FM212 - Principles of Finance Michaelmas Term: Asset Pricing Problem Set 4 - Valuing Government Bonds...

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FM212 - Principles of Finance Michaelmas Term: Asset Pricing Problem Set 4 - Valuing Government Bonds 1. The one to five year spot rates are given in the table below. The spot rates shown are effec- tive annual rates. Year Spot Rate 1 0.25% 2 0.50% 3 0.75% 4 1.00% 5 1.25% (a) Calculate the following implied forward rates, 1f1, 2f1, 3f1 and 4f1. (b) Calculate the PVs of the following government bonds. i. 0.5% annual coupon bond with a maturity of 5 years and a face value of 1000. ii. 1.5% annual coupon bond with a maturity of 5 years and a face value of 1000. (c) Calculate the yield to maturity of bonds i and ii. Explain intuitively why the yield to maturity on the 1.5% coupon bond is less than that on the 0.5% coupon bond. (d) Why is the 0.5% coupon bond selling at discount (price < face value) and the 1.5% coupon bond selling at premium (price > face value)? 2. Suppose the YTM of a three year 1.5% annual coupon government bond increases from 0.745% to 0.76%. The face value of the bond is 1000. Use the modified duration of the bond to estimate the new price of the bond. 3. A six-year 6% annual coupon bond yields 12% and a six-year 10% annual coupon bond yields 8%. All bonds have a face value of 1000. Calculate the six-year spot rate. 1 FM212 - Principles of Finance Michaelmas Term: Asset Pricing Problem Set 4 - Valuing Government Bonds 1. The one to five year spot rates are given in the table below. The spot rates shown are effec- tive annual rates. Year Spot Rate 1 0.25% 2 0.50% 3 0.75% 4 1.00% 5 1.25% (a) Calculate the following implied forward rates, 1f1, 2f1, 3f1 and 4f1. (b) Calculate the PVs of the following government bonds. i. 0.5% annual coupon bond with a maturity of 5 years and a face value of 1000. ii. 1.5% annual coupon bond with a maturity of 5 years and a face value of 1000. (c) Calculate the yield to maturity of bonds i and ii. Explain intuitively why the yield to maturity on the 1.5% coupon bond is less than that on the 0.5% coupon bond. (d) Why is the 0.5% coupon bond selling at discount (price < face value) and the 1.5% coupon bond selling at premium (price > face value)? 2. Suppose the YTM of a three year 1.5% annual coupon government bond increases from 0.745% to 0.76%. The face value of the bond is 1000. Use the modified duration of the bond to estimate the new price of the bond. 3. A six-year 6% annual coupon bond yields 12% and a six-year 10% annual coupon bond yields 8%. All bonds have a face value of 1000. Calculate the six-year spot rate. 1