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Bonds A and B are both risk-free government bonds and have two years to maturity. Bond A has a coupon rate of 5% and bond B has a coupon rate of 8%. The price of Bond A is £1,001.40 and the price of Bond B is £1,058.02. Bond C, which is also a risk-free government bond, has three years to maturity, a coupon rate of 4% and a price of £924.45. All bonds pay their coupons annually and each has a face value of £1,000.
Question i. What is the term structure of spot rates for maturities of 1, 2 and 3 years in this setting? Comment on and interpret its shape.
Question ii. A three-year corporate bond has a yield to maturity of 7%. The price of £1000 worth of face value of the bond is £947.51. What is its coupon rate?
Question iii. What is the price of a risk-free government bond with the same coupon rate, face value and maturity as the corporate bond in (ii)?
Question iv. Compare the prices of the bonds discussed in (ii) and (iii) and give some intuition to explain which is larger. Proceed to explain which of the two bonds will have the greater yield to maturity and why.
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