Suppose the term structure of annualized interest rate is flat at 5%. Consider the following three bonds with face value $100: Bond 1: a 10-year zero coupon bond; • Bond 2: a 1.5-year semi-annually paid floating rate bond with zero spread; • Bond 3: a 3-year annually paid coupon bond, with coupon rate 6%. 1) What are the current prices for the three bonds? 2) Compute the Duration and Convexity for each of the three bonds. 3) Assume that you have 10 units of Bond 3, how to conduct delta hedge and convexity hedge using Bond 1 and Bond 2?

Suppose the term structure of annualized interest rate is flat at 5%. Consider the following three bonds with face value $100: Bond 1: a 10-year zero coupon bond; • Bond 2: a 1.5-year semi-annually paid floating rate bond with zero spread; • Bond 3: a 3-year annually paid coupon bond, with coupon rate 6%. 1) What are the current prices for the three bonds? 2) Compute the Duration and Convexity for each of the three bonds. 3) Assume that you have 10 units of Bond 3, how to conduct delta hedge and convexity hedge using Bond 1 and Bond 2?

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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Suppose that the prices of zero-coupon bonds with various maturities are given in the following table. The face value of each bond is $1,000. Maturity (Years) 1 2 3 4 5 Price $983.78 865.89 797.92 732.00 660.24 Required: a. Calculate the forward rate of interest for each year. b. How could you construct a 1-year forward loan beginning in year 3? c. How could you construct a 1-year forward loan beginning in year 4?
Suppose the current interest rate on a one-year bond is 2% and the current interest rate on a two-year bond is 4%. The term premium on a two-year bond is 1%. According to the expectations hypothesis, what interest rate should we expect on a one-year bond next year? Answer as a percentage to one decimal place and do not include symbols (e.g. $, %, commas) in your answer. Answer:
Let's denote the price of a nonmaturing bond (called a consol) as P. The equation that indicates this price is Pn =-, where I is the annual net income the bond generates and r is the nominal market interest rate. a. Suppose that a bond promises the holder $200 per year forever. The nominal market interest rate is 6 percent. Calculate the bond's current price: S. (Round your answer to the nearest whole dollar.)
Suppose that the prices of zero-coupon bonds with various maturities are given in the following table. The face value of each bond is $1,000. Maturity (Years) 1 2 3 4 5 Required: a. Calculate the forward rate of interest for each year. b. How could you construct a 1-year forward loan beginning in year 3? c. How could you construct a 1-year forward loan beginning in year 4? Required A Price $940.93 Complete this question by entering your answers in the tabs below. 868.39 800.92 735.40 670.48 Required B Maturity (years) 2 3 Calculate the forward rate of interest for each year. Note: Round your answers to 2 decimal places. Required C Forward Rate % % Prov 12 of 12 Next
Consider the following pure discount bonds with face value $1,000: Maturity Price 1 952.38 2 898.47 3 847.62 4 799.64 5 754.38 a). Find the spot rates and draw a yield curve.b). Assume that there is a constant liquidty premium that is equal to 1% across all maturities. Find the forward rates and the expected one period future interest rates.
Consider the following bonds: •Bond A: A 2-year zero-coupon bond with a face value of $100 and 6% YTM. •Bond B: A 2-year par-value bond with a face value of $100 and 6% coupon rate. *Bond C: A 2-year par-value bond with a face value of $100 and 7% coupon rate. Suppose the yield curve shifts upwards by one percent. Which bond among bonds A, B, and C will experience the largest percentage price change? Which will have the lowest percentage price change? O a. Bond A; Bond C O b. Bond A; Bond B O c. Bond B; Bond C O d. Bond C; Bond B
Suppose you can observe that 1-year bond interest rate is 4%, 2-year bond interest rate is 8%, and 3-year bond interest rate is 10% at time t. It is also known that the term premium on a 2-year bond is 1% and the term premium on a 3-year bond is 1.5%. a) What are the market's expected 1-year bond interest rates for the next two years from time t? b) How to interpret those expected short-term interest rates? (what would be the "possible" economic meanings in the expected short- term interest rates?) Discuss as least two "candidates" to explain them.
Assume the real risk-free is 1% and the average annual expected inflation rate is 4%. The DRP and LP for bond A are each 3%, and the applicable MRP is 3%. What is Bond A's interest rate?
Assume that the real risk free rate is 3% and the average annual expected inflation rate is 5%. The DRP and LP for Bond A are each 1% and the applicable MRP is 2%. What is bond A’s interest rate?
Consider a 25-year bond with a face value of $1,000 that has a coupon rate of 5.8%, with semiannual payments. a. What is the coupon payment for this bond? b. Draw the cash flows for the bond on a timeline. a. What is the coupon payment for this bond? The coupon payment for this bond is $ *** (Round to the nearest cent.)
The current zero-coupon yield curve for risk-free bonds is as follows: What is the price per $100 face value of a two-year, zero-coupon, risk-free bond? The price per $100 face value of the two-year, zero-coupon, risk-free bond is $ Data table (Click on the following icon in order to copy its contents into a spreadsheet.) Maturity (years) 1 2 YTM 4.99% 5.53% Print 3 5.72% Done (Round to the nearest cent.) 4 5.92% 5 6.07% X
Consider a semi-annual bond that has a par value of 100, a 15-year maturity, a 5% coupon rate. Monthly interest rate is 0.412%. (a) What is the price of the bond (without calculation)? And explain why you can determine the price of the bond without calculation? (b) Using answers from (a), calculate the modified duration of this bond. (c) Using answers from (a) and (b), suppose that the bond’s yield to maturity decreases to 3.5%. How much will the bond price increase by applying the duration rule?

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