ps4_sol - Homework #4, Investment Analysis Suggested...

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Unformatted text preview: Homework #4, Investment Analysis Suggested solutions 1. Bond arbitrage. a. The yields are computed using the formula: Using a numerical solver (e.g. the Excel one), we have ya = 3.63% and yb = 3.68%. b. To see if there is an arbitrage, we need to find no ­arbitrage zero coupon bond prices. In equations, we need to solve: multiplying the first equation by 2 and subtracting it from the second we have b3 = 0.9. Plugging this into the first equation we get b1+b2 = 1.87. There are many solutions, but we can choose one so that it leads to non ­increasing zero prices, for example, b1=0.95, b2=0.92, b3=0.90. As a consequence, there is no arbitrage. c. The no-arbitrage price of the two-year bond is: 6b1+106b2. The highest possible price sets b2 as large as possible, that is sets b2=b1, and plugging into b1+b2=1.87, b1=b2=0.9350, which gives the bond price 104.72. The lowest possible price would set b2 as low as possible, or b2=b3=0.90, and b1=1.87 ­0.90=0.97. And this gives a price for the bond of 101.22. d. If the forward rate is 3.26%, then b1/b2=1.0326, or b1=1.0326b2. Plugging into b1+b2=1.87, we get b2=1.87/2.0326=0.9241 and b1=0.9451. Plugging in we get the bond price 6b1+106b2=103.62 2. Using the rates given, b1=1.02 ­1=0.9804, and b3=1.06 ­3=0.8396. The lowest possible two ­year zero coupon bond price is 0.8396, with an associated rate of 9.13%. The highest possible two ­year zero coupon bond price is 0.9804, with an associated rate of 0.995%. 3. Liability hedging. If you use one through five ­year zeros, you would match cash flows; buy $500,000 in face value of one through five ­year zeros. Using the spot rates of 3%, the cost is ...
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