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Show all answers to three decimal places; do not round intermediate calculations. Excel has buttons labeled "Increase Decimal" and "Decrease Decimal." Submit your homework via Canvas before the due date. Name the file "FIN 311 - Homework 2 - Last name, First name." Many of these questions involve filling out tables; to make the tables easier to read, I have included blue highlights to show which parameters I am changing relative to the first row. Name: 1. Compute the duration of the following bonds. (50 points) (Note: When computing duration, you should calculate the EXACT price of the asset instead of using the price column, since the price column has values rounded to 3 decimal places.) \begin{tabular}{|c|c|c|c|c|c|} \hline Price & Yield & Coupon payment & Face & Maturity & Duration \\ \hline \hline$962.092 & 20% & $90 & $1,000 & 2.5 & 2.112 \\ \hline$859.311 & 26% & $90 & $1,000 & 2.5 & \\ \hline$1,064.443 & 20% & $117 & $1,000 & 2.5 & \\ \hline$1,148.369 & 20% & $90 & $1,300 & 2.5 & \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|c|} \hline Price & Yield & Coupon payment & Face & Maturity & Duration \\ \hline \hline$962.092 & 20% & $90 & $1,000 & 2.5 & 2.112 \\ \hline$909.230 & 20% & $90 & $1,000 & 12.5 & \\ \hline$900.852 & 20% & $90 & $1,000 & 25 & 5.472 \\ \hline & & & & & \\ \hline Price & Yield & Coupon payment & Face & Maturity & Duration \\ \hline \hline$643.666 & 20% & $6 & $1,000 & 2.5 & 2.461 \\ \hline$146.758 & 20% & $6 & $1,000 & 12.5 & 9.431 \\ \hline$68.007 & 20% & $6 & $1,000 & 25 & \\ \hline \end{tabular} 2. Suppose you want to buy an 18% coupon bond with a face value of $1,000, maturity of 2.5 years, and yield of 20%. Further suppose that you want to raise enough money to buy this bond by issuing a pair of zero-coupon bonds: one with a maturity of 6 months, and another with a maturity of 4.5 years. Both bonds will have a yield of 20%. If you also want the duration of your liabilities to match the duration of your asset, what should be the price and face values of each of these zero-coupon bonds? (20 points) (Note: As your first step, you should calculate the exact price and duration of the asset--NOT the price or duration rounded to 3 decimal places--to see exactly what you need to match.) Price of the 6-month zero-coupon bond: Price of the 4.5-year zero-coupon bond: Face value of the 6-month zero-coupon bond: Face value of the 4.5-year zero-coupon bond: 3. Suppose there is a bond with a 14% yield, 2.5% coupon rate, $1,000 face value, and 1.5 -year maturity. Compute the duration, convexity measure, duration-implied prices, and duration-and-convexity implied prices for this bond. ( 30 points.) (Note: I recommend calculating the true duration and convexity, then using numerical derivatives to doublecheck that your duration and convexity estimates are correct.) Duration: Convexity measure: \begin{tabular}{|c|c|c|c|} \hline (New) Yield & Actual price & D-implied price & DX-implied price \\ \hline \hline 12% & $873.032 & & \\ \hline 14% & $849.102 & & \\ \hline 16% & $826.046 & $825.616 & $826.053 \\ \hline \end{tabular} Show all answers to three decimal places; do not round intermediate calculations. Excel has buttons labeled "Increase Decimal" and "Decrease Decimal." Submit your homework via Canvas before the due date. Name the file "FIN 311 - Homework 2 - Last name, First name." Many of these questions involve filling out tables; to make the tables easier to read, I have included blue highlights to show which parameters I am changing relative to the first row. Name: 1. Compute the duration of the following bonds. (50 points) (Note: When computing duration, you should calculate the EXACT price of the asset instead of using the price column, since the price column has values rounded to 3 decimal places.) \begin{tabular}{|c|c|c|c|c|c|} \hline Price & Yield & Coupon payment & Face & Maturity & Duration \\ \hline \hline$962.092 & 20% & $90 & $1,000 & 2.5 & 2.112 \\ \hline$859.311 & 26% & $90 & $1,000 & 2.5 & \\ \hline$1,064.443 & 20% & $117 & $1,000 & 2.5 & \\ \hline$1,148.369 & 20% & $90 & $1,300 & 2.5 & \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|c|} \hline Price & Yield & Coupon payment & Face & Maturity & Duration \\ \hline \hline$962.092 & 20% & $90 & $1,000 & 2.5 & 2.112 \\ \hline$909.230 & 20% & $90 & $1,000 & 12.5 & \\ \hline$900.852 & 20% & $90 & $1,000 & 25 & 5.472 \\ \hline & & & & & \\ \hline Price & Yield & Coupon payment & Face & Maturity & Duration \\ \hline \hline$643.666 & 20% & $6 & $1,000 & 2.5 & 2.461 \\ \hline$146.758 & 20% & $6 & $1,000 & 12.5 & 9.431 \\ \hline$68.007 & 20% & $6 & $1,000 & 25 & \\ \hline \end{tabular} 2. Suppose you want to buy an 18% coupon bond with a face value of $1,000, maturity of 2.5 years, and yield of 20%. Further suppose that you want to raise enough money to buy this bond by issuing a pair of zero-coupon bonds: one with a maturity of 6 months, and another with a maturity of 4.5 years. Both bonds will have a yield of 20%. If you also want the duration of your liabilities to match the duration of your asset, what should be the price and face values of each of these zero-coupon bonds? (20 points) (Note: As your first step, you should calculate the exact price and duration of the asset--NOT the price or duration rounded to 3 decimal places--to see exactly what you need to match.) Price of the 6-month zero-coupon bond: Price of the 4.5-year zero-coupon bond: Face value of the 6-month zero-coupon bond: Face value of the 4.5-year zero-coupon bond: 3. Suppose there is a bond with a 14% yield, 2.5% coupon rate, $1,000 face value, and 1.5 -year maturity. Compute the duration, convexity measure, duration-implied prices, and duration-and-convexity implied prices for this bond. ( 30 points.) (Note: I recommend calculating the true duration and convexity, then using numerical derivatives to doublecheck that your duration and convexity estimates are correct.) Duration: Convexity measure: \begin{tabular}{|c|c|c|c|} \hline (New) Yield & Actual price & D-implied price & DX-implied price \\ \hline \hline 12% & $873.032 & & \\ \hline 14% & $849.102 & & \\ \hline 16% & $826.046 & $825.616 & $826.053 \\ \hline \end{tabular}
