A portfolio comprises of two bonds. Bond X, worth £10 million, has a daily volatility of 0.5%. Bond Y, worth £30 million, has a daily volatility of 1%. The correlation coefficient between the two bonds is -0.4.

(1)  Calculate the value at risk (VaR) of bond X and bond Y (separately) over a 5-day time period at 99% confidence level. 

(2) Calculate the VaR of the portfolio holding the two bonds over a 5-day time period at 99% confidence level. 

(3) Calculate the benefit of diversification.                        

      

 

b)  Bond Z pays annual coupon of 8% and has a par value of £10,000, redeemable in 10 years. Alternatively, the bond-holders can convert it into 100 common shares at maturity. The current share price is £85 per share. Analysts forecast the share price to increase 8% per year for the next 3 years, then 2% in perpetuity. The cost of debt is 6%. 

Calculate:

(1)   The market value of each convertible bond.                   

(2)  The floor value of each convertible bond.                     

(3) The conversion premium per share.