The following spot rates are observed today. Maturity Spot rate (%) 1 year 0.75 2 year 1.50 3 year 2.30 4 year 2.75 5 year 3.25 If an investor with a five-year investment horizon expects that two-year rates will be 5% at the end of three years, what should the investor do?
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The following spot rates are observed today.
| Maturity | Spot rate (%) |
| 1 year | 0.75 |
| 2 year | 1.50 |
| 3 year | 2.30 |
| 4 year | 2.75 |
| 5 year | 3.25 |
If an investor with a five-year investment horizon expects that two-year rates will be 5% at the end of three years, what should the investor do?
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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 = ?Question 2. Suppose the current ZCB prices for maturity in two years and in five years are 0.8 and 0.7, respectively. Suppose the two-year forward three-year libor rate is 4%. Determine if there is an arbitrage opportunity. If so, find an arbitrage portfolio. Make sure that you verify the portfolio is an arbitrage portfolio. Hint: In your arbitrage portfolio you will need to include a forward rate agreement.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 :
- 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.Assume that the Pure Expectation Theory determines interest rates in the markets. Today's market rates for different maturities follow an interesting pattern. The spot rate for investing for 1 year is 4%. After that, the rate increases by 1% for each year. So, in general, the rate for year Y is simply 4% +1%*(Y-1). Given this information, what is the implied interest rate to invest for 1 year, starting in 3 years?Define the stated (quoted) or nominal rate INOM as well as the periodic rate IPER. Will the future value be larger or smaller if we compound an initial amount more often than annually—for example, every 6 months, or semiannually—holding the stated interest rate constant? Why? What is the future value of $100 after 5 years under 12% annual compounding? Semiannual compounding? Quarterly compounding? Monthly compounding? Daily compounding? What is the effective annual rate (EAR or EFF%)? What is the EFF% for a nominal rate of 12%, compounded semiannually? Compounded quarterly? Compounded monthly? Compounded daily?
- The pure expectations theory, or the expectations hypothesis, asserts that long-term interest rates can be used to estimate future short-term interest rates. Based on the pure expectations theory, is the following statement true or false? Q1. A certificate of deposit (CD) for two years will have the same yield as a CD for one year followed by an investment in another one-year CD after one year. a. True b. False Q2. The yield on a one-year Treasury security is 4.9200%, and the two-year Treasury security has a 5.9040% yield. Assuming that the pure expectations theory is correct, what is the market’s estimate of the one-year Treasury rate one year from now? (Note: Do not round your intermediate calculations.) a. 5.8627% b. 6.8973% c. 7.8629% d. 8.7596% Q3. Recall that on a one-year Treasury security the yield is 4.9200% and 5.9040% on a two-year Treasury security. Suppose the one-year security does not have a maturity risk premium, but the two-year security does and it is 0.2%. What is…An investor wants a real rate of return i′ of 6% per year. If the expected annual inflation rate for the next several years is 2.5%,what interest rate i should be used in project analysis calculations?Suppose on can invest in a money market instrument that matures in 70 days that offers 8% nominal annual interest rate, what is the effective annual interest return on this security? Effective Annual Return
- Assume that the Pure Expectations Theory of the term structure is correct. Also assume that the interest rate today on a 9-year security is 6.40%, while the interest rate today on a 15-year security is 8.00%. Finally assume that the interest rate on a 3-year security to be bought at Year 9 and held over Years 10, 11, and 12 is 6.80%. Given this information, determine the average annual return that investors today must expect that they will receive from investing in a 3-year security in 12 Years (that is, buying the security at Year 12 and holding it over Years 13, 14, and 15). O 13.00% O 12.50% 13.50% O 12.00% O 14.00%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?which of the following investments that pay will $5000 in 12 years have a higher price today? A. The security that earns an interest rate it 8.25% B. The security that earns an interest rate of 5.50%?