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 = ?

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Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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consider the following spot interest rates for maturities of one, two, three, and four years. r1=4.1%, r2=4.5% r3=5.2% r=6.0% what are teh following forward rates, where fk.1 refers toa forward rate beginning in the k years and extending for the 1 year?
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 :
Consider the following spot interest rates for maturities of one, two, three, and four years. r1 = 3.7% r3 = 4.9% What are the following forward rates, where fi₁, k refers to a forward rate for the period beginning in one year and extending for k years? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) 11,1 f1,2 f1,3 r2 = 4.2% 4.70 % % % r4 = 5.7%
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.
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.)
If the one-year and two-year interest rates are 6.5% and 7% respectively, what should be the forward rate for year 2 (according to the expectations theory)? 7% 7.5% 7.75% 7.25% 6.75%. 6.5%
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.
1. Suppose the current one-year rate (one-year spot rate) and expected one-year T-bill rates over the following three year (i.e. years 2, 3, and 4, respectively) are as follows: 。R₁ = 6%, E (R₂) =7% E(₂R)= 7.5% E(R)=7.85% Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, and four-year maturity Treasury securities. Plot the resulting yield curve.
Assume that you must estimate what the future value will be two years from today using the future value of 1 table. (PV of $1, EV of $1. PVA of $1, and FVA of $1) Which interest rate column and number-of-periods row do you use when working with the following rates? (Round percentage answers to 2 decimal places.) Answer is complete but not entirely correct. Number of Periods 1. 12% annual rate, compounded annually 2.8% annual rate, compounded semiannually 3. 12% annual rate, compounded quarterly 4. 12% annual rate, compounded monthly Interest Rate 12.00 2.00 3.00 1.00 % % % % 2 80 24
Suppose that the current 1-year rate (1-year spot rate) and expected 1-year T-bill rates over the following three years (i.e.. years 2, 3, and 4, respectively) are as follows: 1R1 = 6%, E(21) = 7%, Bar1) = 7.5 %, Bar) = 7.85% Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two, three-, and four-year-maturity Treasury securities. (Round your answers to 2 decimal places.) Year 1 2 3 4 Current (Long-term) Rates
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.
For each of the following cases, indicate (a) to what interest rate columns and (b) what number of periods you would refer to in looking up the future value factor. (1) In Table 1 (future value of 1): \table||,Annual Rate, \table[[Number of], [Years Invested]], Compounded], [Case A,5%,5, Annually], [Case 8,8%, 4, Semiannually]]\ table[(a)..(b)], [Case A,%, periods,], [Case B,%, periods,,]] (2) In Table 2 (future value of an annuity of 1): \ table[],Annual Rate,\table[[Number of], [Years Invested]], Compounded], [Case A,4%, 12, Annually), (Case B,6%, 5,Semiannually]] \table[[,(a), (b)].[..%,periods], [Case A,%, periods,]]

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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 = ?