Absolusia, an emerging economy, has just made an issue of coupon-paying bonds, each with 3 years to maturity, and a face value of $1,000,000. Each bond has a coupon rate of 4% per annum, payable half-yearly.
The bonds have a yield of j2 = 6%, that is 6 per cent per annum, compounded half-yearly.
- (a) Calculate the current price of each $1,000,000 bond, correct to the nearer cent.
- (b) Calculate the duration of each bond. (Show 4 places of decimals).
- (c) Calculate the convexity of each bond. (Show 4 places of decimals).
- (d) You have just heard that, immediately after issue, the yield on the bond has increased from 6% per annum, compounded half-yearly, to 6.2% per annum, also compoundedhalf-yearly.
Using the formula (and/or the method) applied in (a) above, calculate the new bond price and the resultant price change, assuming that there are still 3 years until the bond's maturity.
- (e) Before the increase in yield in part (d) above took place, calculate the value of the bond at the duration date, as calculated in (b) above.