of interest rates is 2%. Determine the 2-year discount factor from time 2 back to time 0.following questions: a. What is the mid-rate for each maturity? b. What is the annual forward premium for all maturities? (Click on the icon to import the table into a spreadsheet.) Period spot 1 month 2 months 3 months 6 months 12 months 24 months Period Bid Rate Spot 1.3267 1.3265 1.3263 1.3259 1.3250 1.3228 1.3179 a. What is the mid-rate for each maturity? Calculate the mid-rate for each maturity below: (Round to five decimal places.) Days Forward Ask Rate 0 1.3268 1.3266 1.3264 1.3262 1.3252 1.3233 1.3207 Bid Rate US$/€ 1.3267 Ask Rate US$/€ 1.3268 Mid-rate US$/€Maturity (Years) 1 5 10 20 30 Yield (%) 2.0 3.1 3.8 4.6 5.5 On the following graph, plot the yield curve implied by these interest rates. Place a blue point (circle symbol) at each maturity and interest rate in the table, and the yield curve will draw itself. 10 Yield Curve INTEREST RATE (Percent)
- Suppose we observe the following rates: 1R1 = 6.7, 1R2 = 7.4, and E(2r1) = 6.7. If the liquidity premium theory of the term structure of interest rates holds, what is the liquidity premium for year 2? Please step by step.Example: suppose the following rates on risk-free zeros: Maturity (years) Yield to Maturity (y) 1 2 3 4 2.5% 3.5% 5% 6.5% Forward Rate 4.51% 8.07% 11.1% Calculate the effective 2-year forward rate in 2-years: 2f2Suppose we observe the 3-year Treasury security rate (1R3) to be 8 percent, the expected 1-year rate next year—E(2r1)—to be 4 percent, and the expected one-year rate the following year—E(3r1)—to be 6 percent. If the unbiased expectations theory of the term structure of interest rates holds, what is the 1-year Treasury security rate, 1R1? (Round your answer to 2 decimal places.)
- Suppose the term structure of risk-free interest rates is as shown below: 5 yr 7 yr 10 yr 20 yr Term 1 уг 2 yr 3 yr 3.24 3.79 4.09 5.05 2.07 2.46 2.71 Rate (EAR %) a. Calculate the present value of an investment that pays $1,000 in two years and $3,000 in five years for certain. b. Calculate the present value of receiving $100 per year, with certainty, at the end of the next five years. To find the rates for the missing years in the table, linearly interpolate between the years for which you do know the rates. (For example, the rate in year 4 would be the average rate in year 3 and year 5.) c. Calculate the present value of receiving $1,800 per year, with certainty, for the next 20 years. Infer rates for the missing years using linear interpolation. (Hint: Use a spreadsheet.)The required return of a risk-free asset can be approximated by The pure time value of money and anticipated inflation premium. а. The 20-year T-bond yield. Ob. The 90-day T-bill rate plus the risk premium. C. The 90-day T-bill rate plus anticipated inflation premium. d.Suppose we observe the following rates: 1R1 = 10%, 1R2 = 12%. If the unbiased expectations theory of the term structure of interest rates holds, what is the 1-year interest rate expected one year from now, E(2r1)? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
- Construct a spreadsheet to convert a nominal interest rate compounded m times per year i(m) and convert it to an effective rate jn per 1/n of a year. On the same spreadsheet, also start with an effective rate jm per 1/m of a year and convert it to a nominal rate i(n) compounded n times per year. Use your spreadsheet to solve the following two problems: Given the nominal rate i(12) = 5.700%, find the equivalent effective semi-annual rate. Given the effective semi-annual rate j2 = 2.884%, find the equivalent nominal rate ¡(12).Suppose the term structure of risk-free interest rates is as shown below: 5 yr 7 yr 10 yr 20 yr Term 1 yr 2 yr 3 yr 2.42 2.77 3.31 3.75 4.15 4.93 1.98 Rate (EAR %) What is the present value of an investment that pays $103 at the end of each of years 1, 2, and 3? If you wanted to value this investment correctly using the annuity formula, what discount rate should you use? What is the present value of an investment that pays $103 at the end of each of years 1, 2, and 3? The present value of the investment is $294.08. (Round to the nearest cent.) If you wanted to value this investment correctly using the annuity formula, what discount rate should you use? The discount rate you should use if you want to use the annuity formula is 2.94%. (Round to two decimal places.)ook int ences Problem 2-11 (LG 2-7) Suppose we observe the three-year Treasury security rate (13) to be 4.9 percent, the expected one-year rate next year-E(21)-to be 5.4 percent, and the expected one-year rate the following year-E(31)-to be 6.4 percent. If the unbiased expectations theory of the term structure of interest rates holds, what is the one-year Treasury security rate? (Do not round intermediate calculations. Round your percentage answer to 2 decimal places. (e.g., 32.16)) _________% One-year Treasury security rate