Suppose that the current one-year zero-coupon rate is 2.5% and that the expected one-year rate during each of the subsequent four years is 2.0%, 2.5%, 3.0%, and 3.5%. Under the expectations theory, what is the current 5-year zero-coupon interest rate? Enter the answer in percentage points; for example, if the answer is 5.25%, enter 5.25 rather than .0525.
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- Suppose the current forward curve for one-year rates is the following: Time Period Forward Rate f(0,1) 2.5% f(1,1) 3.6% f(2,1) 4.5% f(3,1) 5.1% Calculate the spot rates for 2-year, 3-years and 4-year spot rates Calculate the forward rates f(1, 2), f(1, 3), and f(2, 2) 3) Use the information to value a 4-year bond that pays 4.5% annual coupons.Suppose the spot rates for the next three years are 4.2%, 4.6% and 4.8% respectively. The one year forward rates are 4.2%, 5.0015% and 5.2012%, respectively as well. Using a value of 10% for the volatility of the one year forward rate, construct a three-year binomial interest rate tree with one year forward rates.Assume that the real interest rate is 2% per year, the default risk premium is 3%, the liquidity premium is 1%, and the maturity risk premium is 2%. Additionally, expected inflation is 2% next year, 5% the year after, and 3% from then on. What is the nominal interest rate over a 10-year period?
- Suppose 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.)According to the concepts underlying the present-value formula, would you prefer to receive (a) P75 one year from now, (b) P85 two years from now, or (c) P90 three years from now, if the relevant market interest rate is 10% and will remain at 10% for the next three years? a. The present values of all three choices are identical b. P75 one year from now c. P85 two years from now d. P90 three years from nowSuppose 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?
- Suppose that the current 6-month, 1-year, 1.5-year and 2-year interest rates are 2.2%,3%, 3.5% and 3.75%, respectively. a) Calculate the prices of a 1-year and 2-year Treasury bonds. In each case, assumethe face value of £100 and the coupon rate of 5% per annum and that coupons arepaid semi-annually. Assume continuous compounding. Compare the obtainedresults. Are they consistent with your expectations? b) Calculate the par yield on the 1-year bond with semi-annual couponsConsider a zero coupon bond that promises to pay $100 each year for the next three years. Suppose we observe the set of zero coupon bond prices and its yields as below a) What is the price of this zero coupon bond? What is its yield to maturity? b) If the observe yield on two-year zero coupon bonds falls to 6% per year, but the other rates remain unchanged. What is your estimation of the value of the three-year annuity paying $100 per year? What is its yield to maturity?Consider the following spot interest rates for maturities of one, two, three, and four years. r1 = 6.10% r2 = 6.00% r3 = 5.80% r4 = 5.50% What are the following forward rates? Hint: f1, k refers to a forward rate for the period beginning in one year and extending for k years. fk,1 refers to a forward rate beginning in k years and extending for 1 year. f1,1 : f1,2 : f1,3 : f2,1: f3,1 :
- The 3-year, 5-year, and 7-year zero rates are 1%, 2%, and 3%. The rates are given per annum with annual compounding. a) What are the zero-coupon bond prices with maturities of 3 years, 5 years, and 7 years? (Assume that you receive a face value of $100 for each of these bonds on their maturity dates). b) What is the forward rate for an investment initiated 3 years from today and maturing 5 years from today? (Give your answer per annum with continuous compounding)? c) What is the forward rate for an investment initiated 3 years from today and maturing 7 years from today? (Give your answer per annum with annual compounding)?Suppose GE plans to issue a note that matures in 2 years and has a 3.67% coupon rate. If the market yield is 4.91%, what is the market price?Suppose that the current one-year rate (one- year spot rate) and expected one-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows: 1R1=6%, E(2r1) =7%, E(3r1) =7.5% E(4r1)=7.85% 1 Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, and four-year-maturity Treasury securities. Show your answers in percentage form to 3 decimal places.