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Part 2

Finance

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Part 2. Theory 
Exercise 1. Bond investments 
Bond X costs 870 USD today, has four years to maturity and a coupon rate of 3%. Bond Y costs 1,300 USD today, has four years to maturity and a coupon rate of 14%. Coupons are paid semiannually in both cases. Interest rates are constant. You aim to maximize your return from your investment. 
A. Which of the two bonds do you prefer to buy today, and why? Please show your computations. 
B. What should you expect to happen for you to change your choice in question A above? Please provide a quantitative example with some computations that corroborate your answer. You are of course allowed to make quantitative assumptions to show your result. 
Exercise 2. Yield curve 
The following term structure of interest rates is given. 
Time to maturity YTM 1 4.0% 2 4.2% 3 4.4% 4 4.6% 
A friend of yours thinks that the term structure of interest rates a year from now will be the same as it is now. She tells you that she has a one-year investment horizon but she does not know whether she should buy a one-year zero coupon bond that will mature next year, or a four-year zero-coupon bond that she will have to sell next year. She informs you that she is interested in achieving the highest return from this transaction. Please show all your computations in your answers to both questions A and B below. 
A. Which of the two strategies should she choose, in your opinion? Why? 
B. Is your friend's expectation on the yield curve consistent with the expectation hypothesis? Why? 
Question 1. 
You want to invest your savings for three years and you are undecided between two bonds, issued by the same entity and with same time to maturity, which differ in their (fixed) coupon rate but not in the frequency of coupon payments. 
Without doing any computation, can you tell if one the two alternatives will make you earn more money than the other? If yes, which one and why? If no, why can you not tell? Explain in detail. 
Question 2. "The duration of a bond increases proportionally to the increase in time to maturity." True of false? Please justify your answer only with a theoretical answer and/or with theoretical formulas, not with any calculation.