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: 2f2
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- Consider the following spot interest rates for maturities of one, two, three, and four years. r₁ = 4.3% 2 = 4.9% √3 = 5.6% r4 = 6.4% What are the following forward rates, where fkn refers to a forward rate beginning in k year(s) and extending for n year(s)? f2,1 = ? f3,1 = ? f2,2 = ?a) Suppose that the current one-year spot rate and expected one-year T-bill rates over the following three years (i.e., years 2, and 3 respectively) are as follows: 1R1 = 3.1%, E(201) = 4.20%, E(3r₁) = 6.6%. Using the unbiased expectation theory, calculate the current long-term rates for one- two and three-year-maturity Treasury securities and plot the current yield curve. Please show each step of your calculation. b) What are the sources of funding for commercial banks? Please also classify the sources of funding and briefly describe each category. c) The unbiased expectation theory and liquidity premium theory are two important theories to explain the shape of yield curve. Discuss and compare the two theories.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 :
- Give typing answer with explanation and conclusion to all parts The real risk-free rate, r*, is 2%, and inflation is expected to be 3.0% this year, 3.5% for the next two years; 4.0% the following year, and then 5.0% thereafter. The maturity risk premium is estimated to be 0.05%(t1), where t = number of years to maturity. Liquidity risk premium is 0.7%, default risk premium is 1%. - What are the Treasury yield for 3 years, and 6 years bonds? - What are the Corporate yield for 3 years, and 6 years bonds?Maturity (years) 1 1-year Forward rate (%) 0-years from now 1.25 1-year from now 1.75 2-years from now 1.908 2 $103 3 Using the binomial model (which assumes that one-year rates undergo a lognormal random walk with volatility o), if o is assumed to be 10%, what is the lower one-year forward rate one year from now given that the higher one-year forward rate one year from now is 1.80%? A 1.474% B. 1.247% OC. 1.10% OD. 1.747% Spot rate (%) 1.25 1.5019 1.70491 Cash flow $3 $3You observe the following yield curve: YTM 1-year Zero 2-year Zero 6.10% 6.20% 3-year Zero 6.30% 4-year Zero 6.40% (Round your final answers to 2 decimal pleces. Enter percentages "as-Is", without the % sign.) a) If you believe that the yield curve next year will be the same as today's, calculate the holding period return (1-year) on the 1-year Zero and the 4-year Zero. 1-year Zero HPR % 4-year Zero HPR | % b) Recalculate the return on the 4-year zero if you believe in the expectations hypothesis. 4-year Zero HPR %
- Suppose 1 -year T-bills currently yield 7.00 % and the future inflation rate is expected to be constant at 4.70% per year. What is the real risk free rate of return 1.84% 2.76 % 2.46 % 1.96 % 2.30%Suppose 1-year T-bills currently yield 7.40% and the future inflation rate is expected to be constant at 3.00% per year. What is the real risk-free rate of return, r*? Disregard any cross-product terms, i.e., if averaging is required, use the arithmetic average. a. 4.40% b. 7.40% c. 10.40% d. 7.62% e. 5.20%Suppose the real risk-free rate of interest is r*=4%�*=4% and it is expected to remain constant over time. Inflation is expected to be 1.60% per year for the next two years and 3.90% per year for the next three years. The maturity risk premium is 0.1×(t−1)%0.1×�−1%, where t� is number of years to maturity, a liquidity premium is 0.45%, and the default risk premium for a corporate bond is 1.40%. The average inflation during the first 4 years is2.37% . What is the yield on a 4-year Treasury bond? 4.30% 8.90% 6.75% 7.05% What is the yield on a 4-year BBB-rated bond? 8.90% 7.50% 7.05% 8.45% If the yield on a 5–year Treasury bond is 7.38% and the yield on a 6–year Treasury bond is 7.83%, the expected inflation in 6 years is . (Hint: Do not round intermediate calculations.)
- 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.)TERM STRUCTURE Using Pure Expectations theory to predict future rates: I ■ Suppose: 1¹₁= 1%, 1¹₂= 2%, 113= 3% What does that imply about the 1-year forward rate in 2 years (f₁), and the 2-year forward rate in 1 year (₂f₂)?Suppose 1-year T-bills currently yield 3.86% and the future inflation rate is expected to be constant at 2.35% per year. What is the real risk-free rate of return, r*? ( as a percent and round your final answer to 2 decimal places.)