You are considering three alternative investments in bonds. The bonds have different times to maturity, but carry the same default risk. You would like to gain an impression of the extent of price volatility for each given alternative change in future interest rates. The investments are:

(i) a two-year bond with an annual coupon of 6 per cent, par value of £100 and the next coupon payment in one year. The present yield to maturity on this bond is 6.5 per cent.

(ii) a ten-year bond with an annual coupon of 6 per cent, a par value of £100 and the next coupon payable in one year. The present yield to maturity on this bond is 7.2 per cent.

(iii) a 20-year bond with an annual coupon of 6 percent, a par value of £100 and the next coupon due in one year. The present yield to maturity on this bond is 7.7 per cent.

(a) Draw an approximate yield curve.

(b) Calculate the market price of each of the bonds.

(c) Calculate the market price of the bonds on the assumption that yields to maturity rise by 200 basis points for all bonds.

(d) Now calculate the market price of the bonds on the assumption that yields to maturity fall by 200 basis points to 4.5 per cent, 5.2 per cent and 5.7 per cent respectively.

(e) Which bond price is the most volatile in circumstances of changing yields to maturity?

(f) Explain the liquidity-preference theory of the term structure of yields to maturity.