Question;Instructions: For problems on this exam involving semiannual payments or discounting, use the convention (1+r/2)t where r is the simple annual interest rate and t refers to the number of semiannual periods.Report all interest rates as a percentage with two digits to the right of the decimal place (e.g., 7.64%). Report dollar values to the nearest penny.1. Assume that the yield curve is upward sloping. Two U.S. Treasury bonds mature in 20 years. One has a 1% coupon and the other has a 10% coupon. The yield curve is upward sloping. Suppose the bonds are currently priced such that they have the same yield to maturity. Does this present an arbitrage opportunity? If yes, describe in some detail what you would buy and what you would sell to exploit that opportunity. If not, explain why there is no mispricing here.2. Calculate the duration (in years) of a bond that matures in 6 years, has a $1,000 face value, and makes annual coupon payments of $65. It?s current market price is $1,012.39.3. In problem 8 you calculated the duration (in years) of a bond that matures in 6 years, sells for $1,012.39, has a $1,000 face value, and makes annual coupon payments of $65. What is this bond?s convexity? If the bond?s yield-to-maturity increases by 25 basis points, what percentage decrease in the bond?s price do you expect based on the bond?s duration and convexity?4. Assume that most investors prefer to invest in short-term securities. To induce them to purchase longer-term securities, those securities must offer a higher expected return. You want to know the current market price of a bond that matures in two years nd pays a 4% coupon. Coment on whether this equation will generate a bond price that is accurate, too high, or too low. Explain your answer.In this equation, r1 refers to the one-year spot rate, and 1f1 is the notation for a forward rate as discussed in my notes and in online sessions.5. Are there any circumstances under which a downward sloping yield curvge should not be interpreted as a sign that investors expect interest rates to fall? Develop an answer using specific concepts that we?ve covered in class.
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