sk 21. Consider the following balance sheet (in millions) for an FI: Assets Liabilities Duration 10 years $950 Duration = 2 years Equity $860 90 a. What is the Fl's duration gap? b. What is the FI's interest rate risk exposure? c. How can the FI use futures and forward contracts to put on a macrohedge? d. What is the impact on the FI's equity value if the relative change in interest rates is an increase of 1 percent? That is, A R/(1 + R) = 0.01. e. Suppose that the FI macrohedges using Treasury bond futures that are cur- rently priced at 96. What is the impact on the FI's futures position if the relative change in all interest rates is an increase of 1 percent? That is, AR/(1 + R) = 0.01. Assume that the deliverable Treasury bond has a duration of nine years. f. If the FI wants to macrohedge, how many Treasury bond futures contracts does it need?

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.)

d.  If you hold the bonds for one year, and interest rates do not change, what total rate of return will you earn, assuming that you pay the market price? Why is this different from the current yield and YTM?

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.)

Suppose the term structure of risk-free interest rates is as shown below. 1 yr Term 2 yr 3 yr 5 yr 7 yr 10 yr 20 yr Rate (EAR %) 2.08 2.42 2.61 3.24 3.87 4.04 5.07 a. Calculate the present value of an investment that pays $5,000 in two years and $3,000 in five years for certain. b. Calculate the present value of receiving $300 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 $2,300 per year, with certainty, for the next 20 years. Infer rates for the missing years using linear interpolation. (Hint: Use a spreadsheet.) a. Calculate the present value of an investment that pays $5,000 in two years and $3,000 in five years for certain, The present value of the investment is $ (Round to the nearest dollar.)

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.

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.)

28. Consider a bank dealer who faces the following spot rates and interest rates. What should he set his 1- year forward ask price at? Bid So(S/E) S1.42 = €1.00 F360(S/E) A. $1.4324/€ B. $1.4358/€ C. $1.4662/€ D. $1.4676/€ Ask $1.45 = €1.00 Borrowing 4.25% APR is je 3.10% APR Lending 4% APR 3% APR

6. Finding the interest rate and the number of years The future value and present value equations also help in finding the interest rate and the number of years that correspond to present and future value calculations. If a security currently worth $9,200 will be worth $15,767.18 seven years in the future, what is the implied interest rate the investor will earn on the security-assuming that no additional deposits or withdrawals are made? 5.83% O6.40% 8.00% O 1.71 % If an investment of $50,000 is earning an interest rate of 8.00%, compounded annually, then it will take a value of $89,052.92-assuming that no additional deposits or withdrawals are made during this time. for this investment to reach Which of the following statements is true-assuming that no additional deposits or withdrawals are made? An investment of $25 at an annual rate of 10% will return a higher value in five years than $50 invested at an annual rate of 5% in the same time. An investment of $50 at an annual rate of…

Suppose we observe the following rates: 1R1 = 0.75%, 1R2 = 1.20%, and E(2r1) = 0.907%. If the liquidity premium theory of the term structure of interest rates holds, what is the liquidity premium for year 2, L2? (Do not round intermediate calculations. Round your answer to 3 decimal places.)