Principles of Finance: Risk-free government bonds

Question 1 [25 marks]
a. Consider the following three risk-free government bonds: A, B, and C. All three
bonds have a face value of £100 and pay annual coupons, but the coupon rates are
different. Bond A has a coupon rate of 5%, B 10%, and C 8%. Both A and B mature
in two years while C matures in three years. Bonds A, B, and C are currently trading
at £100.91, £110.25, and £110.96, respectively.
i. Calculate the 1-year, 2-year, and 3-year spot rate. What is the shape of the
term structure? [6 marks]
ii. Which theories of the term structure can explain the shape above? Explain the
intuition. [4 marks]
iii. Suppose that the unbiased expectation theory holds. What will the prices of
Bonds A, B, and C be one year from today, right after making the annual
coupon payment? [4 marks]
iv. Consider a fourth bond, Bond D. It has a face value of £100, an annual coupon
rate of 6%, four years to maturity, and its current yield to maturity is 4.5%.
Calculate its current price and modified duration. Suppose that the yield to
maturity suddenly drops from 4.5% to 3.5% today. Without calculating the
new bond price, how much do you expect Bond D’s price to change? [5
marks]
b. The current risk-free rate is 5% per period. A stock’s current price is £50. In one
period its price will either rise to £55 or fall to £40.
i. Price a one-period call option on this stock with exercise price £45. [3 marks]
ii. Price a one-period put option on this stock with exercise price £50. [3 marks]

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