Ch 06- Assignment - Interest Rates Attempts Score / 1 1. Cost of money Everyone uses money, and it is important to understand what factors affect the cost of money. Consider the following scenario: A friend comes to you and asks you to invest in his business instead of investing in Treasury bonds. You think he has a good business model, so you tell him you are willing to invest as long as the expected return on the investment is at least four times the return you would have received on the Treasury bonds. Determine which of these fundamental factors is affecting the cost of money in the scenario described: Inflation Risk Time preferences for consumption
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Suppose an investor would like to buy 200 Treasury notes. The investor wants notes with an annual coupon rate of 7%, a 3-year maturity, and semi-annual coupon payments. a. If there were no such Treasury note available, propose a portfolio for this investor (using only Zeroes with maturities up to 3 years) that replicates the cash flows from investing in the Treasury notes above. b. Assuming the yield curve is flat at 4.0% for bonds with maturities of up to 3 years, calculate the prices of the Zeroes in your portfolio from part (a). Using these prices, compute the no-arbitrage price of a Treasury note. c. Now suppose there is a 3-year, 7% coupon rate Treasury note available that has a YTM of 4.5%. Would the investor above prefer to buy 200 Treasury notes or the portfolio of Zeroes identified in part (a)? d. Find a costless and riskless trading strategy that makes an instantaneous profit by buying or selling the Treasury note and the portfolio of zeroes. e. If this costless strategy required that you put up 50% collateral for the short sales, would you be willing to use all of your available capital for collateral in this strategy?
Akash M.
Let us consider a flat initial interest rate curve at 3%. An insurance company has sold the following 2 products to its clients: • a 2% guaranteed (compound) rate product at maturity 4 years. Initial premium: 150 • a 1% guaranteed (compound) rate product at maturity 2 years. Initial premium: 100 Let us consider that the company can invest in the different following bonds: | | Bond A | Bond B | Bond C | | :--- | :--- | :--- | :--- | | Maturity | 1 | 3 | 6 | | Coupon | 0 | 2 | 0 | | Nominal | 100 | 100 | 100 | Initial own funds in accounting view of the company are assumed to be null. 1. Compute the initial economical balance sheet 2. Propose an investment strategy based only on investments in bonds A & C such that the economical own funds of the company are protected against parallel interest rate shifts 3. Considering that strategy suggested at point 2 has been implemented, in case of parallel interest rate shift upwards, do you expect that the value of economical own funds will increase or decrease and why ? 4. Compute the economical own funds change assuming that the interest rate curve instantaneously changes to | Maturity | Compound rate | | :--- | :--- | | 1 | 3,20% | | 2 | 3,10% | | 3 | 3,15% | | 4 | 3,25% | | 5 | 3,40% | | 6 | 3,40% | | 7 | 3,50% | | 8 | 3,60% | | 9 | 3,60% | | 10 | 3,70% | Has the strategy developed at point 2 enabled to protect the economical own funds and why ? 5. Let us assume there would be a third product liability product, i.e. a 1,5% guaranteed (compound) rate product at maturity 3 years with 50 of initial premium, fully invested in bond B while the premiums relative to the two first liability products are invested according to strategy developed at point 2. In case of small parallel interest rate shift upwards, do you expect that the value of economical own funds will increase or decrease and why ?
You are given the following information: at t = 0: the price of a 10‐ year zero coupon bond with FV = $5,000 is $3,500; f3,12 = 6%. A bank is offering the following product: for every $1 that you give the bank at t = 10, the bank will give you back $1.5 at t = 15, or for every $1 that you borrow from the bank at t = 10, you will have to pay back $1.5 at t = 15. a) Write down one equation where the only unknown is r0,3. You do not need to solve the equation. b) b) Suppose r0,3 were 1% less than your answer to part a. Call this new value r'0,3 Describe how you would construct an arbitrage where at t = 0 you are simultaneously receiving and investing $1. For each rate, you must specify whether you are using it to borrow or lend, and how much (the "how much" can be expressed as a function of r'0,3). For the bond, you must specify whether you are going long or short, and how many units. For the contract, you must specify whether you are using it to invest or borrow, and how much. i) use r0,3' for borrowing $1 ii) use f3,12 for borrowing (1+r0,3')3 iii) buy 1/3500 units of the bond iv) use product for lending 5,000/3,500
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