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# UNT FINA 5210 - Probset5

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Probset5Answer5Fina 5210 Problem Set 5 Fall 2014 Prof. Kensinger page 1 Advanced Problems in Arbitrage For preparation prior to problems 1, 2 & 3, see Problem Set 4, Problem 8. Problems 1, 2 & 3 are “warm-up” for the subsequent problems that illustrate how the yield curve is shaped. Problems 1, 2 & 3 illustrate that an upward-sloping yield curve is associated with expectations that short-term interest rates will be rising in the future (under the rational expectations theory). It is also the case that a downward-sloping yield curve is associated with expectations that short-term interest rates will decline in the future. 1. The following prices are observed. Formulate an arbitrage strategy to profit from the situation. • Interest rate is 7.25% compounded daily, for 270-day T-bills in the spot market. • Interest rate is 7.00% compounded daily, for 90-day T-bills in the spot market. • The futures rate is 7.50% for T-bills with 180 days to maturity, to be delivered 90 days from now. 2. The following prices are observed. Formulate an arbitrage strategy to profit from the situation. • Interest rate is 7.25% compounded daily, for 270-day T-bills in the spot market. • Interest rate is 7.10% compounded daily, for 180-day T-bills in the spot market. • The futures rate is 7.50% for T-bills with 90 days to maturity, to be delivered 180 days from now. 3. The following prices are observed. Formulate an arbitrage strategy to profit from the situation. • Interest rate is 7.12% compounded daily, for 180-day T-bills in the spot market. • Interest rate is 7.00% compounded daily, for 90-day T-bills in the spot market. • The futures rate is 7.15% for T-bills with 90 days to maturity, to be delivered 90 days from now. For preparation prior to problem 4, see lecture notes from Topic 10, Slides 2, 3 & 4. This problem begins the series of problems that illustrate how the yield curve is shaped. In this example, there is a “kink” in the yield curve that is the source of the arbitrage opportunity (in this example, the yield curve slopes down, then turns up). 4. The following prices are observed. Calculate the yield to maturity for each bond, and formulate a trading strategy to profit from the situation. • Treasury bonds with 6% coupon and 10 years remaining to maturity are selling at \$75.08 per \$100 of face value (net of accrued interest). • Treasury bonds with 8% coupon and 10 years remaining to maturity are selling at \$79.00 per \$100 of face value (net of accrued interest). • Equivalent risk bonds with 0% coupon and 10 years remaining to maturity are selling at \$36.80 per \$100 of face value. For preparation prior to problem 5, see lecture notes from Topic 10, Slide 9. This problem continues the series of problems that illustrate how the yield curve is shaped. In this example, there is another variety of “kink” in the yield curve that is the source of the arbitrage opportunity (in this example, the yield curve slopes up, then turns down). 5. The following prices are observed. Calculate the yield to maturity for each bond, and formulate a trading strategy to profit from the situation. • Treasury bonds with 6% coupon and 10 years remaining to maturity are selling at \$67.00 per \$100 of face value (net of accrued interest). • Treasury bonds with 8% coupon and 10 years remaining to maturity are selling at \$76.00 per \$100 of face value (net of accrued interest). • Treasury bonds with 10% coupon and 10 years remaining to maturity are selling at \$88.00 per \$100 of face value (net of accrued interest).Fina 5210 Problem Set 5 Fall 2014 Prof. Kensinger page 2 For preparation prior to problems 6 through 10, see lecture notes from Topic 10, Slides 10 through 13. This problem continues the series of problems that illustrate how the yield curve is shaped. In this example, there is a “kink” in the yield curve that is the source of the arbitrage opportunity (in problem 6, the yield curve slopes down, then turns up). 6. The following prices are observed. Formulate a trading strategy to profit from the situation. • Treasury bonds with 6% coupon and 8 years remaining to maturity are selling at \$88.35 per \$100 of face value (net of accrued interest). • Treasury bonds with 6% coupon and 7 years remaining to maturity are selling at \$90.68 per \$100 of face value (net of accrued interest). • Treasury bonds with 6% coupon and 6 years remaining to maturity are selling at \$90.61 per \$100 of face value (net of accrued interest). In problem 7, the yield curve slopes up, then turns down. It can’t change direction. If it is upward sloping anywhere, it must be upward sloping over the entire range (until it becomes flat). 7. The following prices are observed. Calculate the yield to maturity for each bond, and formulate a trading strategy to profit from the situation. • Treasury bonds with 6% coupon and 8 years remaining to maturity are selling at \$88.35 per \$100 of face value (net of accrued interest). • Treasury bonds with 6% coupon and 7 years remaining to maturity are selling at \$87.00 per \$100 of face value (net of accrued interest). • Treasury bonds with 6% coupon and 6 years remaining to maturity are selling at \$90.61 per \$100 of face value (net of accrued interest). In problem 8, the yield curve slopes down, then turns up. It can’t change direction. If it is downward sloping anywhere, it must be downward- sloping over the entire range (until it becomes flat). 8. The following prices are observed. Calculate the yield to maturity for each bond, and formulate a trading strategy to profit from the situation. • Treasury bonds with 6% coupon and 8 years remaining to maturity are selling at \$86.35 per \$100 of face value (net of accrued interest). • Treasury bonds with 6% coupon and 7 years remaining to maturity are selling at \$89.44 per \$100 of face value (net of accrued interest). • Treasury bonds with 6% coupon and 6 years remaining to maturity are selling at \$88.44 per \$100 of face value (net of accrued interest). In problem 9, the yield curve is flat, then turns up. It can’t change direction. Once it becomes flat anywhere, it must remain flat over the entire remaining range of increasing convexity. 9. The following prices

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