Question

Consider the following zero coupon bonds each of which are redeemable at par and have a yield rate of 3.5 % compounded continuously. Bond Face Value (in dollars) 4000 10000 5000 1000 Maturity (in years) 10 15 25 30 (a) Determine the purchase price of each bond: Bond Price (in dollars to closest cent) NOTE: Do not include the $ sign. (b) Determine the present value of the portfolio of bonds.

Answer 1

a) Price of each Bond can be found out by using the formula =FV/(1+Yield Rate/365)^Term*365 as it is continuous compounding. Using the above formula the Price of these bonds are 1. 2818.80; 2. 5915.70; 3. 2084.40 and 4. 349.96.

b) PV value of the portfolio of bonds is adding the purchase price of the bonds i.e. 11,168.86.

c) The bond portfolio duration will be calculated by taking the weights of the zero coupon bonds. Weights will be calculated by dividing the purchase price of bond with the total value of the portfolio for e.g. For Bond 1 the weight will be =2818.80/11168.86 i.e. 0.25 like wise for all the other three bonds the weights will be 0.53; 0.19 and 0.03. The Duration of the Zero Coupon bond will be its maturity thus for Bond 1 it will be 10 for Bond 2: 15; Bond 3: 25; Bond 4: 30. The weighted Duration will be the Duration of this bond portfolio calculation is as under:-

Bond Price	Duration	Wt	Wt Duration
2,818.80	10	0.25	2.52
5,915.70	15	0.53	7.94
2,084.40	25	0.19	4.67
349.96	30	0.03	0.94
11,168.86		1.00	16.07 years

Sol (d) Future Value of Bond Portfolio is 20 000.00, Duration: 16.07 years; Yield Rate: 3.3% thus the present value will be 11,779.01, thus estimated absolute change will be =11,779.01-11,168.86= 610.15 and estimate percentage change in portfolio= 610.15/11168.86= 5.463%